A method and system for MRI continuous sampling and image reconstruction joint optimization

Abstract

The application provides a MRI continuous sampling and image reconstruction joint optimization method and system, and belongs to the field of medical image processing and MRI. The method adopts an end-to-end joint optimization neural network framework to realize magnetic resonance image undersampling collection and reconstruction. A sampling mask corresponding to a target acceleration factor is generated by a trained sampling module, undersampling data collection is completed based on the mask, the data is input into a trained XNET reconstruction module, and a reconstructed image is output. The framework includes a sampling module based on implicit neural representation and an XNET reconstruction module driven by a model. The sampling module takes k-space coordinates as input, learns a continuous mapping from coordinates to sampling probability, and generates a binary sampling mask decoupled from k-space resolution. The XNET reconstruction module takes corresponding undersampling data as input, completes image reconstruction through cascaded iterative reconstruction units, solves the problems of inflexible sampling mode, large parameter quantity and insufficient cooperation with the reconstruction algorithm in the prior art, and realizes efficient and high-quality MRI reconstruction.

Description

Technical Field

[0001] This invention belongs to the field of medical image processing and magnetic resonance imaging technology, specifically relating to a method and system for joint optimization of MRI continuous sampling and image reconstruction. Background Technology

[0002] Magnetic resonance imaging (MRI) is an important non-invasive medical imaging technique, but its data acquisition process is time-consuming. Compressed sensing technology accelerates MRI by undersampling k-space data, but its effectiveness is highly dependent on the design of the sampling strategy and reconstruction algorithm.

[0003] Existing joint optimization sampling and reconstruction methods, such as LOUPE and its variants, typically parameterize the sampling mask as a discrete probability grid with the same size as the image resolution. This approach has inherent drawbacks: first, the number of parameters increases linearly with image resolution, leading to high memory and computational costs in high-resolution or 3D imaging; second, the discrete gridded representation cannot explicitly model the spatial dependencies between k-space sampling points, and the generated sampling patterns often lack spatial continuity; finally, this representation is resolution-bound and difficult to transfer to tasks with different scanning parameters. Recent works have attempted to use multilayer perceptrons or convolutional neural networks to learn dense probabilistic maps to capture local structure, but these methods still suffer from huge parameter counts and do not fundamentally solve the problem of representation discreteness. The patent with publication number CN114913262A provides a magnetic resonance imaging method and system that jointly optimizes the sampling mode and reconstruction algorithm. It adopts a hybrid Laplacian probabilistic generative network model and a differentiable binarization model to construct an MRI reconstruction network ADMM-CSNET+. The sampling mode and reconstruction algorithm are optimized through end-to-end training. The optimal sampling probability distribution is generated by combining prior information in k-space. Differentiable forward and backward propagation is provided in the deep network to replace the traditional proximal operator network. It focuses on solving the problems of long scanning time and easy interference of motion artifacts in magnetic resonance imaging, and the insufficient reconstruction accuracy of the deep learning-based sampling mode and reconstruction algorithm joint optimization method under low sampling conditions.

[0004] Therefore, there is an urgent need for a new method that is parameter-efficient, can generate spatially coherent sampling patterns, and can be deeply co-optimized with reconstruction algorithms. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method and system for joint optimization of continuous MRI sampling and image reconstruction. By applying an implicit neural network (INR) to k-space sampling of MRI, a continuous, resolution-independent sampler is constructed. At the same time, it is combined with an XNET reconstructor embedded with an MRI physical model to achieve end-to-end collaborative optimization of sampling and reconstruction. This method takes into account parameter efficiency, spatial coherence, and physical consistency. While maintaining parameter efficiency and spatial continuity, it significantly improves the reconstruction quality of MRI images under high-magnification acceleration.

[0006] To achieve the above objectives, the present invention provides a method for joint optimization of MRI continuous sampling and image reconstruction, comprising the following steps: An end-to-end jointly optimized neural network framework is used to perform undersampling acquisition and reconstruction of magnetic resonance images: a sampling mask corresponding to the target acceleration factor is generated by the trained sampling module, k-space undersampling data is acquired based on the sampling mask, the acquired undersampling k-space data is input into the trained XNET reconstruction module, and the final reconstructed magnetic resonance image is output. The end-to-end jointly optimized neural network framework includes a sampling module based on implicit neural representation and a model-driven XNET reconstruction module. The sampling module takes k-space coordinates as input, learns a continuous mapping from coordinates to sampling probabilities, and generates a binarized sampling mask decoupled from the k-space resolution. The XNET reconstruction module takes the undersampled k-space data corresponding to the sampling mask generated by the sampling module as input and completes magnetic resonance image reconstruction through cascaded iterative reconstruction units.

[0007] Furthermore, the process of the sampling module generating the binarized sampling mask specifically includes the following steps: A two-dimensional coordinate grid with the same size as the target k-space is constructed. After normalizing the coordinates, the position is encoded by a high-frequency sine function to obtain the encoded high-dimensional coordinate features. A lightweight multilayer perceptron is constructed using a sinusoidal activation network (SIREN). The encoded high-dimensional coordinate features are input into the multilayer perceptron, and the sampling probability logit corresponding to each coordinate position is output. The logit is then converted into an initial sampling probability map by a sigmoid function. Based on the target sampling ratio corresponding to the target acceleration factor, the initial sampling probability map is monotonically scaled to obtain the adjusted probability map, so that the mean of the adjusted probability map is consistent with the target sampling ratio. During the training phase, a sampling mask is generated by random binarization with gradient approximation. During the inference phase, a sampling mask that strictly matches the target sampling rate is generated by thresholding deterministic binarization.

[0008] Furthermore, after the coordinates are normalized, position encoding is performed using a high-frequency sine function to obtain the encoded high-dimensional coordinate features, including: Input k-space coordinate grid ,in , H and W are the height and width of the k-space; Normalize the coordinates to the interval [0,1] using the following formula: ; The normalized coordinates are then sinusoidally encoded using the following formula:

[0009] Where L is the encoding dimension, k is the encoding order, and the final output encoded coordinate feature dimension is 2×2L.

