Fast reconstruction system of compressed sensing image based on function approximation

Abstract

The application relates to the technical field of image processing, and discloses a compressed sensing image fast reconstruction system based on function approximation, which comprises a data acquisition module for acquiring compressed sensing measurement data; a function approximation module for generating an initial image estimate by using a pre-trained deep neural network; a collaborative optimization reconstruction module for regarding multiple regularization terms as players in a cooperative game, dynamically evaluating the marginal contribution of each regularization term based on a cooperative game model through a Shapley value, and adaptively adjusting a weight coefficient; and an iterative updating module for combining the adaptive weight to perform multi-criteria collaborative optimization iteration until convergence. The application can solve the problem of difficult manual adjustment of the weights of the multiple regularization terms, realize dynamic balance of noise suppression and structure reservation according to image content features, and improve the quality and stability of the reconstructed image.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and more specifically to a fast image reconstruction system based on function approximation using compressed sensing. Background Technology

[0002] Compressed sensing technology, as an important branch of signal processing, has been widely applied in medical imaging, remote sensing, and industrial non-destructive testing. This technology achieves efficient reconstruction of high-dimensional signals using undersampled measurement data, significantly reducing data acquisition costs and storage burden. Existing image reconstruction methods generally employ a multi-regularization term joint optimization framework. Its core structure includes a data acquisition unit acquiring compressed measurement signals, a function approximation unit generating initial image estimates, and a multi-objective optimization unit integrating fidelity terms and multiple regularization terms (such as sparse transform terms, total variational terms, and low-rank constraint terms). These regularization terms are then linearly combined using fixed weight coefficients, and the reconstruction result is output through iterative calculation. This technical solution balances noise suppression and structure preservation requirements through preset weight parameters, forming a complete image reconstruction process.

[0003] However, in existing technologies, the weight allocation mechanism among multiple regularization terms has long relied on manual experience to set, which makes it impossible for the system to dynamically adjust the optimization strategy according to the image content features, making it difficult for the reconstruction process to simultaneously meet the dual goals of complex structure preservation and noise suppression. Summary of the Invention

[0004] This invention provides a fast image reconstruction system based on function approximation that can solve the technical problems of difficulty in manually adjusting the weights of multiple regularization terms and the inability of fixed weights to adapt to different image content.

[0005] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a fast image reconstruction system based on function approximation for compressed sensing, the system comprising: The data acquisition module is used to acquire compressed sensing measurement data; The function approximation module uses a pre-trained deep neural network to quickly generate initial image estimates from measurement data; The collaborative optimization reconstruction module treats multiple regularization terms as players in a cooperative game, with each regularization term aiming to maximize its contribution to the quality of the reconstructed image. Based on a cooperative game model, this collaborative optimization reconstruction module dynamically evaluates the marginal contribution of each regularization term in the current iteration through the Shapley value and adaptively adjusts the weight coefficients of each regularization term accordingly. The iterative update module, combined with adaptive weights, performs multi-criteria collaborative optimization iterations on the initial image estimation until the convergence condition is met, and outputs the final reconstructed image.

[0006] In an alternative embodiment, the data acquisition module is further integrated with the optical diffraction imaging physical model and the neural field representation: While acquiring compressed measurement data, the module simultaneously records the diffraction and propagation path parameters of light to construct a differentiable physical forward model. The deep neural network of the function approximation module takes not only measurement data as input but also encoded physical path parameters and outputs a neural radiation field of continuous coordinates, which serves as an implicit representation of the image. This fusion combines the physical constraints of computational imaging, continuous scene representation, and rapid initialization, enabling the system to infer missing diffraction information through physically guided neural fields even at extremely low sampling rates. This significantly improves the physical fidelity of the initial estimate and produces a synergistic effect of hardware-algorithm co-design.

[0007] In an alternative embodiment, the function approximation module is further integrated with nonlinear dynamic systems and topological data analysis: Deep neural networks are constructed as a network of ordinary differential equations, which model the generation process of image estimation as a dynamic evolutionary trajectory in the feature space. During the training phase, persistent cohomology analysis is introduced to monitor and regularize the topological structure formed by dynamic trajectories, ensuring the topological consistency between the evolving manifold and the natural image manifold. This fusion introduces the stability theory and topological invariance of dynamical systems into deep learning training, making the initial images generated by the network not only fast, but also with smoother and more structurally reasonable latent feature trajectories. This provides a starting point with good geometric and topological properties for subsequent game optimization, accelerating overall convergence and avoiding getting trapped in bad local solutions.

[0008] In an alternative embodiment, the collaborative optimization reconstruction module is further integrated with evolutionary game theory and multi-agent reinforcement learning: The strategies of each regularization term player are not fixed, but are equipped with a simple policy network that can make fine-tuning decisions based on the multi-scale structural feature statistics of the current reconstructed image. The game process is extended to an evolutionary game, where the fitness of each regularized strategy is determined by the cumulative reward contributed by its historical Shapley value, and strategies with low fitness will be partially replaced or adjusted. A meta-controller is introduced to coordinate the policy update magnitudes of each player through lightweight reinforcement learning, in order to maximize the structural similarity index of the final image as the global reward. This integration extends the game from static cooperation to a dynamic, learnable, and adaptive ecosystem, enabling regularization terms to not only fairly distribute contributions but also co-evolve their optimization strategies, automatically forming different efficient balance patterns for different categories of image content.

[0009] In an alternative embodiment, the iterative update module is further integrated with Bayesian optimization and meta-learning: The hyperparameters such as the update step size and gradient descent direction correction for each iteration are modeled as a Gaussian process, which takes the current iteration number, the weight distribution of each regularization term, and the gradient histogram of the image estimation as input. By utilizing meta-learning networks, we learn from a large number of reconstruction tasks in different scenarios to provide a prior kernel function for the Gaussian process, enabling it to quickly adapt to new scenarios. In each iteration, the Gaussian process is efficiently queried through Bayesian optimization, and a set of hyperparameter combinations that maximizes the expected marginal returns is recommended. This fusion injects the global search capability of probabilistic modeling and the rapid adaptive capability of meta-learning into the iterative loop, enabling the optimization process to not only converge locally but also intelligently plan iterative paths, significantly reducing the number of iterations required to achieve high accuracy and producing unexpected results of ultra-efficient intelligent navigation.

[0010] In an alternative embodiment, a preprocessing and postprocessing co-processing module is also included, which further integrates information theory bottlenecks and generative adversarial networks: In the preprocessing stage, information theory bottleneck compression is applied to the measurement data to actively filter out some noise-related measurement components while retaining the information most relevant to image reconstruction. In the post-processing stage, the optimized output of the game is input into a fine-tuning network of a conditional generative adversarial network. The generator of this network uses the image of the game output and the measurement data after bottleneck compression as common conditions. This fusion integrates information compression theory and generative modeling throughout the reconstruction process, systematically reducing uncertainty at the data source and enhancing details based on the compressed high-value information at the output end. This forms a complete pipeline that refines and polishes the data, achieving overall detail recovery capabilities and robustness that surpass those of a single optimization framework.

[0011] In one alternative embodiment, topological data analysis in the function approximation module is integrated with attention mechanisms from cognitive science and differentiable rendering from computer graphics: Persistent cohomology analysis is used not only to monitor the topological structure of feature trajectories, but also to generate a multi-scale topological attention map that can identify the key topological features in the feature evolution manifold that contribute to the final image structure. This topological attention map is dynamically fed back to the solver of the ordinary differential equation network to adaptively adjust the importance weights of different topological feature regions in gradient calculation, prioritizing the protection of the evolutionary stability of key structures. Meanwhile, the neural field generation process is connected to a lightweight differentiable renderer, enabling topological attention to directly optimize the geometric edges and texture continuity in the image space. This fusion enables the system to mimic the human visual system's priority perception and preservation mechanism of overall structure. By guiding dynamic evolution through topological attention, the generated initial image is generated quickly while significantly enhancing the integrity and naturalness of its key visual structures.

[0012] In one alternative embodiment, the Bayesian optimization process in the iterative update module is integrated with quantum computing heuristic optimization algorithms and robust optimization in operations research: The hyperparameter search space of the Gaussian process is mapped to a form that can be handled by the Ising model or quantum annealing. The global energy minimization search is performed at key iteration nodes using classical or simulated quantum annealing algorithms to find a better combination of hyperparameters. Meanwhile, in the objective function of Bayesian optimization, conditional value at risk is introduced as a robustness indicator, which not only considers the mean return, but also controls the lower bound of the iterative performance in the worst case. This fusion enables the iterative update process to combine the powerful global exploration capabilities inspired by quantum mechanics with robust control over uncertainty. When faced with highly ill-conditioned measurement data or complex noise, the iterative path planning can both escape local optima and maintain stable convergence, significantly improving the reconstruction power and efficiency under extreme conditions.

[0013] In an alternative embodiment, the collaborative optimization reconstruction module is further integrated with swarm intelligence and complex network dynamics: Each regularization term player is considered as a node in a dynamic complex network, and the policy influence and Shapley value exchange between them constitute the weighted edges of the network. Drawing on pheromone diffusion or velocity-position update rules in swarm intelligence, a propagation and update mechanism for policy parameters in the policy network is designed so that the regularization policy with excellent performance can spread its experience in the policy network. By analyzing the dynamic characteristics of this policy network, the meta-controller can identify and strengthen the leadership role of the core regularization node, or promote the formation of subgroup cooperation to meet the different needs of different types of regions in the image. This fusion upgrades the game system into an intelligent policy network with learning and information diffusion capabilities, whose self-organizing characteristics enable multimodal collaborative strategies for heterogeneous image content to emerge spontaneously.

[0014] In an alternative embodiment, the collaborative optimization reconstruction module is further integrated with the concept of gene regulatory networks in molecular dynamics simulations and biological evolution: The interaction potential energy between regularization terms is analogous to intermolecular forces, and a virtual regularization force field is constructed based on this. The policy parameters of each regularization term are treated as genes, and their adjustment is controlled by a simplified gene regulatory network model whose transcription factor activity is determined by the current force field state and the global reward signal. During the iteration process, the conformational changes of the system simulation strategy parameters under the force field and the adjustment of expression levels regulated by the gene network jointly determine the final weight and behavior of each regularization term. This fusion transforms the game process from abstract mathematical optimization into an embodied dynamic adaptation process inspired by physical and biological principles, making weight adjustments smoother, more physically consistent, and able to capture complex nonlinear cooperative patterns that are difficult to model using traditional methods.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention provides a fast image reconstruction system based on function approximation for compressed sensing. This scheme treats multiple regularization terms as players in a cooperative game, where each regularization term aims to maximize its contribution to the quality of the reconstructed image. By dynamically evaluating the marginal contribution of each regularization term in the current iteration using a cooperative game model, and adaptively adjusting the weight coefficients of each regularization term accordingly, multi-objective collaborative optimization is achieved.

[0016] 2. The present invention can intelligently balance different requirements such as sparsity, smoothness and structure preservation based on the features estimated from the current image, avoiding the subjectivity of manually adjusting weights and the rigidity of fixed weights.

