A Low-Dose PET Reconstruction Method Based on a Total Variational Regularized Diffusion Model

Abstract

This invention provides a low-dose PET reconstruction method based on a total variational regularized diffusion model. This method directly uses the low-dose PET image as the initial state for the reverse diffusion process during the inference phase, completely eliminating the injection of Gaussian noise in traditional diffusion models. Furthermore, a total variational denoising module is integrated into the prediction-correction iterative sampling process to constrain the image state, thereby achieving high-quality reconstruction of normal-dose PET images. Theoretically, this invention improves the Poincaré constant through TV regularization to accelerate the convergence of the Langevin dynamics, significantly increasing inference speed while greatly reducing the number of sampling diffusion iterations, and effectively suppressing image noise and artifacts. The proposed method exhibits excellent reconstruction results in various low-dose scenarios, especially under conditions of high noise and easy loss of structural information, significantly improving the average signal-to-noise ratio and structural similarity of the image, and greatly enhancing lesion contrast.

Description

Technical Field

[0001] This invention belongs to the technical field of medical image processing and biomedical imaging, specifically relating to a low-dose PET reconstruction method based on a total variation regularized diffusion model. Background Technology

[0002] PET (Positron Emission Tomography) is an advanced medical functional imaging technique widely used in fields such as tumor detection and diagnosis of neurological diseases. To obtain high-quality PET images for clinical diagnosis, subjects typically need to be injected with a sufficient dose of radioactive tracer, which inevitably introduces potential radiation risks. Therefore, adhering to the ALARA (As Low As Reasonably Achievable) principle to minimize radiation damage is a necessary trend in clinical practice. However, reducing the radiation dose leads to a significant decrease in the signal-to-noise ratio of the images, accompanied by the loss of key clinical structural information, posing a significant challenge to accurate clinical diagnosis and image interpretation.

[0003] Improving the quality of low-dose PET images has always been a core challenge in practical applications. Traditional iterative reconstruction methods typically use statistical models to formulate low-dose reconstruction as a convex optimization problem. However, these methods are not only computationally expensive, but their pre-defined regularization terms often lead to undesirable oversmoothing, artifacts, or texture distortion in the images. In recent years, deep learning-based methods have become dominant in PET image restoration. Although these data-driven models have made some progress, ensuring high prediction accuracy and robustness of the trained networks remains very difficult. When dealing with highly degraded images, existing networks often produce oversmoothing effects, resulting in loss of structural details and reduced lesion contrast.

[0004] In recent years, diffusion models, as an emerging generative model, have demonstrated powerful distribution mapping capabilities in the field of medical image processing. By simulating the continuous process of forward noise injection and smoothing the transformation of data distribution, combined with inverse denoising, diffusion models can effectively recover high-quality, realistic images. However, traditional diffusion models typically require extremely large iterative sampling steps, often hundreds or even thousands, to complete the mapping of image distribution. This dependence on intensive computing resources leads to extremely long inference times, severely limiting their application in real-time clinical imaging and actual medical procedures.

[0005] In summary, existing low-dose PET image reconstruction techniques suffer from several problems. Traditional deep learning methods are prone to excessive image smoothing and loss of key clinical details. Furthermore, traditional diffusion models suffer from high computational costs and extremely long inference times due to their reliance on numerous iterative sampling steps during the inference phase. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a low-dose PET reconstruction method based on a total variational regularized diffusion model. This method fundamentally innovates in the inference stage by directly using low-dose PET data as initial input, completely eliminating the step of injecting Gaussian noise required in traditional diffusion models. By integrating a TV noise reduction module during iterative sampling, this invention theoretically improves the Poincaré constant of the data, thereby accelerating the convergence of the Langevin dynamics. This innovative image processing method, while significantly reducing the required number of sampling iterations, not only effectively suppresses noise but also significantly enhances key clinical details in low-dose PET images, thus providing a clinically feasible solution for low-dose PET imaging technology that balances high quality and computational efficiency.

[0007] In a first aspect, the present invention provides the following technical solution: a low-dose PET reconstruction method based on a total variational regularized diffusion model, comprising: Fully sampled normal dose PET images are acquired, Gaussian noise is injected through a forward stochastic differential equation, and a fraction-based diffusion model is obtained through denoised fractional matching training. The low-dose PET image to be reconstructed is obtained, and the low-dose PET image is directly used as the initial state for back diffusion. No additional Gaussian noise is injected into the low-dose PET image at the corresponding starting point. The reverse diffusion process is simulated by iterating the image state using the fraction-based diffusion model and the prediction-correction sampler. A total variation minimization operation is applied to the image state during the reverse diffusion process until the preset number of iterations is reached, and the reconstructed PET image is output.

[0008] Compared with the prior art, the beneficial effects of the present invention are as follows: Significantly improves computational efficiency in image processing: This invention completely eliminates the cumbersome step of injecting additional Gaussian noise into the input data in traditional diffusion models by directly using low-dose PET images as the initial state for backdiffusion during the inference stage. This greatly shortens the backdiffusion trajectory. Combined with the TV regularization module, the model requires only a very small number of sampling iterations (only 25 steps) to complete high-quality reconstruction, processing a single PET slice in only about 1 second. This completely breaks through the computational bottleneck of traditional diffusion models, which are time-consuming to infer and cannot meet the needs of real-time clinical applications. A theoretically supported accelerated convergence mechanism: This invention integrates the TV minimization operation depth into the iterative sampling of PC, and uses the TV prior as a strict mathematical constraint to significantly improve the Poincaré constant of the target data distribution from a theoretical perspective. This optimization of the underlying energy landscape ensures that Langevin dynamics can achieve a faster convergence speed in the back sampling process. Excellent denoising and artifact suppression: By continuously introducing the TV denoising module in the iterative loop of the predictor and corrector, this method can effectively suppress statistical noise and stripe artifacts common in low-dose PET imaging while greatly reducing the number of iterations. It performs particularly well in high-noise environments, significantly improving the average signal-to-noise ratio and structural similarity of the reconstructed image and reducing the normalized root mean square error.

[0009] Precise preservation of structural details and high lesion contrast: The conditional constraint mechanism of this invention effectively balances the data fidelity term and the TV prior term, successfully overcoming the problems of excessive image smoothing and texture distortion that are easily caused by traditional deep learning denoising methods. While effectively reducing noise, this method can sharply preserve the boundaries of complex anatomical structures and significantly improve the contrast of lesion areas, providing a more accurate diagnostic basis for clinical tumor detection and quantitative analysis.