[0010] Furthermore, the specific formula for adjusting the sampling rate consistency is as follows: The adjustment formula used for monotonic scaling is:

[0011] in, The mean of the initial probability plot. The size of the k-space data, R is the target sampling ratio, and R is the target acceleration factor. Let (i,j) be the initial sampling probability at coordinate (i,j). This is the adjusted probability plot.

[0012] Furthermore, during the training phase, a sampling mask is generated through random binarization with gradient approximation; during the inference phase, a sampling mask that strictly matches the target sampling rate is generated through thresholded deterministic binarization. Specifically, this includes: During the training phase, a uniformly distributed noise matrix U with the same k-space resolution is generated, and the calculation is performed. Through the binarization operator Generate binary sampling mask The gradient of the binary operator is approximated using dynamic gradient estimation, and the gradient approximation function is:

[0013]

[0014] Among them, control parameters and Updated with annealing in training round e. , , , These are the annealing parameters. Total number of training rounds; During the inference phase, the adjusted probability map is... Sort all elements in descending order, and take the first... The values ​​at each position are used as a threshold. Positions in the probability map that are greater than or equal to the threshold are set to 1, and the rest are set to 0, thus generating the final binarized sampling mask.

[0015] Furthermore, the XNET reconstruction module includes N cascaded reconstruction units. Each reconstruction unit sequentially performs k-space data consistency update Z-update and image domain near-end optimization X-update. The reconstruction process includes: After zero-padding the undersampled k-space data generated by the sampling module, an inverse Fourier transform is performed to obtain the initial image estimate. , as the input to the first reconstruction unit; Image estimates for the current iteration Perform a Fourier transform to obtain the k-space estimate. Combine the undersampled k-space data with the sampling mask, and calculate the updated k-space estimate using the following formula. :

[0016] Where F is the two-dimensional Fast Fourier Transform operator. The sampling mask generated by the sampling module, where y represents the undersampled k-space data. The penalty coefficient is the trainable factor. ` / ` performs element-wise multiplication, and ` / ` performs element-wise division. The updated k-space estimate Perform an inverse Fourier transform, input the transform result into the proximal optimization network ProxNet, and output the image estimate for this iteration. ; The image estimate output from this iteration is input into the next reconstruction unit. After N reconstruction units are used for iterative optimization, the final reconstructed magnetic resonance image is output.

[0017] Furthermore, the ProxNet near-end optimization network consists of four cascaded residual blocks. Each residual block includes a first convolutional layer, a batch normalization layer, a ReLU activation function, a second convolutional layer, and a batch normalization layer. The input of the residual block is directly superimposed on the output of the residual block through a skip connection structure. The convolutional layers all use 3×3 convolutional kernels with a stride of 1, padding of 1, and 64 output channels.

[0018] Furthermore, based on the training dataset, a reconstruction loss function is designed, and the neural network framework is trained in stages using the gradient descent algorithm until the loss function value stabilizes and converges. The trained sampling module and XNET reconstruction module specifically include the following steps: A training dataset is constructed, which consists of multiple fully sampled magnetic resonance images and k-space fully sampled data obtained by Fourier transform of the fully sampled magnetic resonance images; All trainable parameters of the sampling module are frozen, and a random sampling mask is used for fixed training. Only the parameters of the XNET reconstruction module are trained. The training cycle is set to complete the parameter initialization of the reconstruction module. Unfreeze the trainable parameters of the sampling module, and update the parameters of the sampling module and the XNET reconstruction module. Through backpropagation of the reconstruction loss function, achieve end-to-end co-optimization of the sampling strategy and the reconstruction algorithm until the loss function value stabilizes and converges.

[0019] Furthermore, the reconstruction loss function is a weighted sum of L1 norm loss and structural similarity SSIM loss, with a weight ratio of 1:1. The specific formula is as follows:

[0020] in, The image is the reconstructed image output by the XNET reconstruction module, where x is the ground truth value of the fully sampled image. The L1 norm is represented by the SSIM calculation window size of 11×11 and the standard deviation of the Gaussian kernel is 1.5.

[0021] On the other hand, the present invention provides a joint optimization system for MRI continuous sampling and image reconstruction based on implicit neural representation, including an image reconstruction module and a neural network framework construction module; The image reconstruction module is used to perform undersampling acquisition and reconstruction of magnetic resonance images based on the trained sampling module and XNET reconstruction module: the trained sampling module generates a sampling mask corresponding to the target acceleration factor, the k-space undersampling data is acquired based on the sampling mask, the acquired undersampling k-space data is input into the trained XNET reconstruction module, and the final reconstructed magnetic resonance image is output. The neural network framework construction module is used to construct an end-to-end jointly optimized neural network framework, which includes a sampling module based on implicit neural representation and a model-driven XNET reconstruction module. The sampling module takes k-space coordinates as input, learns a continuous mapping from coordinates to sampling probabilities, and generates a binarized sampling mask decoupled from the k-space resolution. The XNET reconstruction module takes the undersampled k-space data corresponding to the sampling mask generated by the sampling module as input and completes magnetic resonance image reconstruction through cascaded iterative reconstruction units.

[0022] Compared with the prior art, the present invention has at least the following beneficial effects: The number of parameters in the sampling module based on implicit neural representation in this invention is completely decoupled from the k-space resolution, which can be directly adapted to imaging at different resolutions such as 256×256 and 320×320, and does not require retraining, making it suitable for high resolution and 3D MRI. The continuous coordinate-probability mapping described in this invention naturally generates a smooth and coherent sampling pattern, effectively preserving the frequency domain correlation in k-space, avoiding the fragmentation problem of discrete masks, and significantly improving the detail fidelity of the reconstructed image. The sampling module based on implicit neural representation designed in this invention contains only a little over one hundred trainable parameters, which is more than 99.9% less than existing discrete methods (millions of parameters), significantly reducing the computational cost of training and inference. Furthermore, the end-to-end joint optimization described in this invention enables the sampling mode to be deeply adapted to the reconstructor, and the reconstruction performance surpasses existing methods across the board at acceleration factors of 4x, 8x, and 10x.