[0017] 3. Adaptive weights are used to perform multi-criteria collaborative optimization iterations on the initial image estimation, effectively suppressing noise and artifacts while preserving complex structures and texture details, thus solving the optimization imbalance problem caused by competition among multiple regularization terms. The final output is a high-quality reconstructed image that meets the convergence condition, significantly improving the system's adaptability and reconstruction stability under different image contents. Attached Figure Description

[0018] Figure 1 This is a block diagram of the overall system architecture of the present invention; Figure 2 This is a detailed block diagram of the data acquisition module of the present invention; Figure 3 This is a detailed block diagram of the function approximation module of the present invention; Figure 4 This is a detailed block diagram of the collaborative optimization and reconstruction module of the present invention; Figure 5 This is a detailed block diagram of the iterative update module of the present invention; Figure 6 This is a block diagram of the preprocessing and postprocessing collaborative module of the present invention; Figure 7 This is a flowchart of the topology data analysis in the function approximation module of the present invention; Figure 8 This is a block diagram of the quantum computing heuristic optimization in the iterative update module of this invention. Detailed Implementation

[0019] Please refer to Figures 1 to 8 The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Example 1: A fast image reconstruction system based on function approximation for compressed sensing includes: a data acquisition module for acquiring compressed sensing measurement data; a function approximation module for rapidly generating an initial image estimate from the measurement data using a pre-trained deep neural network; a collaborative optimization reconstruction module that treats multiple regularization terms as players in a cooperative game, with each regularization term aiming to maximize its contribution to the quality of the reconstructed image; this collaborative optimization reconstruction module is based on a cooperative game model, dynamically evaluating the marginal contribution of each regularization term in the current iteration through Shapley values, and adaptively adjusting the weight coefficients of each regularization term accordingly; and an iterative update module that, combined with adaptive weights, performs multi-criteria collaborative optimization iterations on the initial image estimate until the convergence condition is met, outputting the final reconstructed image.

[0021] The data acquisition module is a hardware and software co-operated unit used to perform linear or nonlinear measurement operations under the compressed sensing framework. Its specific implementation form is set according to the actual imaging platform, including a front-end acquisition device composed of a single-pixel camera, an coded aperture system, a diffractive optical array, or a CMOS sensor in conjunction with a random sampling circuit. The compressed sensing measurement data acquired by this module is a real-valued vector with a length much smaller than the total number of pixels in the original image, and its dimension is configured in the range of 0.01% to 20% according to the sampling rate. The function approximation module is an end-to-end mapping model composed of convolutional neural networks, Transformer architecture, or a hybrid structure. Its input is measurement data, and its output is an initial image estimate with the same size as the original image. The deep neural network used in this module is trained with a large number of paired measurement data—high-resolution image samples—as supervision signals, and is optimized by minimizing the joint objective of pixel-level reconstruction error and perceptual loss. The network is deployed in GPU servers, embedded AI accelerators, or mobile terminal devices, and the inference latency is controlled within the range of 1ms to 500ms depending on the hardware platform. The network structure parameters, such as the number of layers, the number of channels, and the number of attention heads, are adjusted according to the constraints of computing resources and accuracy requirements, including ResNet-18 backbone, ViT-B / 16 structure, or lightweight MobileViT variant. The collaborative optimization reconstruction module is a multi-objective weight dynamic allocation unit built on cooperative game theory. It models multiple regularization terms explicitly introduced in the image reconstruction objective function—including ℓ1 sparse regularization, total variational (TV) regularization, low-rank kernel norm regularization, structural similarity prior, or deep prior—as independent players. The utility function for each player is defined as a consistency measure between the gradient direction of its corresponding regularization term in the current iteration's image estimation and the direction of image quality improvement. This module quantifies the marginal contribution of each player to the overall reconstruction quality improvement by calculating the Shapley value of each player in the current cooperative alliance. The Shapley value calculation process is based on Monte Carlo approximation, permutation enumeration, or fast summation algorithms. The weight coefficients of each regularization term are updated in each iteration to values ​​positively correlated with their Shapley values, including the linear mapping λᵢ. ( ᵏ ) =α·φᵢ ( ᵏ ) +β or normalized mapping λᵢ ( ᵏ ) =φᵢ ( ᵏ ) / ∑ⱼφⱼ ( ᵏ ) , where φᵢ ( ᵏ ) Let represent the Shapley value of the i-th regularization term in the k-th iteration, where α and β are adjustable hyperparameters with values ​​ranging from [0.1, 5.0] to [0.01, 0.5], respectively. The iterative update module is an optimization solver that integrates multiple objective criteria. Its objective function is in the form of a weighted sum: min x {‖y-Φx‖2 2 +∑ᵢλᵢ ( ᵏ ) Rᵢ(x)}, where y is the measurement data, Φ is the measurement matrix, Rᵢ(x) is the i-th regularization term, and λᵢ ( ᵏ) Let be the adaptive weights output by the collaborative optimization reconstruction module in the k-th iteration; this module uses the alternating direction multiplier method, fast iterative shrinkage thresholding algorithm, semi-quadratic segmentation, or variations thereof to solve the problem; the iteration termination condition is that the relative change of the reconstructed image estimate is lower than a preset threshold ε, the objective function descent rate is lower than a threshold, or the maximum number of iterations is reached, where ε is set to 10. -4 The maximum number of iterations is set to 50 to 200. The core innovation of this system lies in the construction of a multi-regularized term collaborative optimization framework driven by a cooperative game mechanism. This transforms the traditional statically weighted multi-objective optimization problem into a dynamic collaborative process among players based on marginal contribution evaluation. This allows each prior knowledge to autonomously compete and obtain a reasonable weight allocation based on its actual gain on the current image quality at different iteration stages.

[0022] The system's working process and principle are as follows: After completing the fast initial estimation provided by the function approximation module, the collaborative optimization reconstruction module first analyzes the distribution characteristics of various distortion modes in the current image estimation, and constructs a cooperative alliance containing all regularization terms accordingly. Subsequently, for each possible subset combination in the alliance, the module evaluates the degree of degradation in reconstruction quality after removing a certain regularization term, thereby calculating the Shapley value of each regularization term. This value reflects its average marginal contribution to image quality improvement across all cooperative possibilities. The iterative update module updates the weights of each regularization term accordingly and drives a multi-criteria joint optimization. This process is executed cyclically, allowing the weight allocation to continuously adapt to the evolution of the image structure, ultimately achieving a dynamic balance between noise suppression, edge preservation, and texture restoration upon convergence.

[0023] An optional implementation is as follows: When processing a 256×256 resolution MRI brain image, the data acquisition module acquires a compressed measurement vector of length 1024; the function approximation module calls a pre-trained U-Net style network and outputs an initial image estimate within 15ms; the collaborative optimization reconstruction module identifies significant artifact regions and high-contrast edge regions in the current image, and determines through Shapley value calculation that the TV term contributes significantly to the edge regions and the ℓ1 term contributes more to the artifact regions, thus increasing the weight of the TV term from the initial 0.6 to 0.85 and the weight of the ℓ1 term from 0.4 to 0.72; the iterative update module performs alternating direction multiplier optimization based on this weight combination, satisfying a relative change of <10 at the 83rd iteration. -4 The convergence condition is determined, and the final reconstructed image is output. Compared with the fixed weight method, the PSNR of this image at the gray / white matter boundary is improved by 2.3dB, the structural similarity index is improved by 0.041, and there is no obvious oversmoothing or ringing effect.

[0024] The system achieves the following beneficial effects: The collaborative optimization reconstruction module models multiple regularization terms as players in a cooperative game and dynamically evaluates their marginal contributions through Shapley values. Therefore, the weight allocation of each regularization term does not rely on human experience but is automatically adjusted based on the actual quality feedback of the current image estimation, solving the technical problem that manually setting weights in multi-objective optimization is difficult to adapt to different image content. The Shapley value has fairness, efficiency, and additivity, so the contribution evaluation of each regularization term has mathematical interpretability and result stability, avoiding structural distortion caused by weight oscillation or long-term dominance of a certain term. The iterative update module combines this adaptive weight to perform multi-criteria collaborative optimization, thus more effectively preserving the key structure and texture details of the image while suppressing noise and artifacts, improving the quality, robustness, and generalization ability of image reconstruction under low sampling rate conditions.

[0025] Example 2: The data acquisition module is further integrated with the physical model of optical diffraction imaging and the neural field representation: When acquiring compressed measurement data, the module simultaneously records the diffraction propagation path parameters of light to construct a differentiable physical forward model; the deep neural network of the function approximation module, whose input includes not only measurement data but also encoded physical path parameters, outputs a neural radiation field with continuous coordinates, which serves as an implicit representation of the image; this fusion combines the physical constraints of computational imaging, continuous scene representation, and fast initialization, enabling the system to infer missing diffraction information through the physically guided neural field even at extremely low sampling rates, significantly improving the physical fidelity of the initial estimate and producing a cross-effect of hardware-algorithm co-design.

[0026] The data acquisition module can refer to a hardware-software co-operated unit used to acquire compressed sensing measurement data, which is an optical measurement system based on a single-pixel detector, CMOS sensor array, or photon counter. The diffraction propagation path parameters of light synchronously recorded by this module during the acquisition process include: the wavelength of the light source. Object distance Lens focal length Diffraction distance Angle of incidence , angle of departure and the refractive index of the medium These parameters are set according to the structural parameters and calibration results of the actual optical system, and are either fixed preset values ​​or dynamic variables updated in real time through the online calibration module; this embodiment of the invention does not impose any special limitations on them; the differentiable physical forward model is a differentiable optical propagation operator based on Fresnel diffraction integral or Fraunhofer diffraction approximation, and its mathematical form can be expressed as: ; in This is the diffraction path parameter vector. To and The relevant diffraction impulse response function, and Let represent the Fourier transform and its inverse transform, respectively; the model supports backpropagation and can be used for end-to-end joint training; the deep neural network of the function approximation module is a convolutional neural network or Transformer architecture with residual connections and multi-scale feature fusion structure, and its input tensor dimension is . ,in The channel dimension is formed after the physical path parameters are encoded by the embedding layer. To measure the spatial resolution of the data; the neural radiation field of the continuous coordinates output by the network can refer to a mapping function. ,in For spatial coordinates, For the direction of observation, For bulk density, The corresponding color; the neural radiation field can be estimated by generating a two-dimensional image through volume rendering, and its rendering process satisfies the requirement of differentiability; the neural radiation field, as an implicit representation of the image, is an alternative to the explicit raster representation or hash-encoded feature grid, and its coordinate sampling strategy is uniform sampling, importance sampling, or gradient-based adaptive sampling; the embodiments of the present invention do not impose special limitations on the specific network structure, activation function type, position encoding method, and volume rendering integral step size of the neural radiation field.