[0010] Strong robustness and cross-dose generalization ability: Thanks to the powerful gradient distribution learning ability and unsupervised training mechanism of the fractional diffusion model, this invention not only performs well in conventional low-dose scenarios, but also maintains excellent and stable reconstruction performance in the face of more stringent ultra-low-dose conditions and cross-motif validation. This characteristic of not depending on specific degradation modes gives the method strong clinical generalization potential and adaptability.

[0011] Preferably, in the step of injecting Gaussian noise through a forward stochastic differential equation and obtaining a score-based diffusion model through denoising score matching, the forward stochastic differential equation is used to describe the evolution of the image from the original data distribution to the noise distribution, and the forward stochastic differential equation is: ; In the formula, The drift coefficient, Where is the diffusion coefficient. For the smallest positive time step, For Brownian motion, Image status; The objective function for training and optimizing the score-based diffusion model is: ; In the formula, This represents the parameters after network optimization. Represents a positive weighting function. Indicates in The time variable of uniform sampling within the interior, This represents the initial normal dose PET image data. Indicates time Image data after being perturbed by noise, This indicates a score-based diffusion model that needs to be trained. Indicates The Gaussian perturbation kernel centered on the center, For mathematical expectation, It is the square of the L2 norm.

[0012] Preferably, the step of directly using the low-dose PET image as the initial state for back diffusion, and not injecting additional Gaussian noise into the low-dose PET image at the corresponding starting point, specifically involves: Directly utilize the acquired low-dose PET images As the initial state for the reverse diffusion process, its initialization formula is expressed as: ; In the formula, This indicates that the reverse diffusion sampling process starts at point 1. The image state of the step, This is the preset total number of iterations; A noise scheduling strategy is employed to set the final noise parameters for the reverse diffusion process. satisfy This is to ensure that the numerical values ​​of the entire denoising process are stable in the final step and that the denoising capability is maintained.

[0013] Preferably, the simulated reverse diffusion process, which iterates the image state using the fraction-based diffusion model and the prediction-correction sampler, includes: The predictor in the prediction-correction sampler is used as a numerical solver for the inverse stochastic differential equation. The next image state is derived in each outer loop, where the update formula for the outer loop prediction step is: ; In the formula, This is the score function predicted by the score-based diffusion model; Conditional constraints are integrated into the predictor, and the update formula for the outer loop prediction step is further expressed as: ; In the formula, The first , The image state of the step, , The first , Noise scheduling parameters for each step Regarding image state gradient operator, For data fidelity based on low-dose PET images, The regularization term for encoding the TV prior is used; The inner loop performs a corrector on the single prediction result. The Langevin dynamics iteration integrates the conditional constraints of low-dose PET images into the sampling process, making the generated image samples more closely approximate the target posterior distribution. The update formula for the corrector is as follows: ; In the formula, They were respectively in the second Under the outer loop of the nth time step sequence Image state after the second inner loop For the first Step length, The injected random Gaussian perturbation.

[0014] Preferably, in the step of applying a total variation minimization operation to the image state during the back-diffusion process until the preset number of iterations is reached, and then outputting the reconstructed PET image, the total variation minimization operation is integrated into the iterative update process of the prediction-correction sampler, and the regularization objective function of the total variation minimization operation is: ; In the formula, The first , The image state of the step, For low-dose PET images, This is a priori for TV regularization.

[0015] Preferably, in the step of applying a total variation minimization operation to the image state during the reverse diffusion process until the preset number of iterations is reached, and then outputting the reconstructed PET image, the total variation minimization operation satisfies the following: ; In the formula, This is the image state after TV regularization processing. The first , The image state of the step, This is the gradient descent step size. The change in image state. For TV norms about gradient, For gradient operators, It is a 2-norm. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of low-dose PET reconstruction based on a total variational regularized diffusion model in an embodiment of the present invention; Figure 2 This is a schematic diagram of the forward and backward processes of SDE during the training phase in an embodiment of the present invention; Figure 3 These are images showing the results of reconstructing horizontal head images using different methods in embodiments of the present invention. Figure 4 These are images showing the results of reconstructing coronal images using different methods in embodiments of the present invention; Figure 5 These are the results of reconstructing the lateral body image using different methods in embodiments of the present invention; Figure 6 These are images showing the results of reconstructing human body simulation data using different methods in embodiments of the present invention; Figure 7 The results of quarter-dose PET reconstruction using different methods are shown in the embodiments of the present invention.

[0018] The embodiments of the present invention will be further described below with reference to the accompanying drawings. Detailed Implementation

[0019] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0020] Example 1 In Embodiment 1 of the present invention, as Figure 1 As shown, a low-dose PET reconstruction method based on a total variational regularized diffusion model includes: S1. Obtain fully sampled normal dose PET images, inject Gaussian noise through forward stochastic differential equations, and obtain a fraction-based diffusion model through denoised fraction matching training. Specifically, step S1 is the model training process, which involves acquiring fully sampled normal dose PET images, injecting Gaussian noise through a forward stochastic differential equation, and training a score-based diffusion model through denoising score matching. The purpose of this step is to allow the network to fully learn the gradient distribution of the features of normal dose PET images, providing reliable score function guidance for the subsequent reverse denoising process.

[0021] The forward stochastic differential equation is: ; In the formula, The drift coefficient, Where is the diffusion coefficient. For the smallest positive time step, For Brownian motion, Image status; Specifically, in order to construct a prior knowledge model that can guide the recovery of low-dose PET images into normal-dose PET images, it is first necessary to complete the training of a score-based diffusion model. The core of this training process is to use the forward diffusion equation to map the data distribution to the noise distribution and learn the score function of its inverse process through a neural network.

[0022] Acquire fully sampled normal-dose PET image data as the initial state. During the forward diffusion process, through continuous diffusion towards Injecting Gaussian noise gradually destroys the details of the image, eventually transforming it into a priori noise distribution that is easy to sample. This forward continuous-time image degradation process is modeled by the general stochastic differential equation above.