[0023] Furthermore, this invention constructs an end-to-end jointly optimized neural network framework and employs a staged training strategy to simultaneously optimize the trainable parameters of the sampling module and the XNET reconstruction module. The deep collaborative optimization mechanism ensures a match between the sampling strategy and the reconstruction algorithm, enabling the sampling module to generate the sampling pattern most beneficial to the reconstruction module in restoring high-quality images, while the reconstruction module can perform efficient image restoration based on this sampling pattern. Compared to existing methods that independently optimize or simply cascade the sampling and reconstruction modules, the joint optimization method in this embodiment achieves superior image reconstruction quality and a higher acceleration factor. Attached Figure Description

[0024] Figure 1 The overall framework diagram for joint optimization of INR-XNet.

[0025] Figure 2 This is a schematic diagram of an INR-based sampling framework.

[0026] Figure 3 A schematic diagram of reconstructing the network pipeline for XNet.

[0027] Figure 4 Visual comparison of different reconstruction methods on a 4x speedup of a brain magnetic resonance imaging dataset.

[0028] Figure 5 This is a visual comparison of joint sampling and reconstruction. Detailed Implementation

[0029] In traditional compressed sensing acceleration techniques for magnetic resonance imaging, the joint optimization of sampling and reconstruction methods uses discrete probabilistic grids to represent sampling masks. This representation results in a linear relationship between the number of parameters and the image resolution, which increases memory usage and computational complexity in high-resolution or 3D imaging scenarios. At the same time, discrete grids cannot model the spatial dependencies between k-space sampling points, resulting in a lack of spatial continuity in the generated sampling patterns. Furthermore, this representation is bound to a specific resolution, making it difficult to adapt to the task requirements of different scanning parameters. The increase in the number of parameters directly restricts the system's deployment capability in resource-constrained environments, and the lack of spatial dependencies further leads to discontinuous sampling point distribution, affecting the stability of the reconstruction process.

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. 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.

[0031] Example 1 This embodiment provides a joint optimization method for magnetic resonance imaging (MRI) based on an end-to-end deep learning system. For example... Figure 1 As shown, it includes two modules that work together: the implicit neural sampler (INR sampler) on the left and the model-driven reconstruction network (XNet reconstructor) on the right.

[0032] At the input end of the data stream, unlike traditional methods that directly process image pixels, this invention first constructs a two-dimensional coordinate grid with the same size as the target k-space as the initial input. The INR sampler learns and generates a continuous sampling probability distribution based on the input coordinates, which is then converted into a binary sampling mask. This sampling mask is multiplied by the fully sampled k-space data to simulate the undersampling process, generating undersampled k-space data. The XNet reconstructor receives the undersampled data and the corresponding mask, and outputs the final reconstructed image through a combination of physical constraints and deep learning. Existing discrete gridded representations cannot explicitly model the spatial dependencies between k-space sampling points, and the generated sampling patterns often lack spatial continuity. The sampling module in this embodiment, by learning continuous mappings, can generate more spatially coherent sampling patterns, which helps improve the intrinsic structural integrity of the undersampled data and is beneficial for subsequent image reconstruction.

[0033] Implicit neural representation is a method that uses neural networks to represent continuous signals or data. The neural network takes coordinates as input and outputs the signal value corresponding to those coordinates. Unlike traditional discrete grid representations, implicit neural representations can learn and represent complex continuous functions in a parametrically efficient manner, thus achieving decoupling from resolution.

[0034] Continuous MRI sampling refers to determining the sampling mode in the k-space (frequency domain) by learning a continuous mapping function during the magnetic resonance imaging data acquisition process, rather than being limited to preset discrete sampling points or grids. Continuity makes the sampling strategy more flexible and precise, adapting to different imaging needs and acceleration factors.

[0035] Joint optimization of image reconstruction refers to the deep integration of undersampling data acquisition strategy of magnetic resonance image with image reconstruction algorithm, and synchronous training and optimization under a unified end-to-end framework. Through joint optimization, the sampling module can learn to generate the sampling mode that is most conducive to the reconstruction module to recover high-quality images, while the reconstruction module can perform efficient image recovery based on the sampling mode, thus achieving synergistic effect between sampling and reconstruction.

[0036] k-space is the frequency domain in which the raw data in magnetic resonance imaging (MRI) resides. During an MRI scan, radiofrequency signals are acquired and converted into data points in k-space, representing information about the image at different spatial frequencies. By performing an inverse Fourier transform on the k-space data, the final MRI image can be obtained.

[0037] The sampling module is a component of the neural network framework. Its main function is to learn and generate a sampling mask based on the input k-space coordinates, indicating which k-space data points need to be sampled. A continuous mapping from coordinates to sampling probabilities is achieved through implicit neural representations.

[0038] The XNET reconstruction module reconstructs high-quality magnetic resonance images from the undersampled k-space data corresponding to the sampling mask generated by the sampling module. This module typically employs a model-driven iterative reconstruction architecture, progressively optimizing image estimates through cascaded reconstruction units.

[0039] The binarized sampling mask is a matrix of 0s and 1s, the size of which corresponds to the k-space data. Elements with a value of 1 indicate that data at that k-space location will be collected, while elements with a value of 0 indicate that data at that location will not be collected.

[0040] Gradient descent is a commonly used optimization algorithm used to minimize an objective function. In neural network training, it calculates the gradient of the loss function with respect to the model parameters and updates the parameters in the opposite direction of the gradient, thereby gradually reducing the value of the loss function and bringing the model performance to its optimal level.