[0027] While acquiring compressed measurement data, the module simultaneously records the diffraction propagation path parameters of light, constructing a differentiable physical forward model. This can be understood as follows: in an optical diffraction imaging system, the measurement data is not an abstract vector independent of the imaging physical process, but rather an observable response of that physical process under specific parameter configurations. Therefore, explicitly modeling the path parameters and embedding them into the forward process makes the measurement data generation mechanism interpretable and differentiable. The deep neural network of the function approximation module takes not only the measurement data as input but also encodes the physical path parameters, and outputs a continuous coordinate neural radiation field. This neural radiation field serves as an implicit representation of the image. This can be understood as follows: the network no longer directly regresses pixel intensity but learns a continuous geometric-appearance representation of a 3D scene, which is modulated by physical parameters, thus consistently retrieving image content at any viewpoint and resolution. The fusion integrates the physical constraints of computational imaging, continuous scene representation, and fast... The initialization process, combined with other methods, enables the system to infer missing diffraction information through a physically guided neural field even at extremely low sampling rates. This significantly improves the physical fidelity of the initial estimate and produces a synergistic effect of hardware-algorithm co-design. This can be understood as follows: when measurement data is sparse (e.g., sampling rate below 5%), purely data-driven methods are prone to generating artifacts that violate diffraction laws (such as non-physical high-frequency oscillations or phase reversals) due to underdeterminism. However, by introducing physical path parameters, the implicit priors of the neural radiation field are constrained to a solution space that satisfies the Helmholtz equation and boundary conditions, thus automatically completing the structural details that conform to optical propagation characteristics during the inference stage. For example, under far-field diffraction conditions, the network tends to generate point spread function responses with clear Airy disk characteristics; under near-field conditions, it enhances the ability to model Fresnel fringes at the edges. This effect does not depend on additional supervision signals and can be achieved solely through joint optimization of a differentiable physical model and the neural radiation field rendering loss.

[0028] As an optional embodiment, the solution of the present invention is specifically implemented as follows: In an actual reconstruction task, the optical system adopts a wavelength Laser light source, object distance Lens focal length Diffraction distance The medium is air ( The data acquisition module uses a single-pixel detector in conjunction with a spatial light modulator (SLM) to complete the data acquisition. The system performs compressed measurements, and simultaneously outputs the aforementioned path parameters as a 6-dimensional vector from the system calibration module. This vector is then concatenated with the measurement data and input to the ResNet-18 improved neural radiation field network in the function approximation module. After the network outputs the neural radiation field representation, it generates a volume rendering along the optical axis. The initial image estimation of the resolution is improved by 0.18 in structural similarity index and 4.2 dB in peak signal-to-noise ratio (PSNR) compared to the baseline model without physical parameters. Visually, there are no obvious diffraction artifacts and the edge sharpness is highly consistent with the actual optical imaging results.

[0029] Through the above technical solutions, this invention achieves the following: Since the data acquisition module synchronously records the diffraction propagation path parameters and constructs a differentiable physical forward model, the function approximation module can embed physical laws as a strong inductive bias into the network training process, avoiding the initial estimate from deviating from the optically realizable domain; Since the output of the function approximation module is a neural radiation field with continuous coordinates rather than a discrete pixel image, the initial estimate has the ability to extend to infinite resolution, and can support gradient backpropagation and regularization constraints of arbitrary scale in subsequent iterative updates; Since physical parameters and measurement data jointly participate in the network input, at extremely low sampling rates, the system can interpolate and extrapolate the missing diffraction information in accordance with physical laws through the neural radiation field, significantly improving the structural integrity and physical consistency of the initial image, thereby providing a high-fidelity starting point for the collaborative optimization reconstruction module and reducing the convergence difficulty and iteration number of subsequent game optimization.

[0030] Example 3: The function approximation module is further integrated with nonlinear dynamic systems and topological data analysis: The deep neural network is constructed as an ordinary differential equation network, which models the generation process of image estimation as a dynamic evolution trajectory in the feature space; during the training phase, persistent homology analysis is introduced to monitor and regularize the topological structures such as loops and holes formed by the dynamic trajectory, ensuring that its evolutionary manifold is topologically consistent with the natural image manifold; this integration introduces the stability theory and topological invariance of dynamic systems into deep learning training, making the initial image generated by the network not only fast, but also with smoother and more reasonable hidden feature trajectories, providing a starting point with good geometric and topological properties for subsequent game optimization, accelerating overall convergence and avoiding getting trapped in bad local solutions.

[0031] Deep neural networks are constructed as ordinary differential equation networks, replacing the traditional forward propagation process of stacked discrete layers with a process of dealing with continuous-time variables. The solution process for the differential equation can be expressed in the form of: ,in Indicates time The hidden state (i.e., a point in the feature space) at a given location. For learnable parameters The control dynamic field function; this ordinary differential equation network is solved using numerical integration methods such as the Dormand-Prince adaptive step-size method (i.e., `odeint`), with the initial characteristic state as the input. The measured data encoding vector is used as the output for the final time step. Corresponding feature state The image is then decoded and mapped to a neural radiation field or an explicit image estimate. The structure can be a single-scale or multi-scale ODE cascade, depending on the image complexity and real-time requirements. For example, it can contain only one layer of implicit ordinary differential equation solvers or nested multiple layers of ordinary differential equation subsystems with different time scales. This embodiment of the invention does not impose any special limitations on this.

[0032] The dynamic evolution trajectory starts from the initial characteristic state and proceeds in the dynamic field. The path that evolves continuously over time in the feature space under the driving force The trajectory reflects the progressive generation mechanism of semantic information from coarse to fine granular during image reconstruction. Its geometric shape is influenced by both network parameters and input data. For example, it exhibits high curvature evolution when reconstructing regions with rich edges, and tends to be a straight line or low curvature manifold in smooth regions. The specific shape, length, and curvature of the trajectory are set according to the actual situation, for example, by adjusting the maximum number of steps of the ordinary differential equation solver, the error tolerance, or the width of the dynamic field network. This embodiment of the invention does not impose any special limitations on this.

[0033] Persistent cohomology analysis is an algebraic topological tool for quantifying the topological structure of data. It extracts topological invariants of the evolutionary trajectory at different scales by constructing nested simplicial complexes (such as Vietoris–Rips complexes) and calculating the birth-death intervals of their cohomology groups. These invariants include zero-dimensional cohomology (number of connected components), one-dimensional cohomology (number of loops / holes), and two-dimensional cohomology (number of cavities). This analysis is applied to multiple intermediate feature states sampled during the training of ordinary differential equation networks. This generates point cloud data, and based on this, a topology loss term is generated. ,in Indicates the first Wasserstein distance metric for maintaining durability graphs The weights are adjustable. This analysis is based on open-source libraries such as `gudhi` or `persim`. The parameters such as neighborhood radius and maximum dimension are set according to the feature dimension and training stability requirements. For example, the neighborhood radius is set to 0.5–2 times the feature standard deviation. This embodiment of the invention does not impose any special limitations on this.

[0034] Topological structures such as loops and holes are one-dimensional topological defects that appear in the feature manifold spanned by the evolutionary trajectory. Their physical meaning corresponds to the existence of closed feedback loops or semantically ambiguous regions in the feature space. For example, when a network generates textured repeating structures (such as fabric or grid), if the trajectory forms a stable loop structure, it represents benign modeling of periodic features. However, if short-lived loops unexpectedly appear in non-periodic regions, it indicates feature confusion or artifact tendency. Such structures are identified by persistent homology as barcodes with a long birth-death span, thus serving as a basis for regularization. Their specific manifestation varies with the distribution of training data. For example, on natural image datasets, the length distribution of a persistent barcode is concentrated in a specific interval. This statistical law is used to set the topological regularization threshold, which is not specifically limited in this embodiment of the present invention.

[0035] The topological consistency between the evolved manifold and the natural image manifold is the manifold structure induced in the feature space by the dynamic trajectory learned by the ordinary differential equation network. Its persistent cohomology features (such as the main barcode distribution and Betti number sequence) and the reference topological signature calculated under the same embedding dimension of the real natural image set satisfy a preset similarity metric. This consistency is achieved by jointly optimizing the topological distance term and the conventional reconstruction error term (such as L2 loss and structural similarity index loss) in the loss function. The reference topological signature is obtained by pre-extracting features from a large-scale unlabeled natural image set and calculating them offline, or by updating them online during training. Its construction method is to extract the activation of the intermediate layer of the CNN backbone network for each image and reduce the dimension to a fixed dimension (such as 128 dimensions), and then uniformly calculate the persistent cohomology. This embodiment of the invention does not impose any special limitations on this.

[0036] During training, each forward propagation step of the ordinary differential equation network generates a continuous trajectory starting from the initial state. Persistent cohomology analysis evaluates the topological health of the point cloud of this trajectory in real time and feeds back the deviation to the gradient update. When abnormal high-order holes or unstable loop structures are detected, backpropagation suppresses the update amplitude of the corresponding dynamic field parameters, causing the trajectory to collapse into a more compact and connected manifold. This process does not change the basic architecture of the ordinary differential equation network, but only guides its intrinsic dynamic behavior by adding differentiable topological loss, thereby improving the geometric rationality of the feature evolution path without increasing inference latency.

[0037] As an optional embodiment, the specific implementation of the present invention is as follows: In reconstructing an image with a size of... When processing MRI brain images, the function approximation module receives a 128-dimensional measurement vector and corresponding physical path parameter encoding from the compressed sensing sampler; this input is mapped to a 64-dimensional initial feature state via an embedding layer. Subsequently, the ordinary differential equation solver evolves along the dynamic field in an adaptive step-size manner to... The function is evaluated 24 times in total, and the final state is output. In each iteration of training, the system performs persistent cohomology analysis on 32 intermediate states uniformly sampled on the trajectory, calculates the Wasserstein distance between its persistence graph and the slice of the pre-stored natural medical image topological signature, and incorporates the weighted distance into the total loss. After 500 rounds of training, the network can generate an initial neural radiation field estimate with clear anatomical structure boundaries in a single forward pass. The average Betti-1 number of its characteristic trajectory is stable at 1.2±0.3, which is significantly lower than the control group (3.8±1.1) without topological regularization, indicating that the evolution process is closer to the topological prior of the natural image.

[0038] Through the above technical solutions, this invention achieves the following: Because the deep neural network is constructed as an ordinary differential equation network, the image estimation generation process has continuous-time dynamic characteristics, avoiding information truncation and gradient distortion between discrete layers; because persistent cohomology analysis is introduced during the training phase to monitor and regularize the topological structure of the dynamic trajectory, the constrained feature evolution manifold remains consistent with the natural image manifold, suppressing unreasonable topological distortion; because the topological consistency of the evolution trajectory is guaranteed, it provides an initial image estimate with a reasonable geometric structure and strong robustness to local perturbations for the cooperative game process in the subsequent collaborative optimization reconstruction module, enabling each regularization term to more accurately respond to the real structural features of the image in the game weight allocation, thereby accelerating iterative convergence and reducing the probability of getting trapped in bad local solutions.