[0023] Furthermore, to more precisely control the variance of noise injection, variance explosion is used to instantiate the above forward process. Under the VE-SDE setting, the drift coefficient is eliminated, and the diffusion coefficient is determined by the derivative of the noise variance, i.e., the following condition is satisfied: , ; in, The noise scaling function is monotonically increasing with time. To reverse the SDE during the inference phase, it is necessary to obtain the gradient of the logarithm of the marginal probability density with respect to the data, i.e., the scoring function. Since the true scoring function is difficult to obtain directly, this embodiment constructs a function with parameters as follows: neural networks To approximate the scoring function; The objective function for training and optimizing the score-based diffusion model is: ; In the formula, This represents the parameters after network optimization. Represents a positive weighting function. Indicates in The time variable of uniform sampling within the interior, This represents the initial normal dose PET image data. Indicates time Image data after being perturbed by noise, This indicates a score-based diffusion model that needs to be trained. Indicates The Gaussian perturbation kernel centered on the center, For mathematical expectation, The square of the L2 norm; Specifically, a loss function is constructed using a denoising score matching strategy, and the network parameters are optimized during training by minimizing the weighted objective function described above. , Specifically, the positive weighting function that changes over time is usually set as follows: To balance the losses at different noise scales; Under the above VE-SDE settings, in the initial state The probability distribution with conditions It is explicitly defined as a Gaussian perturbation transfer kernel: , in, Represents the identity matrix. It follows a Gaussian distribution. Given the time-varying noise variance, based on the properties of this Gaussian distribution, the true gradient of its logarithmic probability can be explicitly and analytically derived as: , By substituting the analytical gradient into the objective function, the neural network can stably learn the gradient field distribution of image features during training through simple mean square error calculation. After completing the model training, it enters the inference and reconstruction stage.

[0024] S2. Obtain the low-dose PET image to be reconstructed, use the low-dose PET image directly as the initial state of the back diffusion, and do not inject additional Gaussian noise into the low-dose PET image at the corresponding starting point. Specifically, step S2 is the initialization step, which acquires the low-dose PET image to be reconstructed. This is directly used as the initial state for reverse time. By not injecting additional Gaussian noise into the low-dose PET image at this starting point, this innovative operation completely eliminates the dependence of traditional diffusion models on additional Gaussian noise during the inference phase, thereby significantly shortening the inverse generation trajectory and accelerating model convergence.

[0025] Specifically, the initialization operation fundamentally reconstructs the traditional diffusion model sampling method. When generating inversely, the traditional diffusion model usually starts by randomly sampling from a pure Gaussian noise distribution. However, in low-dose PET image reconstruction tasks, the low-dose images themselves contain extremely rich low-frequency anatomical structures and some lesion information. Starting reconstruction from pure noise would lead to lengthy iterative calculations.

[0026] Based on this, the present invention defines a discrete noise sequence arranged in ascending order: ,in, For the first The noise of the step.

[0027] Step S2 includes: S21. Directly utilize the acquired low-dose PET images As the initial state for the reverse diffusion process, its initialization formula is expressed as: ; In the formula, This indicates that the reverse diffusion sampling process starts at point 1. The image state of the step, This is the preset total number of iterations; This process completely eliminates the step of injecting additional Gaussian noise into the input low-dose data at the starting point, significantly shortening the trajectory of the image from a degraded state to a high-quality target manifold and accelerating model convergence.

[0028] S22. Using a noise scheduling strategy, set the final noise parameters for the reverse diffusion process. satisfy This is to ensure that the numerical values ​​of the entire denoising process are stable in the final step and that the denoising capability is maintained. To ensure computational robustness with a minimal number of backsampling steps, this embodiment employs a special noise scheduling strategy. The noise parameters at the final time step of the back diffusion process are... Set to a very small constant, by Set as Instead of zero, it can maintain a small Gaussian perturbation in the last step to provide continuous denoising and artifact suppression capabilities, and completely avoid the gradient explosion problem caused by the denominator approaching zero when performing Langevin dynamics correction, thus ensuring numerical stability.

[0029] S3. Simulate the reverse diffusion process by iterating the image state using the fraction-based diffusion model and the prediction-correction sampler; Specifically, step S3 is the reverse diffusion recovery step. By simulating the reverse process and using a PC sampler for iteration, this process alternates between prediction and correction to gradually recover low-dose PET image data. This is done after completing the noise-free initialization in step S2 (i.e., setting...). and Following this, the system enters the reverse diffusion recovery step. This step aims to gradually map the degraded state of low-dose PET images back to the high-quality manifold distribution of normal-dose PET images by simulating stochastic differential equations in reverse time. This invention employs a PC sampler containing outer and inner loops to implement this iterative solution process.

[0030] Step S3 includes: S31. Using the predictor in the prediction-correction sampler as a numerical solver for the inverse stochastic differential equation, the next image state is derived in each outer loop. The update formula for the outer loop prediction step is: ; In the formula, This is the score function predicted by the score-based diffusion model; Specifically, based on the forward SDE defined in step S1, its corresponding inverse SDE can be rigorously expressed mathematically as follows: , in, This represents reverse-time standard Brownian motion. This refers to the pre-trained network in step S1. The approximated score function, in the prediction step of the outer loop, the predictor, as the numerical solver of the inverse SDE, is used to derive the coarse state of the image at the next time step. Under the framework of VE-SDE, by discretizing the inverse SDE, the basic update rule of the predictor is expressed as the formula in step S31. S32. Integrate the conditional constraints into the predictor, and further express the update formula of the outer loop prediction step as follows: ; In the formula, The first , The image state of the step, , The first , Noise scheduling parameters for each step Regarding image state gradient operator, For data fidelity based on low-dose PET images, The regularization term for encoding the TV prior is used; Specifically, in order to achieve targeted low-dose PET images Controllable reconstruction requires incorporating prior conditions into the sampling process. Based on Bayes' theorem, this embodiment further refines the conditional predictor formula into the formula in step S32.

[0031] In the above formula, This constitutes the data fidelity term, which constrains the generated image to be consistent with the input low-dose PET observation data. Maintain the physical consistency of the underlying anatomical structure; and It encodes the TV prior regularization term, which guides the image to evolve towards a smooth and sharp-edged target distribution; S33. Perform the single prediction result through the corrector in the inner loop. The Langevin dynamics iteration integrates the conditional constraints of low-dose PET images into the sampling process, making the generated image samples more closely approximate the target posterior distribution. The update formula for the corrector is as follows: ; In the formula, They were respectively in the second Under the outer loop of the nth time step sequence Image state after the second inner loop For the first Step length, For the injected random Gaussian perturbation; Specifically, in the inner loop correction step, the rough result obtained from a single prediction of the outer loop is used. The corrector uses the Markov chain Monte Carlo method to perform... The Langevin dynamics iteration aims to correct the discretization error generated in the prediction step, making the marginal distribution of image samples closer to the true conditional posterior distribution. The update formula for the inner loop is modeled as the formula in step S33.

[0032] S4. Apply total variation minimization to the image state during the reverse diffusion process until the preset number of iterations is reached, and output the reconstructed PET image. Specifically, step S4 is a regularization step, which applies a TV minimization operation to the image state in the above reverse diffusion process. After the preset number of iterations is reached, the reconstructed PET image is output. By integrating a TV noise reduction module into the PC iterative sampling process to constrain the image state, this method theoretically improves the Poincaré constant to accelerate the convergence of Langevin dynamics. It can effectively suppress image noise and complete reconstruction while greatly reducing the number of sampling diffusion iterations.