[0041] like Figure 1 As shown by the dashed arrows, during training, the error (Loss) between the reconstructed image and the original image is not only used to update the parameters of the XNet reconstructor, but also passes through the binarization operation via the backpropagation algorithm to update the parameters of the front-end INR sampler. This mechanism enables the INR sampler to be aware of the performance of the XNet reconstructor and thus adaptively adjust the sampling strategy.

[0042] Traditional discrete representations are resolution-bound, making them difficult to transfer to tasks with different scanning parameters. The implicit neural representation in this embodiment, due to its resolution-decoupled nature, allows the trained sampling module to more easily adapt to tasks with different k-space sizes or acceleration factors, exhibiting stronger generalization and transferability.

[0043] Example 2 This invention abandons the traditional pixel-wise discrete parameter optimization method and innovatively uses Implicit Neural Representation (INR) to generate the sampling mask. The construction of the INR sampler (sampling module) follows a "pipeline" of coordinate encoding → probability generation → scaling → differentiable binarization, referencing... Figure 2 This paper describes a method for encoding k-space coordinates. By normalizing the input k-space coordinates, the influence of different k-space sizes is eliminated. A high-frequency sine function is used for position encoding, transforming low-dimensional coordinate information into high-dimensional features rich in high-frequency details. This allows subsequent networks to capture fine structural information in k-space. The encoded high-dimensional coordinate features are then input into a lightweight multilayer perceptron constructed using the SIREN sinusoidal activation network. The SIREN network, with its unique sinusoidal activation function, learns a continuous mapping from k-space coordinates to sampling probabilities, outputting the sampling probability logit corresponding to each coordinate position. This logit is then converted into an initial sampling probability map using a sigmoid function. This continuous mapping avoids the limitations of traditional discrete sampling modes. Furthermore, this application introduces a sampling rate consistency adjustment mechanism. Based on the target sampling ratio corresponding to the target acceleration factor, the initial sampling probability map is monotonically scaled, ensuring that the mean of the adjusted probability map is strictly consistent with the target sampling ratio. To achieve end-to-end optimization during the training phase and ensure strict binarization of the sampling mask during the inference phase, this application employs differentiable binarization. During training, a random binarization method with gradient approximation is used to generate the sampling mask, enabling backpropagation of the gradient of the binarization operation and thus optimizing the parameters of the sampling module. During the inference phase, a deterministic thresholding binarization method is used to generate a binarized sampling mask that strictly matches the target sampling rate, ensuring the accuracy and controllability of the actual acquisition.

[0044] The specific implementation steps include: S11, Coordinate Normalization and Encoding S111, Input: k-space coordinate grid ,in , , For k-space resolution; S112, Normalization: Maps the coordinates to the [0,1] interval, the formula is as follows: This eliminates the impact of resolution differences on sampling.

[0045] S113, Sine Position Encoding: Employs a high-frequency sine function to enhance spatial awareness of coordinates. The encoding formula is as follows:

[0046] in, (Encoding dimension), k ranges from 0 to 127, and the final output encoded coordinate dimension is 2×2L=512 dimensions, with 256 real parts and 256 imaginary parts.

[0047] S12, SIREN network probability generation The SIREN network consists of a 4-layer lightweight MLP (Multilayer Perceptron, MLP), with an input dimension of 512 and an output dimension of 1 (sampling probability logit). The logit output by the SIREN network is converted into sampling probabilities using a sigmoid function, as shown in the formula: The initial probability map is obtained. The total number of trainable parameters is 121, which is 99.9% more efficient than the discrete method.

[0048] S13, Sampling Rate Consistency Adjustment Based on the target sampling ratio , As an acceleration factor, for the initial sampling probability map Monotonic scaling is performed to obtain the adjusted probability map. The adjustment formula for monotonic scaling is:

[0049] in, The mean of the initial probability plot. The size of the k-space data.

[0050] S14. Differentiable binarization is divided into training and inference stages.

[0051] The training phase includes: S141, Generate a uniformly distributed noise matrix with the same spatial resolution as k-space. ; S142, Calculation Through the binarization operator Generate a binary mask. Output 1 if the condition is met, otherwise output 0. S143 uses Dynamic Gradient Estimation (DGE) to solve the problem of non-differentiability of the binarization operator. The gradient approximation function is:

[0052]

[0053] Among the control parameters and With training rounds Annealing, the formula is:

[0054] set up Total training rounds The first 50 rounds It gradually increased from 0.1 to 5, and then to 10 in the next 150 rounds. Adjust in sync.

[0055] The reasoning stage includes: S144, Adjusted probability map Sort all elements in descending order, and take the first... The values ​​at each position are used as the threshold; S145, set the positions in the probability graph that are greater than or equal to the threshold to 1 (indicating sampling), and set the remaining positions to 0 (indicating no sampling), to ensure that the sampling ratio strictly matches the target acceleration factor, with an error ≤0.5%.

[0056] The specific process of generating a binarized sampling mask through the sampling module overcomes the limitations of traditional sampling strategies in terms of continuity, differentiability, and precise control of the sampling rate. Coordinate normalization and sinusoidal position encoding enable the sampling module to process k-space data of different sizes and effectively capture high-frequency information, providing a foundation for generating high-quality sampling patterns. Continuous probability mapping generation utilizes the SIREN network to achieve a smooth and fine mapping from coordinates to sampling probabilities, avoiding the rigidity of discrete sampling patterns and making the sampling strategy more flexible and expressive. Sampling rate consistency adjustment ensures that the generated sampling mask strictly conforms to the preset undersampling rate, guaranteeing precise control of magnetic resonance image acquisition efficiency. Differentiable binarization processing allows the entire sampling mask generation process to be integrated into an end-to-end training framework, optimized through gradient descent algorithms, thereby collaboratively learning the optimal sampling strategy and reconstruction parameters with the XNET reconstruction module.