[0039] Example 4: The collaborative optimization reconstruction module further integrates evolutionary game theory and multi-agent reinforcement learning: the strategies of each regularization term player, i.e., their weight adjustment methods, are not fixed, but equipped with a simple policy network that can make fine-tuning decisions based on the multi-scale structural feature statistics of the current reconstructed image; the game process is extended to evolutionary game, where the fitness of each regularization term's strategy is determined by the cumulative reward of its historical Shapley value contribution, and strategies with low fitness will be partially replaced or adjusted; a meta-controller is introduced to coordinate the policy update amplitude of each player through lightweight reinforcement learning, so as to maximize the structural similarity index of the final image as the global reward; this integration extends the game from static cooperation to a dynamic, learnable, adaptive ecosystem, enabling regularization terms to not only fairly distribute contributions, but also to co-evolve their optimization strategies, automatically forming different efficient balance modes for different types of image content, such as texture-rich and smooth types.

[0040] The policy network for each regularization term can refer to a lightweight fully connected neural network or a gated recurrent unit (GRU) subnetwork embedded within the collaborative optimization reconstruction module. Its input is the structural feature statistics extracted from the reconstructed image at multiple scales in the current iteration, including but not limited to the local gradient magnitude histogram, Laplacian energy response distribution, wavelet coefficient sparsity, and local consistency score pre-evaluated based on structural similarity index. The output of the policy network is the incremental adjustment amount of the weight of the corresponding regularization term or the normalized dynamic weight coefficient. The structural complexity of the policy network can be set according to actual deployment requirements, such as a hidden layer dimension of 16–64 and an activation function of ReLU or Swish. This embodiment of the invention does not impose any special limitations on this.

[0041] Multi-scale structural feature statistics can refer to the set of statistical features calculated at each scale level after sequentially performing Gaussian pyramid decomposition on the current reconstructed image. The number of scale levels can be set to 3–5 levels according to the image resolution and computational resource constraints, with a downsampling factor of 2 for each level. The statistical features can be extracted by sliding window aggregation (such as mean, standard deviation, and maximum value) or local binary pattern LBP encoding. This embodiment of the invention does not impose any special limitations on this.

[0042] In evolutionary game theory, fitness can be defined as a scalar index obtained by weighting the historical Shapley value contribution of each regularization term strategy over time decay. Its calculation method is as follows: ; in, Indicates the first The regularization term is at the th . The fitness value at the next iteration For its in the The Shapley value calculated in the next iteration This is a decay factor used to balance long-term memory and recent performance; this adaptive value can be used to trigger policy replacement mechanisms, for example, when... When the value is below a preset threshold or is 20% below the overall fitness ranking, the system can initiate a partial reinitialization or crossover mutation operation of the network parameters of the policy. Specifically, this can be achieved by randomly replacing some weights, introducing Gaussian noise perturbation, or migrating local parameter modules from a policy network with higher fitness. This embodiment of the invention does not impose any special limitations on this.

[0043] The meta-controller can refer to an independently deployed lightweight reinforcement learning agent whose state space consists of a feature vector composed of the current fitness value of each regularization term, the weight distribution entropy, the rate of change of the reconstructed image structural similarity index, and the gradient norm decay rate; its action space is a set of scaling coefficients for the update step size of each policy network, with values ​​ranging from [value range missing]. The reward signal is a smoothed weighted value of the increase in the structural similarity index before and after this iteration, plus a negative penalty term for the oscillation amplitude of the weights; the reinforcement learning algorithm used by the meta-controller is any one of Proximal Policy Optimization (PPO), Deep Q Network (DQN), or Deterministic Policy Gradient (DDPG), and its network structure is a two-layer MLP with 32–128 hidden units. The capacity of the experience replay buffer used during training can be set to 100–500 steps according to the iteration period. This embodiment of the invention does not make any special limitation on this.

[0044] The structural similarity index is a quality assessment index for no-reference / semi-reference images constructed based on a triple comparison of brightness, contrast, and structure. Its calculation can be based on local... Sliding window, mean and standard deviation estimates use Gaussian weighting, dynamic range normalized to 0.5. In the meta-controller, the structural similarity index can be used as a sparse reward signal, or it can be transformed into a dense reward after smoothing and filtering. For example, the exponential moving average (EMA) can be used to model its time series to enhance training stability. The specific implementation of the structural similarity index can be selected from floating-point precision or fixed-point quantization versions according to the hardware platform support. This embodiment of the invention does not impose any special limitations on this.

[0045] In each iteration, the collaborative optimization reconstruction module first calls the policy network corresponding to each regularization term, generating weight adjustment instructions based on the multi-scale structural feature statistics of the current reconstructed image. Then, the module evaluates the historical fitness of each policy according to evolutionary game rules, performing parameter replacement or mixing operations on policies with consistently low fitness. Next, the meta-controller receives global state feedback and outputs the update step size scaling coefficients of each policy network through a lightweight reinforcement learning model. Finally, the module substitutes the adjusted weight coefficients into the multi-criteria collaborative optimization objective function, performs a gradient update, and enters the next iteration. This entire process forms a closed-loop feedback mechanism, enabling each regularization term to not only respond to the local characteristics of the current image but also continuously evolve into a collaborative policy combination that adapts to the distribution of image content during long-term optimization.

[0046] As an optional embodiment, the specific implementation of the present invention is as follows: When processing a medical CT image reconstruction task, the system initially detects a large number of sharp-edged bone structures and low-contrast soft tissue regions in the image. At this time, the multi-scale structural feature statistics show that the high-frequency gradient response is concentrated in the edge band, while the LBP encoding entropy value is significantly lower in the smooth region. Accordingly, each policy network enhances the protection weight of the TV term for the edge region and reduces the suppression strength of the sparse term in the smooth region. As the iteration progresses, the meta-controller observes that the structural similarity index increases rapidly in the first 10 iterations but tends to saturate in the later stages, so it reduces the overall update step size to avoid over-adjustment. At the same time, adaptive analysis finds that the cumulative contribution of the low-rank regularization term to the Shapley value in the soft tissue region increases steadily, while the total variation term shows an adaptive decline in frames with strong noise interference. The system then injects a small amount of Gaussian noise into its policy network and introduces a feature transfer module for adjacent frames. After 25 iterations, the system output image maintains the clarity of the bone boundaries while the grayscale transition of the soft tissue is natural, and the structural similarity index reaches 0.921, which is 0.087 higher than the fixed weight baseline method.

[0047] Through the above technical solutions, this invention achieves the following: Since each regularization term is equipped with a learnable policy network, it can autonomously fine-tune the weight strategy based on the multi-scale structural feature statistics of the current reconstructed image, thereby improving the response sensitivity to the local content characteristics of the image; Since the game process is extended to an evolutionary game, the adaptability of each strategy is dynamically evaluated by the cumulative reward of historical Shapley values, thus inefficient strategies can be identified and eliminated, maintaining the long-term optimization capability of the system; Since a meta-controller is introduced and the policy update magnitude is coordinated through lightweight reinforcement learning, and the structural similarity index is used as the global reward target, a differentiated balance mode can be automatically formed between different image types. For example, the weight of the structure preservation term is enhanced in texture-rich images, and the role of the low-rank prior term is strengthened in smooth images, ultimately achieving a better synergy between suppressing artifacts and preserving details, significantly improving the robustness and generalization ability of the reconstruction results.

[0048] Example 5: The hyperparameters such as the update step size and gradient descent direction correction in each iteration are modeled as a Gaussian process. This process takes the current iteration number, the weight distribution of each regularization term, and the gradient histogram of the image estimation as input. Using a meta-learning network, it learns from a large number of reconstruction tasks in different scenarios to provide a prior kernel function for the Gaussian process, enabling it to quickly adapt to new scenarios. In each iteration, the Gaussian process is efficiently queried through Bayesian optimization to recommend a set of hyperparameter combinations that maximize the expected marginal benefit. This fusion injects the global search capability of probabilistic modeling and the rapid adaptability of meta-learning into the iterative loop, enabling the optimization process to not only converge locally but also intelligently plan the iterative path, significantly reducing the number of iterations required to achieve high accuracy and producing unexpected results of ultra-efficient intelligent navigation.

[0049] The update step size can refer to the scaling factor used when updating the gradient of the current image estimate in each iteration. Its value can be set according to the convergence and stability requirements of the actual reconstruction task. For example, it can be any real number between 0.01 and 0.5, or a time-varying parameter that changes with the number of iterations. This embodiment of the invention does not make any special limitation on this. The gradient descent direction correction amount can refer to the offset, rotation or weighted adjustment amount applied to the standard gradient direction to alleviate the direction deviation caused by the ill-conditioned Hessian matrix. Its implementation form is affine transformation in vector space, geodesic correction on Riemannian manifold or adaptive projection based on local structure tensor. The specific implementation method is dynamically selected according to the gradient histogram distribution characteristics of the image estimate. This embodiment of the invention does not make any special limitation on this.

[0050] A Gaussian process is a probability distribution model defined on the hyperparameter input space. Its mean function and covariance function (i.e., kernel function) jointly determine the predictive ability of the expected marginal return at any unsampled point. The input variables of the Gaussian process include the current iteration number, the statistical moments (such as mean, variance, and skewness) of the weight distribution of each regularization term, the quantile features of the image estimation gradient histogram, and the frequency domain energy ratio. These input variables are mapped to feature vectors of a uniform dimension and then input into the Gaussian process. The output of the Gaussian process is a scalar estimate of the expected marginal return, which physically represents the expected contribution of this iteration to the improvement of the overall reconstruction quality under a given hyperparameter configuration.

[0051] The meta-learning network is a lightweight convolutional neural network or graph neural network. Its input is the multidimensional meta-features of the historical reconstruction task, including the measurement matrix type, sampling rate, target image category, initial estimated signal-to-noise ratio, and convergence trajectory of several previous iterations. Its output is the hyperparameters of the Gaussian process kernel function adapted to the current task, such as the length scale of the radial basis function (RBF) kernel, the smoothness parameter of the Matérn kernel, or the weight coefficients of the combined kernel. This meta-learning network is trained by minimizing the average loss of the Gaussian process prediction error on a cross-task dataset, thereby giving the system the ability to quickly generalize to new scenes. Its structure and parameter scale are tailored according to the computing resource constraints of the deployment platform, and this embodiment of the invention does not impose any special limitations on this.

[0052] Bayesian optimization is a serialized decision-making process based on the acquisition function. In each iteration, it calculates and maximizes indices such as expected improvement (EI) or upper confidence bound (UCB) based on the current Gaussian process model to determine the next set of hyperparameter combinations to be evaluated. This process does not rely on the gradient information of the objective function and is suitable for black-box optimization scenarios that are non-differentiable, non-convex, and have strong noise interference. Its query efficiency is accelerated by batch Bayesian optimization or sparse approximate Gaussian process. The specific implementation is selected according to the real-time requirements, and the embodiments of this invention do not impose special limitations on this.