[0033] The regularization objective function of the total variation minimization operation is: ; In the formula, The first , The image state of the step, For low-dose PET images, This is a priori for TV regularization.

[0034] Specifically, due to the extremely severe Poisson noise and fringe artifacts in low-dose PET images, a pure diffusion model is prone to producing high-frequency noise residues with a small number of steps. Therefore, this invention applies a physically-guided TV minimization operation after each PC step, which is the regularization objective function in the above formula. This is to enforce data fidelity requirements that the generated image does not deviate too far from the original low-dose input. This is the TV penalty term. The TV prior, by minimizing the L1 norm of the image gradient, possesses the excellent physical property of denoising while strictly preserving image edges.

[0035] The process of the total variation minimization operation satisfies: ; In the formula, This is the image state after TV regularization processing. The first , The image state of the step, This is the gradient descent step size. The change in image state. For TV norms about gradient, For gradient operators, It is a norm 2; Specifically, in order to efficiently solve the above objective function numerically, this embodiment adopts a gradient descent algorithm based on manifold constraints, and explicitly defines the specific execution formula of TV regularization as the above equation. This represents the residual distance between the current state and the target state. This represents the gradient descent step size coefficient that controls the regularization strength. In the above formula, the gradient of TV is calculated. By normalizing the image, we can ensure that the image moves smoothly in the state space along the steepest denoising direction. Meanwhile, the underlying physical and mathematical mechanism of introducing TV regularization in step S4 lies in its theoretical acceleration of the convergence speed of Langevin dynamics. In traditional diffusion models, the support set of the target data distribution is often unbounded or extremely broad, resulting in a very large Poincaré constant. According to the logarithmic Sobolev inequality, Langevin dynamics requires hundreds or thousands of iterations to converge to a steady-state distribution. This invention, by forcibly applying TV regularization in each iteration, is equivalent to mathematically imposing a bounded manifold geometric constraint on the data distribution. This constraint effectively truncates the heavy tail of the distribution and limits the variance of the data. Theoretically, this bounded manifold constraint significantly reduces the Poincaré constant of the data distribution. The improvement in the Poincaré constant directly leads to a significant increase in the exponential convergence rate of Langevin dynamics in energy space. Therefore, the method of this invention can break through the computational bottleneck of traditional diffusion models, completing PET image reconstruction that originally required thousands of steps while greatly reducing the number of sampling iterations, thus achieving a perfect closed loop between theoretical support and engineering implementation.

[0036] To verify the effectiveness of this invention, two datasets were used in this embodiment: the BrainWeb simulation phantom dataset and a real clinical whole-body PET dataset. The BrainWeb dataset was divided into 1350 training slides and 450 test slides; the clinical dataset was divided into 6650 training slides and 1330 test slides. All experimental procedures were implemented on the deep learning open-source framework PyTorch. The image detail restoration and noise reduction effects were observed by comparing PET images from normal doses with the reconstruction results from low-dose PET inputs using the method of this invention. The quality of the reconstruction was judged by comparing the levels of quantitative evaluation indicators.

[0037] The experimental platform was configured with a GPU graphics card (Tesla V100-PCIE-16GB).

[0038] This experiment focused on validating data scenarios including: PET image reconstruction using the BrainWeb phantom at a quarter dose, and image restoration and noise reduction performance of real-world clinical datasets at extreme half-dose and quarter-dose scenarios. Quantitative evaluation metrics used to assess image quality primarily included MSNR, SSIM, RMSE, and CR for lesion regions.

[0039] like Figure 2As shown, the forward process first models the continuous degradation process of fully sampled normal-dose PET images, using forward stochastic differential equations. Multi-scale Gaussian noise is gradually injected to destroy the high-frequency structures and anatomical details in the image, ultimately transforming it into a priori noise distribution. Subsequently, the reverse process is performed through inverse stochastic differential equations. Continuous-time simulations were performed to progressively restore PET images from a purely noisy state to those with normal doses. During the model training phase, to achieve accurate execution... Figure 2 The reverse recovery process shown requires solving for the only uncertainty in the inverse SDE: the score function of the time data distribution. Normal-dose PET images and their corresponding perturbation states at specific time points are input into a fractional neural network for training. This network, once it obtains the noise level of the image at each specific time point, can determine the log probability density gradient of the data distribution at a specific time point using a denoising fractional matching strategy. In this process, the pre-trained network fully learns the feature distribution and structural priors of the PET images while preserving Gaussian noise injection, thereby establishing a model to guide subsequent denoising and reconstruction. In the actual inference and reconstruction stages, this invention... Figure 2 The standard backdiffusion path shown has been fundamentally improved. Specifically, the system directly acquires the low-dose PET image to be reconstructed as the initial state for backsampling, completely eliminating the step of injecting initial Gaussian noise into the input in traditional methods. In solving the inverse SDE, this embodiment uses a PC sampler instead of a single numerical method for iteration. In each discrete small time step, the predictor derives the next image state based on the current image state and the score function predicted by the network, and combines the data fidelity of the low-dose image with the TV prior into the conditional update formula. Subsequently, the corrector performs multiple fine-tuning approximations of the single prediction result using the incremental form of Langevin dynamics. During the execution of the inverse simulation, the time step starts from the preset total number of iterations. Decrease to 0, combined with a very small and non-zero final noise parameter setting ( This ensures extremely high accuracy and numerical stability in the approximation process, enabling the model to reconstruct PET images in very few iterations.