[0057] Example 3 The XNET reconstructor employs a model-driven unconvolutional architecture, comprising 10 cascaded reconstruction units. Each unit alternately performs k-space data consistency updates and image domain proximal optimization. Figure 3 Specifically, it includes: S21, Input initialization includes: Input data, undersampled k-space data generated by the INR sampler and the corresponding sampling mask , This represents a 2D Fast Fourier Transform; Initial image estimation, for undersampled k-space data Zero-padding is performed, filling unsampled locations with 0s, and then an Inverse Fast Fourier Transform (IFFT) is executed to obtain the initial image estimate. , as the input for the 0th iteration.

[0058] S22, Single Reconstruction Unit Execution Flow Each reconstruction unit comprises two core steps: Z-update (k-space data consistency update) and X-update (image domain proximal optimization), specifically including: (1) k-space data consistency update (Z-update) Input parameter: Image estimate for the current iteration Undersampled k-space data Sampling mask Penalty coefficient Penalty coefficient It is trainable, with an initial value set to 1.0.

[0059] Calculation process: 1) Estimated value of the current image Perform a Fast Fourier Transform to obtain the corresponding k-space estimate. ; 2) Calculate the (n+1)th k-space estimate using the following formula. By integrating measurement data with estimated values, data consistency can be ensured.

[0060] in, " / " indicates element-wise multiplication, and " / " indicates element-wise division. The sampling position ( When the sampled location is not sampled, the result is a weighted average of the measured data and the estimated value; at unsampled locations ( When ), the result is directly the k-space estimate of the current image.

[0061] 3) Image domain near-end optimization (X-update, ProxNet) Input data: the (n+1)th k-space estimate The result after inverse fast Fourier transform Regularization parameters (Trainable, initial value set to 0.01).

[0062] The ProxNet network structure consists of four cascaded residual blocks. The internal structure of each residual block is Conv-BN-ReLU-Conv-BN, with the following specific parameters: 1) The convolutional layer uses a 3×3 kernel with a stride of 1, padding of 1, and 64 output channels; 2) The BN layer is a batch normalization layer with a momentum of 0.9 and a weight decay coefficient of 1e-5. 3) The activation function is the ReLU function; 4) The skip connection design uses additive skip connection, which directly superimposes the input of the residual block onto the output to avoid gradient vanishing.

[0063] The output is the image estimate for the (n+1)th iteration. .

[0064] S23, Multi-stage Iterative Optimization (1) Iterative configuration: 10 reconstruction units are cascaded in sequence (Stage 1 to Stage 10). The first 5 units focus on correcting data consistency, and the last 5 units focus on restoring image details.

[0065] (2) Parameter settings: All reconstruction units share globally trainable parameters. and ProxNet does not share weights between layers, and each residual block is trained independently to adapt to the image restoration needs of different iteration stages.

[0066] In this context, N cascaded reconstruction units refer to multiple computational modules with identical or similar structures connected sequentially. The output of one module serves as the input of the next. The cascaded structure allows information to be processed step-by-step at different stages, enabling complex nonlinear mapping and feature extraction. In the field of image reconstruction, cascaded units are often used to simulate iterative optimization processes, with each unit performing one iteration to progressively improve image quality.

[0067] Z-update, or k-space data consistency update, is an operation that forces the reconstruction result to remain consistent with the actually acquired undersampled data in the k-space (frequency domain). Its purpose is to ensure that the reconstructed image does not deviate from the original measurement value in the sampled k-space region. X-update, or image domain near-end optimization, refers to regularizing or denoising the current image estimate in the image domain (spatial domain) to eliminate artifacts, improve image smoothness, or restore image details. It utilizes prior knowledge of the image (such as sparsity and local smoothness) to constrain the reconstruction process and compensate for the information loss caused by undersampling.

[0068] The XNET reconstruction module employs N cascaded reconstruction units. Within each unit, k-space data consistency updates and image domain proximal optimization are performed alternately, constructing a sophisticated iterative reconstruction framework. Starting from an initial image estimate, it gradually eliminates artifacts caused by undersampling and restores the image's fine structure and details through multiple rounds of correction and optimization. k-space data consistency updates ensure a high degree of consistency between the reconstruction results and the actual acquired data, avoiding data distortion. Meanwhile, image domain proximal optimization utilizes the powerful representational capabilities of neural networks to effectively denoise and regularize the image, compensating for information loss caused by undersampling. This reconstruction strategy, combining traditional iterative thinking with the advantages of deep learning, significantly improves the reconstruction quality and robustness of magnetic resonance images under highly undersampling conditions, resulting in reconstructed images with fewer artifacts, sharper edges, and richer details.

[0069] Example 4 The core of joint training is to collaboratively optimize the INR sampler parameters through backpropagation of the reconstruction loss. and XNET Reconstructor Parameters This forms a closed loop of sampling-reconstruction-loss feedback-parameter update (corresponding to the appendix). Figure 1 The specific steps are as follows: S31, Training Data Loading and Augmentation Batch loading: Set the batch size to 4, randomly select 4 fully sampled images from the training set each time, and convert them into k-space data through Fast Fourier Transform. .

[0070] Data augmentation: Gaussian noise (standard deviation of 0.01) is added to the k-space data during the training phase to simulate the noise interference of clinical MRI equipment and improve the robustness of the model; at the same time, the k-space data is randomly flipped (horizontally or vertically) to expand the distribution range of the training data.

[0071] S32, Forward Propagation Process Sampling process: Input the k-space coordinates into the INR sampler to generate a binary mask. Undersampling is performed on the k-space data \(k\) to obtain undersampled data. ; Reconstruction process: Reconstructing undersampled data and sampling mask The XNET reconstructor is input, and after iterative optimization using 10 reconstruction units, the output is a reconstructed image. ; Loss calculation: using The weighted sum of the loss and the SSIM loss is used as the reconstruction loss, with a weight ratio of 1:1. The calculation formula is as follows:

[0072] in For the true value of the fully sampled image, express The norm, the window size for SSIM calculation is set to 11×11, and the standard deviation is 1.5.