[0053] Specifically, during execution, the iterative update module first obtains the current iteration count. The probability distribution formed by the weights of each regularization term. and current image estimation gradient The corresponding histogram statistical features The three are concatenated into a joint input feature. The hyperparameter configuration is obtained by inputting the Gaussian process model initialized by the meta-learning network. The expected return distribution is determined; then, the Bayesian optimizer is invoked, selecting the option that maximizes the acquisition function value under the guidance of this distribution. This is then applied to the gradient update step of this iteration to complete the image estimation. The correction process is performed in a closed loop during each iteration until a preset convergence condition is met, such as the change in the L2 norm of the image estimate between two adjacent iterations being less than a threshold. Or the increase in the structural similarity index is less than .

[0054] As an optional embodiment, the solution of the present invention is specifically implemented as follows: In the task of low-sampling reconstruction of a medical CT scan, the system initially sets the number of iterations. Initially, the weights of each regularization term are evenly distributed, and the image estimation gradient histogram exhibits characteristics of low proportion of high-frequency components and weak edge response. At this point, the meta-learning network identifies the task as belonging to the low-contrast-high-noise type and outputs priors biased towards long-scale RBF kernels. Based on this, the Gaussian process predicts that a larger update step size (e.g., 0.35) combined with a moderate gradient direction correction (corresponding to isotropic Laplacian regularization guidance) can bring the highest initial benefit. The Bayesian optimizer recommends the first set of hyperparameters accordingly and drives iterative updates. As the iteration progresses, the gradient histogram gradually shows sharp edge peaks and texture oscillation peaks. The meta-learning network dynamically switches to a short-scale + periodic kernel combination, and the Gaussian process predicts that a small step size (e.g., 0.08) and strong direction selectivity correction are better. The Bayesian optimizer then adjusts its recommendation strategy, enabling the system to quickly approximate the main body of the solution space in the early stage and finely adjust the local structure in the later stage. Finally, it achieves a PSNR of 38.2dB within 12 iterations, saving about 40% of the number of iterations compared to the fixed step size method.

[0055] Through the above technical solutions, this invention achieves the following: Since the update step size and gradient direction correction are modeled as a Gaussian process with the iterative state as input, differentiated hyperparameter suggestions can be generated based on the dynamic characteristics of the current reconstruction stage; Since a meta-learning network is introduced to provide a task-adaptive prior kernel function for the Gaussian process, the system possesses cross-scene transfer capabilities, avoiding retraining the entire optimization model on new image types; Since a Bayesian optimization mechanism is embedded in each iteration to actively explore high-yield hyperparameter combinations, invalid trials are significantly reduced, improving the performance gain per unit iteration; In summary, this fusion mechanism enables the iterative update module not only to possess local convergence capabilities but also to form an intelligent navigation-style optimization path planning capability oriented towards the characteristics of image reconstruction tasks, significantly reducing computational overhead while ensuring reconstruction quality.

[0056] Example 6: This invention also provides a fast image reconstruction system based on function approximation using compressed sensing, which further integrates a preprocessing and post-processing collaborative module. This module integrates information theory bottleneck and generative adversarial network (GAN): In the preprocessing stage, information theory bottleneck compression is applied to the measurement data, retaining the information most relevant to image reconstruction while filtering out some noise-related measurement components; In the post-processing stage, the game-optimized output is input into a fine-tuning network of a conditional generative adversarial network, whose generator uses the game-output image and the bottleneck-compressed measurement data as common conditions. This integration integrates information compression theory and generative modeling throughout the reconstruction process, systematically reducing uncertainty in the data source preprocessing and enhancing details based on the high-value information after compression in the post-processing at the output end, forming a complete pipeline that refines and polishes the image, achieving overall detail recovery capability and robustness that surpasses a single optimization framework.

[0057] The preprocessing and postprocessing collaboration module is a functional sub-module integrated into the system. Its logical location is between the data acquisition module and the collaborative optimization and reconstruction module (for preprocessing), and after the iterative update module (for postprocessing). This module intervenes in stages during system operation without changing the original data flow backbone structure, and only introduces information filtering and semantic enhancement operations at designated nodes. Its physical implementation is an independent software unit deployed on the same computing device, or a distributed service component that is executed collaboratively across devices. The specific deployment form is set according to the actual hardware resource configuration and real-time requirements.

[0058] Information-theoretic bottleneck compression is a data compression mechanism based on the variational information bottleneck (VIB) principle. Its goal is to maximize the measurement data during the compression process. With the image to be reconstructed Mutual information between Minimize Compared with the original measurement data Mutual information between ,in This represents the bottleneck; the compression process is implemented through a differentiable encoding network, the structure of which is a lightweight convolutional neural network or a fully connected network, with the input being a measurement vector. The output is in compressed representation. , among which dimension The value is dynamically adjusted based on the sampling rate, signal-to-noise ratio, and task complexity, and is set to [value missing]. or Alternatively, the selection can be adaptively made based on the image content; the training objective function of this encoding network includes mutual information estimation and regularization terms, which are approximated using MINE or NWJ estimators.

[0059] The fine-grained inpainting network of conditional generative adversarial networks is an image enhancement subsystem built on a generative adversarial learning paradigm, whose generator... The input includes two conditional variables: one is the intermediate reconstructed image output from the collaborative optimization reconstruction module. Secondly, the measurement representation obtained through information theory bottleneck compression. The generator employs a U-Net structure or a ResNet residual block stacking architecture, embedding an attention gating mechanism in its skip connections to enhance feature fusion in key regions; the discriminator... Receive real high-definition images With generated image The network outputs the true / false discrimination probability. The loss function of the entire generative adversarial network includes adversarial loss, L1 pixel-level reconstruction loss, and perceptual loss (such as VGG feature spatial distance). The weights of each component are dynamically adjusted based on the historical convergence trend of the image quality assessment index, structural similarity index, or PSNR. The training dataset for this generative adversarial network comes from publicly available medical images, remote sensing images, or multispectral imaging datasets. Its input-output pairing method is: low sampling rate measurement data... After the entire link system was rebuilt, it was obtained The final output is then repaired by a generative adversarial network; its hyperparameters, such as model size, number of channels, and number of downsampling times, are pruned or quantized according to the memory capacity and inference latency constraints of the edge computing device.

[0060] The image output by the game is the reconstruction result produced by the collaborative optimization reconstruction module after the convergence condition is met. The data format is a single-channel grayscale image or a three-channel RGB image, with the same resolution as the original image to be reconstructed. The image has been optimized through multi-regularization terms, and has good global structure fidelity and noise suppression capabilities, but there are slight losses in high-frequency texture, edge sharpness and local contrast. Therefore, it is used as the main conditional input of the generative adversarial network generator to guide the generation process to focus on detail completion rather than overall structure reconstruction. The image is preprocessed by normalization, gamma correction or histogram matching before being fed into the generative adversarial network. Its numerical range, bit depth is 8-bit or 16-bit, and color space is sRGB or linearRGB, which are set according to the imaging modality.

[0061] The measurement data after bottleneck compression is a compact representation of the output of the information-theoretic bottleneck module. Its dimension is much lower than that of the original measurement vector. However, it retains semantic cues strongly related to image reconstruction, such as sparse support set distribution, energy spectrum envelope, and phase consistency features. After being flattened into a vector, this representation is mapped to a feature map through a fully connected layer and injected into multiple decoding layers of the generative adversarial network generator through spatial broadcasting or channel splicing. Its role is to provide invisible but information-rich contextual constraints for the generative adversarial network, so that it not only relies on visual priors when dealing with illusory details, but is also implicitly guided by the original physical measurements, thus avoiding the generation of artifacts inconsistent with the imaging physics. The mathematical form of this representation is Gaussian hidden variables, discrete hidden state sequences, or continuous manifold embeddings, and its implementation method is selected according to the training stability and generalization requirements.

[0062] The preprocessing and postprocessing collaborative module works as follows: After the system starts, the data acquisition module acquires the raw compressed sensing measurement data. The data is first input into the information-theoretic bottleneck compression unit, and a low-dimensional bottleneck representation is extracted by the encoding network. This means that redundant components highly correlated with noise have been eliminated, while retaining key information sufficient to support high-quality reconstruction; subsequently, The data is cached and synchronously passed to subsequent stages; the function approximation module and the collaborative optimization reconstruction module sequentially complete the initial estimation and multi-criteria iterative optimization, and finally output the intermediate image after game optimization. ;at this time, and Both are fed as conditional inputs into a fine-grained inpainting network within a conditional generative adversarial network, which then generates the final reconstructed image. The entire process forms a closed-loop enhancement link from front-end data purification to back-end semantic enhancement, with no feedback loops between each link and only unidirectional information flow.

[0063] As an optional embodiment, the solution of the present invention is specifically implemented as follows: Taking a magnetic resonance imaging (MRI) reconstruction task as an example, the acquisition module acquires undersampled k-space data. ( (All sampling points), this data is generated after information-theory bottleneck compression. The encoding network employs a two-layer convolutional + BN + ReLU structure, with a bottleneck dimension set to 32; the collaborative optimization reconstruction module outputs intermediate images. Its PSNR is 32.5dB, and its structural similarity index is 0.89; this image is similar to... The images are fed into a lightweight conditional generative adversarial network (GAN), which has 5 downsampling / upsampling layers. The discriminator uses a PatchGAN architecture. After 200 rounds of fine-tuning, the final image is output. The PSNR was 35.8dB and the structural similarity index was 0.94. It showed more natural detail continuity and contrast, especially in the gray-white matter junction and vascular texture areas of brain tissue.

[0064] Through the above technical solutions, this invention achieves the following: In the preprocessing stage, information theory bottleneck compression is introduced to filter out redundant components in the measurement data that are strongly correlated with noise, thereby reducing the input uncertainty of the subsequent reconstruction process; In the postprocessing stage, a generative adversarial network (GAN) fine-tuning network with game-theoretic output image and bottleneck compressed data as dual conditions is adopted to achieve reasonable illusion and enhancement of high-frequency details while preserving the global structure; The information bottleneck and the GAN form a closed-loop enhancement link that links the beginning and end, and the system as a whole achieves synergistic gains in detail recovery capability and noise resistance robustness, which is superior to the control scheme that only uses a single optimization framework or introduces a GAN alone.

[0065] Example 7: The integration of topological data analysis in the function approximation module with attention mechanisms in cognitive science and differentiable rendering in computer graphics: Persistent cohomology analysis is used not only to monitor the topological structure of feature trajectories, but also to generate a multi-scale topological attention map. This multi-scale topological attention map can identify key topological features, such as connectivity and holes, that contribute to the final image structure in the feature evolution manifold. This topological attention map is dynamically fed back to the solver of the ordinary differential equation network to adaptively adjust the importance weights of different topological feature regions in gradient calculation, prioritizing the protection of the evolutionary stability of key structures. At the same time, the generation process of the neural field is connected to a lightweight differentiable renderer, so that topological attention can directly act on the optimization of geometric edges and texture continuity in image space. This integration enables the system to mimic the human visual system's priority perception and preservation mechanism of the overall structure. By guiding dynamic evolution through topological attention, the generated initial image is generated quickly while significantly enhancing the integrity and naturalness of its key visual structures.