[0040] like Figure 1 As shown, the process is divided into two core stages: the first part demonstrates the forward diffusion and model training process based on normal-dose PET images, while the second part demonstrates the reverse inference reconstruction process starting directly from low-dose PET images and incorporating TV regularization. Please refer to [link / reference]. Figure 2The first part of the training process begins by using fully sampled normal-dose PET images as input. The forward pass smoothly transforms the PET images into a priori noise distribution by continuously injecting multi-scale Gaussian noise. During this process, a score-based neural network is used to learn prior knowledge of the data to solve for the only uncertainty in inverse reconstruction: the score function of the temporal data distribution. In a specific embodiment, the present invention uses the NCSN++ network as the backbone architecture for score prediction. This network structure can effectively capture multi-scale anatomical features in medical images. Through a denoising score matching strategy, the network only needs to obtain the noise level at each time point to accurately estimate the log probability gradient of the image under different states. Once the network training converges, the fixed weight parameters are directly applied to subsequent inverse reconstruction guidance. In the TV-diff reconstruction stage, such as... Figure 1 As shown in the second half, this invention abandons the inefficient paradigm of traditional diffusion models that sample from pure Gaussian noise. Specifically, the system directly uses the low-dose PET image to be processed as the initial state of the inverse simulation path to begin iterative solving. During the iteration process, a PC sampler is used instead of a single numerical solver. In each discrete time step, the predictor combines a pre-trained scoring network to deduce the next image state. Subsequently, the corrector uses Langevin dynamics to fine-tune the prediction results multiple times to approximate the true posterior distribution. Crucially, after each prediction-correction iteration, a TV minimization operation is integrated into the algorithm. This TV module regularizes the current image state, effectively suppressing high-frequency Poisson noise and fringe artifacts under low-dose conditions, and significantly accelerating the overall convergence speed of the model by improving the Poincaré constant. With the decrease of the inverse time step, after a very small number of iterations, a normal-dose PET image with high contrast and clear details is successfully recovered from the degraded low-dose input.

[0041] like Figure 3 The figure shows a comparison of the reconstruction and restoration results of lateral head images using different methods in an embodiment of the present invention. This experiment was thoroughly validated for a half-dose PET imaging scenario. The first row of the figure shows the restored images of the reference ground truth image, the method of the present invention, and various existing comparison methods; the second row shows the residual plots between each restored image in the first row and the reference ground truth. In the residual plots, the darker the signal and the closer it is to zero, the more consistent the restoration result is with the ground truth and the smaller the reconstruction error. To clearly illustrate the technical advantages of the method of the present invention, the following is a comparison... Figure 3 A detailed analysis of the images and their features corresponding to each label (a)-(j) in the table is conducted: Figure 3 (a) in the image is a normal-dose PET image. This image has clear brain tissue outlines, distinct gray-white matter boundaries, and extremely low background noise, and serves as a high-quality reference image and gold standard for evaluation in this embodiment. Figure 3 In the image (j), the original input image of half-dose PET is shown. Due to the extremely low count statistics, the image is severely contaminated by statistical noise, and the fine anatomical structures such as sulci and gyri are blurred, which seriously affects the clinical diagnostic value of the image. Figure 3 (i) Figure 3 (h) in Figure 3 (g) and Figure 3 Figure (f) shows the reconstruction results using nonlocal mean filtering (NLM), conventional denoising methods (Denoise), a back-projection-based generative network (Bp2img), and an image translation network (Pix2pix), respectively. It can be seen that... Figure 3 (i)NLM and Figure 3 While traditional filtering methods such as (h)Denoise smooth noise to some extent, they also lead to severe over-smoothing effects, erasing a large amount of organizational details. Figure 3 (g)Bp2img and Figure 3 While conventional deep learning methods such as (f) Pix2pix attempt to recover the structure, they fail to effectively reconstruct the fine edges of the brain due to limitations in model expressive power or generalization ability. This is particularly evident in the corresponding second row of residual plots: the residual plots show a large number of bright tissue outlines, indicating that extremely important anatomical structural information was lost during the denoising process. Figure 3 (e) Figure 3 (d) and Figure 3 Image (c) shows reconstructed images based on conventional denoising diffusion probability model (DDPM), diffusion posterior sampling (DPS), and denoising diffusion sampling (DDS), respectively. Although diffusion models possess powerful generative capabilities, conventional methods struggle with highly degraded half-dose PET data. Figure 3 (e)DDPM is prone to structural distortion and unnatural artifact residues; while the introduction of posterior constraints Figure 3 (d) DPS and Figure 3 Although the (c)DDS method improves data fidelity, there are still obvious reconstruction errors at complex edges, and clear structural error signals can still be seen in the corresponding residual plot. Figure 3 Image (b) in the figure is the reconstructed image of the TV-diff model proposed in this embodiment of the invention. Compared with all eight comparison methods mentioned above, the reconstruction result of this invention is visually the closest. Figure 3 (a) is a normal-dose PET reference image. This method not only completely removes high-frequency statistical noise from the background but also perfectly preserves the complex anatomical structures and tissue edge details of the brain. This superior performance is most strongly evidenced in the residual plot in the second row: Figure 3The residual map corresponding to (b) is the "cleanest," with the error signal at the lowest level among all methods, indicating that almost no useful tissue structure information was lost or distorted during the reconstruction process. The reason why the method of this invention can achieve such excellent dual effects of denoising and detail preservation is that in the inverse iterative solution process, low-dose data is directly used as the initial state to avoid the deviation of the generation path. At the same time, TV regularization is used as a strong constraint to effectively punish local artifacts, thereby achieving superior image restoration performance far exceeding existing cutting-edge technologies in half-dose scenarios.

[0042] like Figure 4 The image shown is a comparison of the results of reconstructing and restoring coronal images using different methods in this embodiment of the invention. This comparison still focuses on the half-dose test conditions. Figure 4 The layout is divided into two lines: the first line visually displays the final reconstructed image of each algorithm, while the second line precisely presents the residual image between the reconstructed image of the corresponding algorithm and the gold standard. In the visual representation of the residual image, the wider the dark area and the lower the brightness, the smaller the reconstruction error and the less physiological details are lost. Now, regarding... Figure 4 (a) in Figure 4 The specific performance of each label (j) in the table is analyzed one by one as follows. Figure 4 Image (a) is a normal-dose PET image, which clearly shows the contours of internal organs and the distribution of high-uptake areas in the human torso, without any obvious noise interference. It serves as an ideal reference value in this comparison. In stark contrast is... Figure 4 The half-dose PET raw input image in (j) exhibits strong statistical speckle noise throughout due to the halved acquisition count, severely weakening and obscuring the edges of organs within the torso and high-contrast pathological / physiological uptake foci. In contrast methods, Figure 4 NLM in (i) and Figure 4 In the (h) section, "Denoise" represents a conventional filtering and denoising algorithm. While these two methods forcefully suppress background noise, they also cause a severe tissue texture smearing effect, resulting in extremely blurred boundaries of internal organs. This defect can be seen in the corresponding second row of the residual image—large areas of bright organ outlines appear in the residual image, indicating that structural signals were lost during the denoising process. Figure 4 Bp2img and (g) in Figure 4 Pix2pix (f) in the example, as a typical translation-based deep learning network, improves global contrast compared to traditional methods. However, due to the lack of physical prior constraints for the complex anatomical structures in medical images, the edges of the generated high-intake regions are not sharp enough, and noticeable patchy error signals remain in its residual map. In the field of diffusion models, Figure 4In (e), DDPM needs to complete a large-scale denoising mapping in a very small number of steps, resulting in incomplete denoising and abnormal artifact generation. The overall torso image presents an unnatural sense of clumping. Figure 4 DPS in (d) and Figure 4 Although DDS in (c) has made progress in the fidelity of the overall anatomical structure as an improved diffusion method that introduces data consistency constraints, it is still difficult to perfectly fit the target distribution at the extremely complex soft tissue junctions in the coronal plane. Its residual map shows that there is still a certain degree of information loss in the high-frequency edge areas of some organs. Figure 4 Image (b) in the diagram represents the reconstructed image using the TV-diff model employed in this invention. Among all the algorithms tested, the reconstruction result of this invention visually resembles... Figure 4 (a) in the sample has the highest degree of agreement. It not only completely eliminates... Figure 4 The full-band speckle noise in (j) is analyzed, and the true boundaries between various organs and high-uptake foci are pinpointed with extreme precision. The residual plot in the second row provides the most intuitive and objective assessment: Figure 4 The residual map corresponding to (b) shows the darkest background and the weakest bright color error signal, proving that this method minimizes the loss of useful anatomical signals while achieving high-quality restoration. The TV-diff model stands out in the complex environment of coronal imaging because it abandons the conventional diffusion path of Gaussian noise initialization and cleverly utilizes the smoothing and edge-preserving properties of TV regularization on image gradients, thereby achieving excellent reconstruction with high fidelity and extremely low error in low-dose whole-body PET imaging.