[0073] S33, Backpropagation and Parameter Update Optimizer configuration: The Adam optimizer is selected, the initial learning rate is set to 1e-4, and the weight decay coefficient is set to 1e-6.

[0074] Learning rate scheduling: A cosine annealing learning rate scheduling strategy is adopted, in which the learning rate is halved every 50 rounds, and the minimum learning rate is reduced to 1e-6.

[0075] Gradient handling: Prune the gradient norm of all trainable parameters by setting max_norm=1.0 to avoid gradient explosion.

[0076] Training phase division: The total number of training rounds is 200. The first 50 rounds are the warm-up phase, in which only the parameters of the XNET reconstructor are updated and the parameters of the INR sampler are frozen. The last 150 rounds are the joint optimization phase, in which the parameters of the INR sampler and the XNET reconstructor are updated at the same time to ensure that the two are adapted together.

[0077] S34, Model Validation and Storage Validation frequency: The model performance is evaluated on the validation set every 10 rounds, and three metrics are calculated: PSNR (Peak Signal-to-Noise Ratio), SSIM (Structural Similarity), and NRMSE (Normalized Root Mean Square Error).

[0078] Model saving: Saves the optimal model weights (including INR sampler parameters) on the validation set. and XNET Reconstructor Parameters The training process is recorded in the format of a PyTorch .pth file, along with the loss curve and validation metric change curve during the training process, for subsequent analysis.

[0079] Through the aforementioned technical solution, the near-end optimization network ProxNet is designed to consist of four cascaded residual blocks. Each residual block contains a specific convolutional layer, a batch normalization layer, and a ReLU activation function, supplemented by a skip-connection structure. Simultaneously, the convolutional kernel parameters are standardized, effectively addressing the problems of insufficient learning ability, training instability, and limited detail recovery in traditional near-end optimization networks when dealing with artifacts in complex magnetic resonance image reconstruction. The introduction of residual blocks and their skip-connection structure significantly enhances the network's depth and learning ability, alleviating the gradient vanishing problem in deep network training, enabling ProxNet to stably learn finer image features and more robust denoising mappings. Specific convolutional kernel size, stride, and padding settings ensure that spatial details of the image are fully preserved during multi-level feature extraction, while the output channel count ensures that the network has sufficient capacity to represent and process complex image information.

[0080] Furthermore, this application addresses the instability and convergence difficulties that may arise from direct end-to-end joint optimization by dividing the training process of the neural network framework into two stages. In the warm-up training stage, by freezing the parameters of the sampling module and fixing the use of a random sampling mask, the XNET reconstruction module can focus on learning the basic ability to reconstruct images from undersampled k-space data under relatively stable input conditions. The reconstruction module parameters are initially and effectively initialized, thus avoiding the negative impact on sampling strategy optimization due to insufficient reconstruction capability in the early stages of training. In the joint optimization stage, the parameters of the sampling module are unfrozen and updated synchronously with those of the XNET reconstruction module. At this point, since the XNET reconstruction module already possesses a certain reconstruction capability, the sampling module can more effectively receive the backpropagation signal from the reconstruction loss function. Based on the actual performance of the reconstruction module, the sampling module can learn to generate a sampling mask that is more conducive to high-quality image reconstruction. This staged training strategy allows the two modules to mutually promote each other, evolving together towards the goal of minimizing reconstruction error, ultimately achieving end-to-end co-optimization of the sampling strategy and reconstruction algorithm, thereby obtaining better MRI image reconstruction results.

[0081] Furthermore, employing a weighted sum of L1 norm loss and structural similarity-based (SSIM) loss as the reconstruction loss function, with a 1:1 weight ratio, effectively addresses the limitations of a single loss function in MRI image reconstruction. L1 norm loss ensures the numerical accuracy of the reconstructed image at the pixel level, helping to reduce reconstruction errors and maintain image clarity; while SSIM loss, from the perspective of human visual perception, optimizes the structure, brightness, and contrast of the reconstructed image, avoiding image blurring or loss of detail that may result from traditional pixel-level losses. This combination allows the model to simultaneously consider the objective accuracy and subjective visual quality of the reconstructed image during training, thereby generating more usable and reliable MRI images for medical diagnosis.

[0082] Example 5 To verify the superiority of the technical solution, two types of experiments were designed, referencing... Figure 4 and Figure 5 The specific implementation steps include: 1. Reconstructor performance verification experiment, refer to Figure 4 .

[0083] The purpose of this experiment is to verify the reconstruction performance of the XNET reconstructor alone, excluding the influence of the sampling module. The experiment is designed with a fixed random sampling mask (one mask for each speedup factor, shared by all comparison methods) to compare the performance of XNET with reconstruction methods such as ADMMCS-Net, MD-Rec-Net, MoDL, and SwinIR.

[0084] The implementation steps for the reconstructor performance verification experiment include: 1) Generate a fixed random mask: Generate a random binary mask according to the target sampling ratio (alpha) to ensure uniform spatial distribution of the mask; 2) Model training: All comparison methods are trained on the same training set. XNET is set according to the parameters mentioned above, and other methods are configured according to the parameters in their original literature. 3) Performance Evaluation: Calculate PSNR, SSIM, and NRMSE for each method on the test set, and plot a visual comparison chart of the reconstructed images for reference. Figure 4 It places images of fine structural areas such as cerebral sulci and gyri to visually demonstrate the ability to recover details; at the same time, it calculates the inference delay of each method to evaluate its real-time performance.

[0085] 2. Joint framework performance verification experiments, refer to Figure 5 .

[0086] The objective of this experiment is to verify the overall performance of the joint optimization framework of INR sampler and XNET reconstructor. The experimental design compares INR-XNET with mainstream joint optimization methods such as LOUPE, PUERT, and SeqMRI, covering three acceleration factors: 4×, 8×, and 10×.