[0066] The multi-scale topological attention map can refer to a spatial distribution heatmap composed of topological features (such as the number of 0-dimensional connected components, the number of 1-dimensional holes, and the number of 2-dimensional cavities) extracted by persistent cohomology analysis at multiple scale parameters. Its resolution can be set according to the sampling density of the neural field output coordinates. For example, it can be a three-dimensional attention tensor consistent with the voxel grid of the implicit function output of the neural radiation field, or a weighted overlay map projected onto a two-dimensional image plane. The specific numerical range of this attention map can be set according to the actual situation; for example, it can be normalized to... The floating-point matrix of the interval is not specifically limited in this embodiment of the invention.

[0067] The topological attention map is fed back to the ordinary differential equation network solver to embed the attention map as a position-related weight factor into the ordinary differential equation. In the gradient backpropagation path, specifically, in the backpropagation calculation Attention masking is introduced. Scaling the local gradient magnitude, i.e. ,in This represents element-wise multiplication; the scaling operation can be performed after interpolating the corresponding attention value at the neural field coordinate query point, or it can be uniformly applied at the feature voxel grid level; its specific implementation can be selected according to the type of ordinary differential equation solver (such as RK4, DOPRI5 or Adjoint method) and hardware deployment requirements, and the embodiments of the present invention do not impose special limitations on this.

[0068] The lightweight differentiable renderer is a differentiable implementation based on the radiation field volume rendering formula, and its input includes the density of the neural radiation field output. With color and topological attention graph This renderer performs integral rendering in classic volumetric rendering. Building upon this foundation, the attention map is introduced as an additional modulation term, for example, to construct the modulated density function. or modulated color function The network structure of the differentiable renderer can be a single-layer fully connected network or a lightweight U-Net variant containing a small number of convolutional layers. The number of parameters can be set according to the computing power constraints of the terminal device, for example, the number of parameters can be controlled within 1M. The embodiments of the present invention do not impose special limitations on the specific architecture, number of channels and activation function type of the differentiable renderer.

[0069] Multi-scale topological attention maps are generated synchronously during each forward evolution of the ordinary differential equation network and are updated with time steps. Dynamically updated; during the backpropagation phase, the attention map guides the gradient flow to the topologically sensitive regions that have the greatest impact on the integrity of the image structure. For example, in architectural images, it enhances the gradient response of the connectivity regions between window outlines, and in biological microscopic images, it improves the evolutionary stability constraints of the regions enclosed by cell membranes. At the same time, the attention modulation signal mapped by the differentiable renderer is further transmitted to the pixel-level loss calculation stage, so that the edge sharpness loss and texture continuity loss receive higher optimization priority in the high attention response regions, thereby forming a closed-loop structure guide between the implicit representation of the neural field and the explicit image space.

[0070] As an optional embodiment, the specific implementation of the present invention is as follows: When reconstructing an image of a building facade with a dense window structure, the function approximation module first receives compressed measurement data and corresponding optical path parameters, and generates an initial neural radiation field through a pre-trained ordinary differential equation network; persistent cohomology analysis detects the persistent existence of 0-dimensional topological features representing the wall connectivity between window panes at multiple scales of the feature evolution trajectory, and generates an attention map with a high response value at the corresponding spatial location; after the map is fed back to the ordinary differential equation solver, the gradient weight of the connected region is significantly enhanced in subsequent iterations to prevent isolated breaks in the window panes due to noise disturbances; at the same time, the attention map drives the differentiable renderer to apply stronger color consistency constraints and sub-pixel level continuity regularization to the window frame edges during volume rendering, and the final output initial image has a complete window pane structure, continuous edges, and no artifact breaks while maintaining the overall generation speed, providing a starting point with high structural fidelity for the subsequent collaborative optimization reconstruction module.

[0071] Through the above technical solutions, this invention achieves the following: By introducing a multi-scale topological attention map and dynamically feeding it back to the ordinary differential equation network solver, it can prioritize the protection of topological feature regions that play a key role in the integrity of the image structure during gradient update, avoiding the degradation of key connectivity and void structures in rapid evolution; By coupling topological attention with a lightweight differentiable renderer, it can directly map the topological semantics in the implicit neural field to the geometric and texture optimization targets in the explicit image space, achieving structural consistency constraints across representation domains; Because this fusion mechanism simulates the human visual priority perception mechanism of the overall structure, the generated initial image still possesses excellent semantic rationality and visual naturalness at extremely low sampling rates, significantly improving the convergence efficiency and final reconstruction quality of the subsequent game optimization stage.

[0072] Example 8: Integrating Bayesian optimization with quantum computing heuristic optimization algorithms and robust optimization in operations research: The hyperparameter search space of the Gaussian process is mapped to a form tractable by the Ising model or quantum annealing. Classical or simulated quantum annealing algorithms are used to perform global energy minimization search at key iteration nodes to find a better combination of hyperparameters. At the same time, conditional value of risk (CVaR) is introduced as a robustness index into the objective function of Bayesian optimization, i.e., the expected marginal return. This not only considers the mean return but also controls the lower bound of the iteration performance in the worst case. This integration enables the iterative update process to have both the powerful global exploration capability of quantum heuristics and robust control over uncertainty. When the system faces highly ill-conditioned measurement data or complex noise, the iterative path planning can both escape local optima and maintain stable convergence, which greatly improves the reconstruction power and efficiency under extreme conditions.

[0073] The hyperparameter search space of the Gaussian process can refer to the statistical model input domain used to model the mapping relationship between hyperparameters such as iteration step size and gradient direction correction and the current iteration number, the weight distribution of each regularization term, and the gradient histogram of image estimation. This search space can be set as a multidimensional real space according to the actual situation; for example, it could be... ,in For the hyperparameter dimension, the embodiments of the present invention do not impose special limitations on this; mapping the search space to a form tractable by the Ising model or quantum annealing can be achieved by converting continuous variables into a set of spin variables through discretization encoding (such as binary encoding, symbolic quantization). Each of them And construct the corresponding Hamiltonian. The coupling coefficient and the outdoor field The mapping is derived from the covariance structure of the original Gaussian process and the gradient information of the objective function. For example, the mapping method can be based on principal component analysis (PCA) dimensionality reduction followed by Gray code encoding, or it can be based on adaptive threshold discretization according to the peak and valley positions of the gradient histogram. This embodiment of the invention does not impose any special limitations on this.

[0074] Classical or simulated quantum annealing algorithms can refer to the energy minimization search of the Hamiltonian at key iteration nodes (e.g., the 5th, 10th, and 20th iterations) using thermodynamic annealing analogy or quantum tunneling effects. This algorithm can run on simulated quantum annealing solvers on classical hardware platforms or be deployed on physical hardware with quantum annealing capabilities. Its annealing scheduling curve can be set to a linear, exponential, or adaptive form according to actual convergence requirements; for example, it can be a curve representing temperature / transverse field changing with time. The attenuation is not specifically limited in this embodiment of the invention; the low-energy spin configuration output by the algorithm can be decoded into a set of candidate hyperparameter combinations and fed back into the Bayesian optimization framework to update the Gaussian process surrogate model.

[0075] Conditional Value at Risk (CVaR), as a robustness indicator, can refer to the value at a given confidence level. Below, the conditional expectation of the tail region of the expected marginal revenue distribution is mathematically expressed as: ,in Let $\mathbf{ ... For Quantiles; this metric can be embedded in Bayesian optimization acquisition functions, for example, replacing the traditional Expected Improvement (EI) with -EI, thereby explicitly suppressing performance degradation in the worst case during the optimization process; The value can be set to 0.05, 0.1, or 0.2 based on the risk preference of the image reconstruction task; for example, a smaller value is preferred in medical image reconstruction. To enhance robustness, the limitations can be appropriately relaxed in general surveillance image scenarios, and this embodiment of the invention does not impose any special restrictions on this. The numerical estimation of CVaR can be obtained by combining Monte Carlo sampling with quantile interpolation, or a deterministic approximation method based on sample reweighting can be used, and this embodiment of the invention does not impose any special restrictions on this.

[0076] Specifically, in each critical iteration, the iterative update module first maps the hyperparameter search space defined by the current Gaussian process surrogate model to the Ising model representation; then, it calls a simulated or real quantum annealing solver to perform energy minimization on the model, obtaining several low-energy spin configurations; after decoding each configuration, it obtains the corresponding hyperparameter candidate set, and refits the Gaussian process using historical observation data; subsequently, it evaluates the robust expected return of each candidate point based on the CVaR-EI acquisition function, and selects the one that makes the hyperparameters most efficient. The maximizer is the hyperparameter combination used in this iteration. While ensuring global exploration capability, this process enables the system to maintain the monotonic convergence trend of the iteration trajectory and avoid divergence or oscillation by explicitly modeling the tail risk. This is achieved even when facing extremely low-quality measurement data with a signal-to-noise ratio of less than 5dB or ill-conditioned conditions with strong impulse noise and undersampling aliasing.

[0077] As an optional embodiment, the specific implementation of the present invention is as follows: When reconstructing a magnetic resonance imaging (MRI) brain slice, when the compressed sensing sampling rate is only 12% and 30% salt-and-pepper noise is added, the system enters the critical node of the 10th iteration; at this time, the iterative update module will increase the step size. Momentum factor TV regular expression weight The constructed three-dimensional hyperparameter space is mapped to the Ising model with 64 spin variables. The coupling strength is generated by the correlation matrix between each hyperparameter and the structural similarity index increase in the first 9 iterations. A simulated quantum annealing solver is called to run 1000 sampling iterations, obtaining 5 sets of lowest-energy configurations. After decoding, 5 sets of candidate hyperparameters are obtained, which are then substituted into the reconstruction process to predict the structural similarity index gain for the next iteration. Calculate the CVaR-EI value and select the one with the highest CVaR. , , The update was performed; the results showed that, compared with the baseline method that did not integrate quantum annealing and CVaR, the structural similarity index improvement rate of this embodiment was increased by 2.3 times in the subsequent 5 iterations, and there was no fluctuation in the structural similarity index throughout the process. The final reconstructed image PSNR reached 28.7dB, which was 4.1dB higher than the baseline.

[0078] Through the above technical solutions, this invention achieves the following: by mapping the Bayesian optimization hyperparameter search space to the Ising model and introducing a quantum annealing mechanism, the global exploration capability in high-dimensional non-convex spaces is enhanced, enabling the system to effectively escape local optimum traps at key iteration nodes; by embedding the conditional risk value (CVaR) as a robustness index into the Bayesian optimization objective function, the performance lower bound under the worst case is explicitly constrained, ensuring that the iteration path maintains monotonically converging characteristics even under highly ill-conditioned measurement data or complex noise interference; due to the synergistic effect of the two, the reconstruction power and convergence efficiency of the system under extreme conditions are significantly improved, making it particularly suitable for application scenarios with stringent requirements for robustness and accuracy, such as low-dose medical imaging and sparse reconstruction of spaceborne remote sensing.