[0043] Figure 5 This study presents comparative results of restoring lateral body images using different processing methods. These experiments were also conducted under half-dose conditions. The top row of the figures shows the final tomographic visual effect output by each algorithm, while the bottom row shows the residual maps calculated between the corresponding algorithm output and the gold standard. In the logic of the residual map presentation, the more obvious the structural outline and the higher the pixel brightness, the more real anatomical information the algorithm has mistakenly deleted during the denoising process; conversely, lower pixel brightness indicates higher fidelity. The following section discusses... Figure 5 (a) in Figure 5 A detailed analysis of the various comparative indicators and technical characteristics of (j) in the table is provided: Figure 5 Image (a) is a reference image from a normal-dose PET scan, demonstrating an excellent signal-to-noise ratio and smooth, natural soft tissue transitions, making it the absolute gold standard for evaluating the clinical usability of all reconstruction algorithms. In stark contrast is... Figure 5In the (j) half-dose PET raw input image, due to the significant loss of photon capture rate, the entire cross-sectional field of view is swallowed by dense granular statistical noise, resulting in extreme deterioration of the boundaries of the lungs, mediastinum, and surrounding soft tissues, thus losing the ability to make accurate diagnoses. In conventional repair methods, Figure 5 (i)NLM and Figure 5 In the diagram, (h)Denoise represents the traditional spatial domain filtering strategy. Both of these strategies, while forcibly smoothing out particle noise, come at an extremely high resolution cost. Bright and complete torso contours can be clearly observed in the corresponding residual plots below them, conclusively demonstrating that a large amount of real physiological boundary information is ruthlessly stripped away as high-frequency noise during the filtering and smoothing process. Further observation... Figure 5 (g)Bp2img and Figure 5 In the (f) Pix2pix images, two deep learning-based image translation models, although they suppress noise in the global perception due to the advantage of data-driven processing, the generative network shows obvious edge fitting in the face of the extremely complex organ junctions in the transverse body. The corresponding residual map still has significant anatomical error patches. Figure 5 In the (e) DDPM model, as the baseline diffusion model, in the absence of effective prior constraints and with limited sampling steps, it not only failed to thoroughly purify the background, but also induced false patchy textures within the tissue, resulting in severe image distortion. Figure 5 (d) DPS and Figure 5 (c)DDS, as an improved diffusion sampling algorithm that introduces observational data constraints, has indeed achieved a leap in anatomical fidelity, significantly reducing unnatural artifacts. However, cross-sectional torso images contain extremely rich low-contrast soft tissue features, which these two cutting-edge methods still struggle to perfectly reproduce. Observing their residual maps reveals that the outlines of tissue boundaries still faintly emerge in the high-frequency regions of complex textures, indicating that they still exhibit slight anatomical signal dissipation. Figure 5 (b) in the figure represents the reconstruction result output by the TV-diff model claimed in this embodiment of the invention. Considering both the visual presentation of the top row and the quantization error of the bottom row, this method achieves an overwhelming advantage. In terms of visual texture, Figure 5 The smoothness of (b) and the sharpness of the organ edges both reached the level of [missing information]. Figure 5 (a) is almost at the same level, perfectly overcoming the challenge of reconstructing the transverse body section. Regarding error assessment, Figure 5The residual map corresponding to (b) in the diagram shows the darkest and most uniform state in the entire group, with negligible error signal. This means that the reconstruction process achieves near-lossless preservation of physiological structure signals. This embodiment avoids the inefficient pure noise mapping path by directly extracting low-dose scan data as the starting point for inverse solving. At the same time, it creatively couples a TV regularization term into the iterative engine. This not only tightens the Poincaré constant at the theoretical level to achieve extremely fast convergence, but also forces a variational constraint on the image gradient at the physical level, thereby achieving zero loss of complex anatomical details while filtering out massive high-frequency noise in the lateral body.