[0087] The implementation steps for the joint framework performance verification experiment include: 1) Model training: All methods are trained end-to-end on the same dataset, with 200 training rounds for each method. Other training parameters are set to their original configurations. 2) Performance Evaluation: Calculate quantitative metrics (PSNR, SSIM, NRMSE) on the test set, plot the reconstructed image and error map, and refer to... Figure 5 The error map uses grayscale mapping, with higher brightness indicating greater error; it also displays the sampling masks of each method under a 4× speedup factor to compare the spatial coherence of the sampling patterns. 3) Efficiency evaluation: The training time (time spent in a single round of training) and the total number of model parameters of each method are statistically analyzed to verify the parameter efficiency advantage of INR-XNET.

[0088] Based on the technical concepts of embodiments 1-4 above, the present invention provides a joint optimization system for MRI continuous sampling and image reconstruction, including an image reconstruction module and a neural network framework construction module; The image reconstruction module is used to perform undersampling acquisition and reconstruction of magnetic resonance images based on the trained sampling module and XNET reconstruction module: the trained sampling module generates a sampling mask corresponding to the target acceleration factor, the k-space undersampling data is acquired based on the sampling mask, the acquired undersampling k-space data is input into the trained XNET reconstruction module, and the final reconstructed magnetic resonance image is output. The neural network framework construction module is used to construct an end-to-end jointly optimized neural network framework, which includes a sampling module based on implicit neural representation and a model-driven XNET reconstruction module. The sampling module takes k-space coordinates as input, learns a continuous mapping from coordinates to sampling probabilities, and generates a binarized sampling mask decoupled from the k-space resolution. The XNET reconstruction module takes the undersampled k-space data corresponding to the sampling mask generated by the sampling module as input and completes magnetic resonance image reconstruction through cascaded iterative reconstruction units.

[0089] The sampling module includes a coordinate encoding unit, a continuous probability mapping unit, a sampling rate adjustment unit, and a binarization unit; The coordinate encoding unit is used to input k-space coordinate grids ,in , H and W are the height and width of the k-space; the coordinates are normalized to the interval [0,1], and the normalization formula is: ; The normalized coordinates are then sinusoidally encoded using the following formula:

[0090] Where L is the encoding dimension, k is the encoding order, and the final output encoded coordinate feature dimension is 2×2L.

[0091] The continuous probability mapping unit can employ a sinusoidal activation network (SIREN) consisting of four hidden layers, each containing 256 neurons, and using a sinusoidal activation function. This network takes the encoded high-dimensional coordinate features as input, outputs the sampling probability logit corresponding to each coordinate position, and converts it into an initial sampling probability map using a sigmoid function.

[0092] The sampling rate adjustment unit adjusts the sampling rate according to the target sampling ratio. , As an acceleration factor, for the initial sampling probability map Monotonic scaling is performed to obtain the adjusted probability map. The adjustment formula for monotonic scaling is:

[0093] in, The mean of the initial probability plot. The size of the k-space data.

[0094] The binarization unit generates a uniformly distributed noise matrix U with the same k-space resolution during the training phase, and calculates... Through the binarization operator Generate binary sampling mask The gradient of the binary operator is approximated using dynamic gradient estimation, and the gradient approximation function is:

[0095]

[0096] Among them, control parameters and Updated with annealing in training round e. , , , These are the annealing parameters. Total number of training rounds; During the inference phase, the adjusted probability map is... Sort all elements in descending order, and take the first... The values ​​at each position are used as a threshold. Positions in the probability map that are greater than or equal to the threshold are set to 1, and the rest are set to 0, thus generating the final binarized sampling mask.

[0097] The XNET reconstruction module includes N cascaded reconstruction units, each of which includes a k-space update subunit and an image domain optimization subunit. The k-space update subunit is used to perform a Fourier transform on the image estimate of the current iteration to obtain the k-space estimate, combine the undersampled k-space data with the sampling mask to complete the data consistency update, and output the updated k-space estimate. The image domain optimization subunit incorporates a ProxNet network for performing inverse Fourier transform on the updated k-space estimate, thereby completing the proximal optimization of the image domain and outputting the image estimate for this iteration.

[0098] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for joint optimization of MRI continuous sampling and image reconstruction, characterized in that, Includes the following steps: An end-to-end jointly optimized neural network framework is used to perform undersampling acquisition and reconstruction of magnetic resonance images: a sampling mask corresponding to the target acceleration factor is generated by the trained sampling module, k-space undersampling data is acquired based on the sampling mask, the acquired undersampling k-space data is input into the trained XNET reconstruction module, and the final reconstructed magnetic resonance image is output. The end-to-end jointly optimized neural network framework includes a sampling module based on implicit neural representation and a model-driven XNET reconstruction module. The sampling module takes k-space coordinates as input, learns a continuous mapping from coordinates to sampling probabilities, and generates a binarized sampling mask decoupled from the k-space resolution. The XNET reconstruction module takes the undersampled k-space data corresponding to the sampling mask generated by the sampling module as input and completes magnetic resonance image reconstruction through cascaded iterative reconstruction units.

2. The MRI continuous sampling and image reconstruction joint optimization method according to claim 1, characterized in that, The process of generating a binary sampling mask by the sampling module specifically includes the following steps: A two-dimensional coordinate grid with the same size as the target k-space is constructed. After normalizing the coordinates, the position is encoded by a high-frequency sine function to obtain the encoded high-dimensional coordinate features. A lightweight multilayer perceptron is constructed using a sinusoidal activation network (SIREN). The encoded high-dimensional coordinate features are input into the multilayer perceptron, and the sampling probability logit corresponding to each coordinate position is output. The logit is then converted into an initial sampling probability map by a sigmoid function. Based on the target sampling ratio corresponding to the target acceleration factor, the initial sampling probability map is monotonically scaled to obtain the adjusted probability map, so that the mean of the adjusted probability map is consistent with the target sampling ratio. During the training phase, a sampling mask is generated by random binarization with gradient approximation. During the inference phase, a sampling mask that strictly matches the target sampling rate is generated by thresholding deterministic binarization.