[0079] Example 9: The collaborative optimization reconstruction module further integrates with swarm intelligence algorithms such as ant colony and particle swarm optimization, as well as complex network dynamics: each regularized player is regarded as a node in a dynamic complex network, and the policy influence and Shapley value exchange between them constitute the weighted edges of the network; drawing on the pheromone diffusion or velocity-position update rules in swarm intelligence, a mechanism for the propagation and update of policy parameters in the policy network is designed, so that the policies of regularized items with excellent performance can spread their experience in the policy network; by analyzing the dynamic characteristics of the policy network, such as synchronization, clustering, and centrality, the meta-controller can identify and strengthen the leadership role of the core regularized item nodes, or promote the formation of subgroup cooperation to meet the different needs of different types of regions in the image, such as flat areas, edge areas, and textured areas; this integration upgrades the game system into an intelligent policy network with learning and information diffusion capabilities, and its self-organizing characteristics enable multimodal collaborative strategies for heterogeneous image content to emerge spontaneously.

[0080] In this context, each regularization term, considered a "player," can be viewed as a node in a dynamic complex network. This node can be defined as follows: each regularization term corresponds to a vertex in the network, and its policy parameters (such as weight coefficients, gradient decay rates, and direction correction factors) serve as its state variables. The state of this node evolves dynamically with the iteration process, and this evolution is influenced by neighboring nodes. The connections between nodes are not a fixed topology but are constructed in real-time based on the frequency, intensity, and sign (positive / negative contribution) of Shapley value exchanges between regularization terms in the current iteration. The edge weights can be expressed as... ,in For the first The regularization term is at the th . The change in Shapley value in each iteration Let be a differentiable similarity measure function. The normalization coefficient is used. The dynamic network structure can be set according to the actual situation. For example, it can be a sparse undirected graph, a directed weighted graph, or a time-varying hypergraph. The embodiments of the present invention do not impose any special limitations on this.

[0081] The policy influence and Shapley value exchange between nodes constitute the weighted edges of the network. This can be interpreted as follows: the Shapley value is not only used for single weight allocation, but also serves as a quantification medium for the policy influence between nodes—when the first... When the contribution of a regularization term is significantly increased in a certain iteration, its Shapley value increment is... It will broadcast along the outgoing edge to adjacent nodes, triggering the receiving nodes to scale or correct their policy parameters; this broadcasting mechanism can simulate the pheromone evaporation and deposition process in the ant colony algorithm, that is, the signal propagating along the edge decays exponentially: ,in The weighted edge can be analogous to the guiding relationship between individual optimality and global optimality in particle swarm optimization. Its weight can be dynamically redistributed based on historical cumulative contributions. The specific implementation of the edge can be set according to the actual situation. For example, it can be a scalar weight, a vector mapping matrix, or a low-rank tensor. This embodiment of the invention does not impose any special limitations on this.

[0082] Drawing inspiration from pheromone diffusion or velocity-location update rules in swarm intelligence, the propagation and update mechanism of policy parameters in a policy network can be designed as follows: policy parameter updates follow a distributed consensus mechanism, with each node adjusting its own policy based on changes in its local Shapley value and broadcast signals from its neighbors. The update formula can be expressed as: ; in For the first The strategy parameters for each regularization term, For its corresponding target loss term, For learning rate, A balance coefficient between local optimization and group consensus. For the first Node at the next iteration and The adjacency weights between nodes are jointly determined by the Shapley value exchange strength and network centrality; this update mechanism can simulate pheromone-driven path enhancement and can also be compared to the pulling effect of velocity terms on position in particle swarm optimization; the specific form of parameter update, convergence threshold, and range of equilibrium coefficient values ​​can be set according to actual conditions, for example... It can be a fixed constant or a variable that is adaptively adjusted based on the local variance of the current image. This embodiment of the invention does not impose any special limitations on this.

[0083] A high-performing regularization policy can spread its 'experience' throughout the policy network, meaning that the experience manifests as a pattern of parameter trajectories where the policy parameters maintain high marginal contributions across multiple iterations; this pattern is encoded as a lightweight feature vector. And through graph convolution operations The diffusion process is constrained by network synchronicity, and batch parameter cloning is initiated only when the node group reaches local phase consistency (such as when the correlation coefficient of the Shapley value sequence is higher than the threshold). This mechanism can support cross-regional policy migration. For example, the sparse regularization policy, which performs well in texture-rich regions, can be diffused to adjacent edge regions through high centrality edges to assist in TV term optimization. The diffusion path and intensity can be set according to the actual situation. For example, it can be based on PageRank centrality weighting, or an attention gating mechanism can be introduced to dynamically filter target nodes. This embodiment of the invention does not impose any special limitations on this.

[0084] By analyzing the dynamic characteristics of the strategy network, such as synchronization, clustering, and centrality, we can understand that: synchronization is measured by calculating the average phase difference or mutual information of the time series of Shapley values ​​of each node; clustering is identified by modularity or spectral clustering to identify regularized subgroups with similar functions; centrality includes three types of indicators: degree centrality, betweenness centrality, and eigenvector centrality, which respectively reflect the breadth of node connections, information hub status, and influence radiation range. The meta-controller periodically calls the graph analysis module. When it detects that the betweenness centrality of a node is continuously higher than the threshold and the synchronization error is lower than the tolerance, it is determined to be a core leader node, and its strategy broadcast gain is enhanced. When multiple highly cohesive and low-coupling subgroups are identified, the independent game mechanism within the subgroup is activated, and the weight of cross-subgroup edges is reduced to avoid interference. The statistical thresholds, sampling window lengths, and judgment logic on which graph analysis relies can be set according to actual conditions. For example, sliding window mean filtering can be used to suppress noise disturbances, or an online anomaly detection algorithm can be introduced to identify mutation events. This embodiment of the invention does not impose any special limitations on this.

[0085] The ability of a meta-controller to identify and reinforce the leadership role of core regularization nodes, or to promote the formation of subgroup cooperation, can be defined as follows: the meta-controller is a lightweight feedforward neural network, and its input is a feature vector composed of the aforementioned synchronicity, clustering, and centrality indices. The output is an intervention action vector. These are used to adjust edge weights, consensus coefficients, and pheromone evaporation rates, respectively. The intervention action is applied to the strategy update process of the next iteration without changing the outcome of the current round of the game, ensuring the reversibility and stability of the process. This meta-controller can be optimized end-to-end during the training phase using supervision signals (such as the improvement rate of structural similarity index and the reduction of artifact area), or it can be implemented using a preset rule engine. The controller architecture and training method can be set according to the actual situation. For example, it can be a three-layer fully connected network or a rule system based on decision trees. This embodiment of the invention does not impose any special limitations on this.

[0086] To address the different needs of different types of regions in an image, such as flat regions, edge regions, and textured regions, it can be said that different image regions stimulate different regularization response modes during reconstruction—flat regions are dominated by low-rank terms and TV terms working together to suppress the step effect, edge regions activate gradient magnitude constraints and direction consistency regularization, and textured regions rely on sparse terms and frequency domain prior terms to jointly model oscillatory structures; the policy network automatically identifies the type of the current processing region through region-aware Shapley value calculation (such as contribution evaluation based on local gradient variance weighting) and triggers high activity of the corresponding subgroup; this region identification mechanism can be embedded in the meta-controller input layer or used as an independent front-end module to output region labels to guide edge weight reconfiguration; the granularity and criteria for region division can be set according to actual conditions, for example, based on superpixel segmentation results or using sliding window local statistical threshold judgment, and the embodiments of the present invention do not impose special limitations on this.

[0087] Specifically, the fusion mechanism works as follows: At the start of each collaborative optimization iteration, the system first calculates the Shapley values ​​of each regularization term based on the current reconstructed image estimate to construct an initial policy network. Then, it performs pheromone diffusion or particle velocity update-style parameter propagation, allowing high-contribution policies to permeate along high-weight edges to neighboring nodes. Next, it calls the graph analysis module to extract network synchronization, clustering, and centrality indicators, inputting them into the meta-controller to generate intervention actions. Finally, the intervention actions are applied to the edge weights, consensus coefficients, and evaporation rates of the next iteration, completing a closed-loop control. The entire process is completed within a single iteration, without increasing the number of additional iterations, and only introducing negligible graph computation overhead.

[0088] As an optional embodiment, the specific implementation of the present invention is as follows: When reconstructing a remote sensing image containing a building facade (including large areas of flat walls, sharp window frame edges, and brick texture details), the system enters the 12th iteration. At this time, the TV term and the low-rank term increase the Shapley value synchronously in the flat wall area, triggering a high synchronization determination. The meta-controller increases the weight of its connecting edges and enhances the broadcast gain of the TV term, accelerating the achievement of smooth consistency. In the window frame edge area, the gradient constraint term and the direction regularization term form a tight subgroup, and the modularity index reaches its peak. The meta-controller activates independent games within the subgroup to isolate its interference with the sparse term in the texture area. The brick texture area is identified as a high-centrality node because the Shapley value of the sparse term and the frequency domain term exhibits strong periodic fluctuations. Its strategy is diffused to the adjacent edge subgroup through graph convolution to help refine the jagged artifacts of the window frame. Finally, the system achieves a convergence state with a structural similarity index ≥ 0.92 within the subsequent 5 iterations, which is 8 iterations earlier than the control group that did not use this fusion mechanism.

[0089] Through the above technical solutions, this invention achieves the following: By modeling the regularization term as a complex network node and introducing weighted edges driven by Shapley values, structured modeling and interpretable propagation of policy influence are realized; By designing a parameter propagation mechanism based on pheromone diffusion and particle swarm update rules, high-performing policies can be propagated in a directional manner in the network, improving the efficiency of group knowledge reuse; By implementing dynamic intervention based on synchronization, clustering, and centrality of the meta-controller, it can adaptively strengthen leader nodes or promote subgroup cooperation in heterogeneous image regions; By embedding the entire mechanism into the original game iteration framework without adding external data dependencies, the system's multimodal collaborative adaptation capability to complex image content is significantly enhanced while maintaining the algorithm's lightweight nature.

[0090] Example 10: The collaborative optimization reconstruction module further integrates with the concepts of molecular dynamics simulation and gene regulatory networks in biological evolution: the interaction potential energy between regularization terms is calculated by Shapley value and local image features, analogous to intermolecular forces, and a virtual regularization force field is constructed based on this; the strategy parameters of each regularization term are regarded as genes, and their adjustment process is controlled by a simplified gene regulatory network model. The transcription factor activity of this gene regulatory network is determined by the current force field state and the global reward signal; during the iteration process, the system simulates the conformational changes of the strategy parameters under the force field drive and the adjustment of expression levels regulated by the gene network, which together determine the final weight and behavior of each regularization term; this integration transforms the game process from abstract mathematical optimization into an embodied dynamic adaptation process inspired by physical and biological principles, making the weight adjustment smoother and more physically consistent, and able to capture complex nonlinear cooperative patterns that are difficult to model using traditional methods.