[0044] Figure 6 The study showcases comparative reconstruction experiments based on human phantom data under half-dose conditions. Unlike real, complex anatomical structures, phantoms typically contain multiple target areas of varying sizes with strictly defined uptake concentrations. This data allows for extremely rigorous testing of the algorithm's ability to restore contrast and ensure background uniformity. Figure 6 The overall layout follows the previous example: the upper array shows the reconstructed phantom cross-section, and the lower array shows the residual mapping obtained by subtracting the corresponding algorithm from the reference standard. The more prominent the bright spots in the residual map, the more severe the signal distortion or loss of target area details in that region. Now, regarding... Figure 6 (a) to Figure 6 The specific performance of (j) in the evaluation is analyzed in depth as follows: Figure 6 The (a) normal-dose PET image in the image exhibits excellent geometric fidelity: the pixel distribution in the background area is highly uniform, and the boundaries of each highly active target area are clear and the morphology is full. In contrast, Figure 6 In the (j) half-dose PET input image, the sharp reduction in photon capture number results in strong statistical fluctuation noise throughout the image. This not only makes the phantom background mottled but also risks completely overwhelming small target areas with intense noise. Traditional smoothing and denoising techniques are examined... Figure 6 (i)NLM and Figure 6 While the (h)Denoise method effectively suppresses background random fluctuations, it comes at the cost of severe edge blurring. Observing the residual plots corresponding to these two methods, bright target region outlines can be clearly seen, indicating that the traditional filter kernel, while suppressing noise, incorrectly erases the high-frequency effective signals representing the target region boundaries. In conventional deep learning methods, Figure 6 (g)Bp2img and Figure 6The (f)Pix2pix algorithm reshapes the macroscopic geometry of the phantom to some extent, but the background region generated by the network still contains nodular spurious patches, and some circular target areas exhibit irregular deformation and compression. The numerous fragmented bright spots in its residual plot reveal the model's insufficient generalization ability in this type of quantitative task. For the diffusion model, Figure 6 In the (e)DDPM model, under the constraint of a very small number of sampling steps, a complete structural collapse occurred. Not only did it fail to effectively remove noise, but it also fabricated a large number of severe radial artifacts out of thin air, completely losing its value for quantitative analysis. As an improvement scheme... Figure 6 (d) DPS and Figure 6 (c) DDS, by introducing likelihood guidance from the observed data, significantly improves the fidelity of the phantom structure. However, comparing the reconstructed and residual images reveals that slight texture undulations still remain in the homogeneous background area of ​​the phantom, and the residual signal around the target area is not completely darkened, indicating that there is still an irreconcilable compromise between smoothness and edge sharpness. For the embodiments of this invention... Figure 6 (b) TV-diff model. Among the algorithms evaluated, Figure 6 (b) is not only the most visually faithful to the reference image. Figure 6 In (a), its quantization error performance is also the most outstanding. From a visual perspective, Figure 6 (b) in the model completely smooths out the statistical noise in the background area, while maintaining extremely sharp edges and pure internal contrast for target areas of all sizes.

[0045] Figure 7 This demonstrates the reconstructed imagery from head PET images at a quarter-dose condition. Limited by an extremely low photon detectivity of only 25% of the standard dose, Figure 7 In (j) a quarter-dose PET scan, the signal-to-noise ratio of the raw image plummeted, and the complex cortical sulci and gray-white matter interfaces of the brain were completely obscured by extremely dense and chaotic speckles, greatly increasing the difficulty of clinical image interpretation. In contrast, Figure 7 (a) Normal dose PET in the text presents a detailed and layered view of the brain's physiological anatomy, which serves as the gold standard for guiding all algorithms. Figure 7 The second half simultaneously presents the prediction results and... Figure 7 The difference map obtained by subtracting (a) from the image shows that the deeper and darker the image, the closer the structure depicted by the algorithm is to the real physiological and anatomical structure. Conventional spatial filtering paradigms are ineffective in dealing with such drastic image degradation. Figure 7 (i)NLM and Figure 7The (h)Denoise algorithm, while forcibly removing noise from the entire image, caused a severe halo diffusion effect, blurring the originally sharp tissue boundaries within the brain over a large area. This is conclusively verified in the difference map below—the bright, complete brain outline highlights a large number of high-frequency physiological details that have been forcibly filtered out as noise. Turning to the basic end-to-end mapping network... Figure 7 (g)Bp2img and Figure 7 Although (f)Pix2pix remodels the macroscopic cortical morphology, the network exhibits characteristic hallucinations and contrast imbalances when dealing with extremely low doses, resulting in uneven artifact color patches appearing inside the brain tissue. The scattered bright spots in the difference map also reveal its inaccuracy in pixel-level fitting. Figure 7 In the (e)DDPM, the generated trajectory deviated severely during the short-step inverse solution. Not only did it fail to complete the effective mapping at extremely low doses, but it also generated a large area of ​​radial network artifacts, and the image structure was completely destroyed. Figure 7 (d) DPS and Figure 7 While (c)DDS forcibly brought the brain outline back on track through its data consistency penalty mechanism, it still failed to accurately penetrate heavy noise to reach microscopic details under the extreme stress test of a quarter dose. The bright lines remaining in the brain gyri gaps in the difference map indicate that it still has blind spots in the reconstruction of extremely fine brain folds. In contrast, Figure 7 (b) The TV-diff model stood out among all the participating arrays, not only visually resolving the originally severely degraded... Figure 7 (j) in the middle recovered to almost Figure 7 The extremely high resolution of (a) perfectly removes stubborn noise and reproduces the groove texture, and the difference map below it shows the purest state in the entire field, proving that the structural distortion rate is reduced to the lowest in the entire group. The reason why this method can achieve image quality reversal in the extreme case of only one-quarter of the effective signal is that it abandons the traditional pure noise starting mode and directly anchors to the low-dose image itself to prevent iterative divergence. It also proactively incorporates TV regularization to lock the variational boundary of the image. Thus, under the extreme low signal-to-noise ratio limit, it can still accurately sculpt high-fidelity normal dose level medical images with very few steps.

[0046] The results shown in Tables 1 to 4 are the reconstruction MSNR / SSIM / NRMSE results of the method of the present invention and other comparative methods from the DIGITMI 930 PET / CT scanner in 7 patients using different methods, the CR image reconstruction of 3 patients and 5 lesions using the DigitMI 930 PET / CT scanner using different methods, the reconstruction MSNR / SSIM / NRMSE results of human body simulation data, and the reconstruction MSNR / SSIM / NRMSE results of body quarter-dose data.

[0047] Table 1. MSNR / SSIM / NRMSE results of 7 patients reconstructed using a DIGITMI 930 PET / CT scanner using different methods.

[0048] Table 1 details the quantitative assessment results of seven patients using eight different reconstruction methods on a DIGITMI 930 PET / CT scanner. In Table 1, the first row for each patient represents MSNR, the second row represents SSIM, and the third row represents NRMSE. These methods specifically include Bp2img, Denoise, NLM, Pix2pix, DDPM, DPS, DDS, and the TV-diff model proposed in this invention. Through specific numerical analysis of the three core indicators—MSNR, SSIM, and NRMSE—the superior performance of the method proposed in this invention under various clinical individual differences is fully demonstrated. Regarding MSNR, the TV-diff model of this invention achieved the highest value in the reconstruction tests of all seven patients, exhibiting extremely strong noise robustness. Taking patient 1 as an example, the MSNR of the TV-diff model reached 49.166 dB, a significant improvement of 2.205 dB compared to the deep learning baseline network Bp2img (46.961 dB), and also an improvement of 0.635 dB compared to the conventional denoising diffusion probability model DDPM (48.531 dB). In terms of NRMSE, the TV-diff model also achieved extremely significant error approximation. For example, in the test on patient 5, the NRMSE of the method of this invention was as low as 0.669, a significant reduction of approximately 24.1% compared to the error value of 0.882 of the DDPM model, and even better than the leading-edge DPS algorithm with an error of 0.771 and the DDS algorithm with an error of 0.735. This demonstrates its extremely high accuracy in restoring the true anatomical structure. Furthermore, regarding SSIM, although some traditional filtering algorithms such as Denoise or NLM may achieve superficially high values ​​on individual data due to global oversmoothing, this forced smoothing comes at the cost of sacrificing lesion details. In contrast, the TV-diff model of this invention achieves top-tier structural similarity performance while strictly preserving the high-frequency edges and texture realism of tissues. For example, in patients 4 and 7 with complex structural features, the SSIM of the method of this invention reached the optimal absolute value levels of 0.9014 and 0.8967, respectively, far exceeding the conventional DDPM of 0.8694 and 0.7504. These detailed quantitative comparison data strongly demonstrate that the noiseless initialization and TV regularization constraint techniques integrated in this invention can fundamentally suppress reconstruction errors and improve the signal-to-noise ratio without causing excessive smoothing defects, thereby providing high-quality reconstruction results with high clinical reliability for extremely low-dose PET imaging.