3. The MRI continuous sampling and image reconstruction joint optimization method according to claim 2, characterized in that, After coordinate normalization, position encoding is performed using a high-frequency sine function to obtain the encoded high-dimensional coordinate features, including: Input k-space coordinate grid ,in , H and W are the height and width of the k-space; Normalize the coordinates to the interval [0,1] using the following formula: ; The normalized coordinates are then sinusoidally encoded using the following formula: Where L is the encoding dimension, k is the encoding order, and the final output encoded coordinate feature dimension is 2×2L.

4. The MRI continuous sampling and image reconstruction joint optimization method according to claim 2, characterized in that, The specific formula for adjusting the sampling rate consistency is as follows: The adjustment formula used for monotonic scaling is: in, The mean of the initial probability plot. The size of the k-space data, R is the target sampling ratio, and R is the target acceleration factor. Let (i,j) be the initial sampling probability at coordinate (i,j). This is the adjusted probability plot.

5. The MRI continuous sampling and image reconstruction joint optimization method according to claim 2, characterized in that, During the training phase, a sampling mask is generated through random binarization with gradient approximation. During the inference phase, a sampling mask that strictly matches the target sampling rate is generated through thresholded deterministic binarization. Specifically, this includes: During the training phase, a uniformly distributed noise matrix U with the same k-space resolution is generated, and the calculation is performed. Through the binarization operator Generate binary sampling mask The gradient of the binary operator is approximated using dynamic gradient estimation, and the gradient approximation function is: Among them, control parameters and Updated with annealing in training round e. , , , These are the annealing parameters. Total number of training rounds; During the inference phase, the adjusted probability map is... Sort all elements in descending order, and take the first... The values ​​at each position are used as a threshold. Positions in the probability map that are greater than or equal to the threshold are set to 1, and the rest are set to 0, thus generating the final binarized sampling mask.

6. The MRI continuous sampling and image reconstruction joint optimization method according to claim 1, characterized in that, The XNET reconstruction module comprises N cascaded reconstruction units. Each reconstruction unit sequentially performs k-space data consistency update Z-update and image domain near-end optimization X-update. The reconstruction process includes: After zero-padding the undersampled k-space data generated by the sampling module, an inverse Fourier transform is performed to obtain the initial image estimate. , as the input to the first reconstruction unit; Image estimates for the current iteration Perform a Fourier transform to obtain the k-space estimate. Combine the undersampled k-space data with the sampling mask, and calculate the updated k-space estimate using the following formula. : Where F is the two-dimensional Fast Fourier Transform operator. The sampling mask generated by the sampling module, where y represents the undersampled k-space data. The penalty coefficient is the trainable factor. ` / ` performs element-wise multiplication, and ` / ` performs element-wise division. The updated k-space estimate Perform an inverse Fourier transform, input the transform result into the proximal optimization network ProxNet, and output the image estimate for this iteration. ; The image estimate output from this iteration is input into the next reconstruction unit. After N reconstruction units are used for iterative optimization, the final reconstructed magnetic resonance image is output.

7. The MRI continuous sampling and image reconstruction joint optimization method according to claim 6, characterized in that, The ProxNet near-end optimization network consists of four cascaded residual blocks. Each residual block includes a first convolutional layer, a batch normalization layer, a ReLU activation function, a second convolutional layer, and a batch normalization layer. The input of the residual block is directly superimposed on the output of the residual block through a skip connection structure. The convolutional layers all use 3×3 convolutional kernels with a stride of 1, padding of 1, and 64 output channels.

8. The MRI continuous sampling and image reconstruction joint optimization method according to claim 1, characterized in that, Based on the training dataset, a reconstruction loss function is designed, and the neural network framework is trained in stages using the gradient descent algorithm until the loss function value stabilizes and converges. The trained sampling module and XNET reconstruction module specifically include the following steps: A training dataset is constructed, which consists of multiple fully sampled magnetic resonance images and k-space fully sampled data obtained by Fourier transform of the fully sampled magnetic resonance images; All trainable parameters of the sampling module are frozen, and a random sampling mask is used for fixed training. Only the parameters of the XNET reconstruction module are trained. The training cycle is set to complete the parameter initialization of the reconstruction module. Unfreeze the trainable parameters of the sampling module, and update the parameters of the sampling module and the XNET reconstruction module. Through backpropagation of the reconstruction loss function, achieve end-to-end co-optimization of the sampling strategy and the reconstruction algorithm until the loss function value stabilizes and converges.

9. The MRI continuous sampling and image reconstruction joint optimization method according to claim 8, characterized in that, The reconstruction loss function is a weighted sum of L1 norm loss and structural similarity SSIM loss, with a weight ratio of 1:

1. The specific formula is as follows: in, The image is the reconstructed image output by the XNET reconstruction module, where x is the ground truth value of the fully sampled image. The L1 norm is represented by the SSIM calculation window size of 11×11 and the standard deviation of the Gaussian kernel is 1.

5.

10. A joint optimization system for MRI continuous sampling and image reconstruction based on implicit neural representation, characterized in that, Includes an image reconstruction module and a neural network framework construction module; The image reconstruction module is used to perform undersampling acquisition and reconstruction of magnetic resonance images based on the trained sampling module and XNET reconstruction module: the trained sampling module generates a sampling mask corresponding to the target acceleration factor, the k-space undersampling data is acquired based on the sampling mask, the acquired undersampling k-space data is input into the trained XNET reconstruction module, and the final reconstructed magnetic resonance image is output. The neural network framework construction module is used to construct an end-to-end jointly optimized neural network framework, which includes a sampling module based on implicit neural representation and a model-driven XNET reconstruction module. The sampling module takes k-space coordinates as input, learns a continuous mapping from coordinates to sampling probabilities, and generates a binarized sampling mask decoupled from the k-space resolution. The XNET reconstruction module takes the undersampled k-space data corresponding to the sampling mask generated by the sampling module as input and completes magnetic resonance image reconstruction through cascaded iterative reconstruction units.

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