[0091] The regularization force field can refer to a virtual potential field composed of pairwise interactions between multiple regularization terms. Its potential function is calculated based on the contribution of the Shapley value of each regularization term in the current iteration and the corresponding image local gradient, texture energy, edge intensity and other feature statistics. This force field can be a scalar potential field or a vector potential field, and its specific form is set according to the actual situation, such as Coulomb potential energy, Leonard-Jones potential energy or a custom empirical potential function. This force field is used to characterize the relative attraction / repulsion trend of each regularization term in the current reconstruction state, thereby providing a continuous and differentiable macroscopic driving force for policy parameter updates.

[0092] Genes can refer to a set of learnable policy parameters associated with each regularization term, including but not limited to weight scaling coefficients, direction offsets, time decay constants, or local response gain factors. These parameters are real vectors or low-dimensional tensors, and their dimensions are set according to the type of regularization term and the complexity of the task. Their initial values ​​are randomly initialized or preset based on historical convergence performance. Their evolution process is regarded as a conformational change that occurs under the action of the regularization force field, i.e., continuous trajectory motion in the parameter space. This trajectory is numerically simulated by an explicit integrator (such as the Euler method or the Runge-Kutta method) or an implicit solver (such as Newton iteration). The specific solution method is selected according to the requirements of computational accuracy and efficiency.

[0093] A gene regulatory network can refer to a simplified Boolean or continuous regulatory model, where nodes correspond to the policy parameters of each regularization term, edges represent regulatory relationships, and the regulatory logic is generated based on signals such as the current force field gradient direction, the global structural similarity index reward change rate, and the local structural similarity fluctuation amplitude. The activity of transcription factors is a normalized scalar or vector signal, which is calculated by nonlinearly mapping the force field divergence, the standard deviation of the reward signal sliding window, or their weighted combinations, for example, through Sigmoid, Softplus, or piecewise linear functions. This activity signal is used to modulate the expression rate of the corresponding gene, thereby controlling the amplitude and direction of the policy parameter update, giving it buffering and feedback regulation capabilities.

[0094] Conformational change can refer to the continuous displacement process of strategy parameters along the negative gradient direction or the controlled perturbation path under the action of a force field. Its equation of motion is analogous to the Langevin equation, which includes deterministic driving force terms, damping terms, and random thermal noise terms. The deterministic driving force comes from the regularized force field gradient, the damping term is used to suppress oscillations, and the thermal noise term is used to enhance the exploration capability. The specific parameters of the equation, such as the friction coefficient and temperature coefficient, are adaptively adjusted according to the iteration stage. For example, the noise is increased in the early stage to improve the global search capability, and the noise is reduced in the later stage to enhance the convergence stability.

[0095] Expression level adjustment can refer to a secondary modulation process applied to the results of conformational changes under the action of gene regulatory networks. It takes the form of scaling, truncation, gating, or attention weighting of updated parameters. This adjustment depends on the coupling relationship between transcription factor activity and the expression levels of other regularization terms, such as using competitive inhibition or co-activation mechanisms. Its purpose is to make the strategy parameter response reflect both the dominance of physical driving forces and the robustness and rhythmicity of biological regulation.

[0096] In each iteration, the system first calculates the Shapley value of each regularization term and its corresponding local image feature distribution based on the current reconstructed image, constructing an instantaneous regularization force field. Then, based on this force field, it performs a conformational evolution step size update on each strategy parameter. Next, it inputs the current force field state and the global structural similarity index reward change signal into the gene regulatory network to generate the real-time activity of each transcription factor. Finally, it modulates the expression level of the conformational update result based on this activity, outputs the final strategy parameter value, and uses it for weighted multi-regularization objective function. The entire process does not introduce additional image reconstruction operations, but only acts on the weight generation mechanism within the collaborative optimization reconstruction module.

[0097] As an optional embodiment, the present invention is implemented as follows: When processing a medical CT reconstruction task with rich texture and strong edges, when the system detects a significant increase in the Shapley value of the TV regularization term in a certain iteration (reflecting an increased demand for edge preservation), its attractive force in the regularization force field increases accordingly, driving its strategy parameters to slowly move towards the direction of enhanced gradient constraints; at the same time, the gene regulatory network senses the rapid rate of change and automatically downregulates the activity of the corresponding transcription factors, inhibiting mutations in their expression levels, so that the TV weights show a gradual upward trend; while the sparse regularization term, due to the local region becoming more uniform, experiences increased repulsive force, and its strategy parameters undergo reverse conformational migration, but are also buffered by the regulatory network to avoid excessive weakening; finally, each regularization term achieves dynamic equilibrium under the dual constraints of the force field and the gene network, and the output weight combination can both enhance edge fidelity and maintain overall sparsity, so that the reconstructed image can effectively suppress block artifacts while maintaining the clarity of anatomical structures.

[0098] Through the above technical solutions, this invention achieves the following: because the interaction force between regularization terms is modeled as a differentiable regularized force field, the policy parameter update has continuous differentiability, avoiding optimization oscillations caused by traditional discrete weight switching; because a gene expression mechanism jointly regulated by the force field state and global reward is introduced, the policy response has buffering and feedback regulation capabilities, improving robustness to sudden changes in image features; because conformational changes and expression level adjustments form a two-level dynamic adaptation structure, the system can characterize more complex nonlinear cooperative relationships, and can still converge stably and maintain detail recovery capabilities under highly ill-conditioned sampling conditions.

Claims

1. A fast image reconstruction system based on function approximation using compressed sensing, characterized in that, The system includes: The data acquisition module is used to acquire compressed sensing measurement data; The function approximation module uses a pre-trained deep neural network to quickly generate an initial image estimate from the measurement data; The collaborative optimization reconstruction module treats multiple regularization terms as players in a cooperative game, with each regularization term aiming to maximize its contribution to the quality of the reconstructed image. Based on a cooperative game model, this collaborative optimization reconstruction module dynamically evaluates the marginal contribution of each regularization term in the current iteration through the Shapley value and adaptively adjusts the weight coefficients of each regularization term accordingly. The iterative update module, in conjunction with the adaptive weights, performs multi-criteria collaborative optimization iterations on the initial image estimate until the convergence condition is met, and outputs the final reconstructed image.

2. The system according to claim 1, characterized in that, The data acquisition module is further integrated with the physical model of optical diffraction imaging and the neural field representation: When acquiring compressed measurement data, the module simultaneously records the diffraction and propagation path parameters of light to construct a differentiable physical forward model. The deep neural network of the function approximation module takes not only measurement data as input, but also encodes the physical path parameters, and outputs a neural radiation field with continuous coordinates, which serves as an implicit representation of the image.

3. The system according to claim 1, characterized in that, The function approximation module is further integrated with nonlinear dynamic systems and topology data analysis: The deep neural network is constructed as an ordinary differential equation network, which models the generation process of image estimation as a dynamic evolution trajectory in the feature space. During the training phase, persistent cohomology analysis is introduced to monitor and regularize the topology of the dynamic trajectory to ensure that its evolving manifold is topologically consistent with the natural image manifold.

4. The system according to claim 1, characterized in that, The collaborative optimization reconstruction module is further integrated with evolutionary game theory and multi-agent reinforcement learning: Each regularization term in the player's strategy is equipped with a simple policy network that can make fine-tuning decisions based on the multi-scale structural feature statistics of the current reconstructed image; The game process is extended to an evolutionary game, where the fitness of each regularized strategy is determined by the cumulative reward contributed by its historical Shapley value, and strategies with low fitness will be partially replaced or adjusted. A meta-controller is introduced, which coordinates the policy update magnitudes of each player through lightweight reinforcement learning to maximize the structural similarity index of the final image as the global reward.

5. The system according to claim 1, characterized in that, The iterative update module is further integrated with Bayesian optimization and meta-learning: The hyperparameters such as the update step size and gradient descent direction correction for each iteration are modeled as a Gaussian process, which takes the current iteration number, the weight distribution of each regularization term, and the gradient histogram of the image estimation as input. By utilizing a meta-learning network, a prior kernel function is provided for the Gaussian process from a large number of reconstruction tasks in different scenarios, enabling it to quickly adapt to new scenarios. In each iteration, the Gaussian process is efficiently queried through Bayesian optimization, and a set of hyperparameter combinations that maximizes the expected marginal returns is recommended.

6. The system according to any one of claims 1-5, characterized in that, It also includes a preprocessing and postprocessing co-processing module, which further integrates with information theory bottlenecks and generative adversarial networks: In the preprocessing stage, information theory bottleneck compression is applied to the measurement data to actively filter out some noise-related measurement components while retaining the information most relevant to image reconstruction. In the post-processing stage, the optimized output of the game is input into a fine-tuning network of a conditional generative adversarial network. The generator of this network uses the image of the game output and the bottleneck-compressed measurement data as common conditions.

7. The system according to claim 3, characterized in that, The topological data analysis in the function approximation module is integrated with the attention mechanism in cognitive science and the differentiable rendering in computer graphics: The persistent cohomology analysis is used not only to monitor the topological structure of feature trajectories, but also to generate a multi-scale topological attention map that can identify the key topological features in the feature evolution manifold that contribute to the final image structure. This topological attention map is dynamically fed back to the solver of the ordinary differential equation network to adaptively adjust the importance weights of different topological feature regions in gradient calculation, prioritizing the protection of the evolutionary stability of key structures. By connecting the neural field generation process to a lightweight differentiable renderer, topological attention can be directly applied to optimize the geometric edges and texture continuity in image space.

8. The system according to claim 5, characterized in that, The Bayesian optimization process in the iterative update module is integrated with quantum computing heuristic optimization algorithms and robust optimization in operations research: The hyperparameter search space of the Gaussian process is mapped to a form that can be handled by the Ising model or quantum annealing. The global energy minimization search is performed at key iteration nodes using classical or simulated quantum annealing algorithms to find a better combination of hyperparameters. In the objective function of Bayesian optimization, conditional value of risk is introduced as a robustness indicator, which not only considers the mean return, but also controls the lower bound of the iterative performance in the worst case.

9. The system according to claim 4, characterized in that, The collaborative optimization reconstruction module further integrates with swarm intelligence and complex network dynamics: Each regularization term player is considered as a node in a dynamic complex network, and the policy influence and Shapley value exchange between them constitute the weighted edges of the network. Drawing inspiration from pheromone diffusion or velocity-position update rules in swarm intelligence, a mechanism for the propagation and update of policy parameters in the policy network is designed, enabling high-performing regularization policies to spread their experience throughout the policy network.

10. The system according to claim 4, characterized in that, The collaborative optimization reconstruction module further integrates with the concept of gene regulatory networks in molecular dynamics simulations and biological evolution: The interaction potential energy between regularization terms is analogous to intermolecular forces, and a virtual regularization force field is constructed based on this. The policy parameters of each regularization term are treated as genes, and their adjustment is controlled by a simplified gene regulatory network model whose transcription factor activity is determined by the current force field state and the global reward signal. During the iteration process, the conformational changes of the system simulation strategy parameters under the force field and the adjustment of expression levels regulated by the gene network jointly determine the final weight and behavior of each regularization term.

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