[0049] Table 2. CR image reconstruction of 3 patients and 5 lesions using a DigitMI 930 PET / CT scanner, employing different methods.

[0050] Table 2 details the quantitative evaluation results of contrast recovery after reconstructing five lesions in three patients using different algorithms with a digital positron emission tomography (PET) scanner. Looking at the overall data, traditional filtering algorithms such as Denoise and NLM, as well as conventional deep learning networks such as Bp2img and Pix2pix, all showed low contrast recovery values ​​in each lesion. This reflects the inevitable excessive smoothing and attenuation of the lesion signal when suppressing background noise. Although DDPM and diffusion models such as DPS and DDS with posterior constraints alleviated feature loss to some extent, the TV-diff model proposed in this embodiment achieved the highest values ​​in the reconstruction evaluation of all five lesions, demonstrating superior lesion highlighting ability. Taking lesion four, which suffered from severe feature degradation, as an example, the contrast recovery value of the TV-diff model of this invention climbed to 4.460, a significant improvement of 1.438 compared to the DDS algorithm's value of 3.022, and an improvement of 1.590 compared to the conventional DDPM value of 2.870, even surpassing the normal dose reference standard of 3.085. Similarly, in the pathological region of lesion five, the model of this invention achieved a peak performance of 4.629, a significant leap of 2.515 compared to the traditional Denoise algorithm's 2.114. These precise comparative data fully and objectively demonstrate that the regularized inverse evolution mechanism constructed in this invention can almost losslessly lock and reshape the high-frequency contrast features of lesion regions under extremely harsh low-dose noise interference, thus providing a highly valuable and engineering-potential imaging guarantee for the accurate identification and targeted diagnosis of clinical pathological regions.

[0051] Table 3. MSNR / SSIM / NRMSE results of human simulation data reconstruction

[0052] Table 3 systematically presents the quantitative evaluation results of the reconstructed human body simulation data using eight different algorithms, comprehensively covering the three major evaluation indicators: MSNR, SSIM, and NRMSE. From the horizontal comparison of the data, it is clear that the TV-diff model constructed in this embodiment of the invention achieves absolutely optimal performance in all three evaluation dimensions. Specifically, in terms of MSNR, which characterizes image noise resistance, the TV-diff model of this invention reaches a global highest value of 43.043, a significant improvement of 2.789 compared to the second-best performing traditional Denoise algorithm (40.254), and a substantial improvement of 4.474 compared to the conventional denoising diffusion probability model DDPM (38.569). In terms of SSIM, which measures the fidelity of image anatomical structure, the TV-diff model also ranks first with a value of 0.7566, surpassing not only the 0.7465 of the frontier diffusion posterior sampling (DPS) algorithm but also significantly exceeding the 0.6334 of the DDPM baseline model. Furthermore, in the NRMSE dimension, which reflects pixel-level overall reconstruction bias, the model of this invention achieves a minimum quantization error of 0.131, lower than the 0.133 of the Denoise algorithm and the 0.143 of the DDS algorithm. These precise and comprehensive quantization comparisons strongly demonstrate that the regularized inverse generation mechanism proposed in this invention can effectively balance high-fidelity structural reconstruction and precise suppression of deep random noise in rigorous quantitative testing of human body simulation data, exhibiting superior reconstruction accuracy and technical advantages.

[0053] Table 4. Reconstructed MSNR / SSIM / NRMSE results for quarter-dose data in the body

[0054] Table 4 details the quantitative evaluation results obtained using eight different reconstruction algorithms for quarter-dose data of extremely degraded bodies. Under these stringent imaging conditions with extremely low counts, the TV-diff model proposed in this embodiment of the invention achieved the best performance across the entire spectrum in the three core evaluation metrics: MSNR, SSIM, and NRMSE. Specifically, in terms of peak signal-to-noise ratio (PSNR), which measures noise suppression capability, the model of this invention achieves a value as high as 54.716, a significant improvement of 1.932 compared to the conventional denoising diffusion probability model DDPM's 52.784, and steadily surpasses the second-best performing image translation network, Pix2pix, at 54.697. In the SSIM dimension, which characterizes the fidelity of anatomical structures, the TV-diff model ranks first with an absolute advantage of 0.8877, exceeding the leading diffusion posterior sampling (DPS) algorithm's 0.8441 by 0.0436, fully demonstrating its outstanding ability to preserve tissue boundaries and textures under severe noise interference. Furthermore, in terms of NRMSE, which reflects pixel-level overall reconstruction bias, the model of this invention achieves a minimum quantization error of 0.725. This value not only completely avoids the structural collapse of the base network Bp2img, which is as high as 26.890, but also achieves a significant error reduction of 0.449 compared to the 1.174 of the denoising diffusion sampling DDS method. The above precise numerical comparison strongly confirms that the TV regularization inverse generation framework constructed in this invention can still break through the bottleneck of existing cutting-edge generation technologies, even at extremely low doses with only one-quarter of the effective signal, providing high-quality PET images with extremely high quantization accuracy and structural fidelity for clinical use.

[0055] The low-dose PET reconstruction method proposed in this invention, based on a total variational regularized diffusion model, effectively solves various image inverse problems with high noise and low signal-to-noise ratio through its noiseless initialization and regularized inverse evolution architecture. Specifically, it can be widely applied in practical scenarios such as medical image processing (CT and MRI), astronomical observation, remote sensing satellite image denoising, low-light night vision image enhancement, and industrial non-destructive testing, achieving high-fidelity denoising and reconstruction of images under complex degradation environments.

[0056] The low-dose PET reconstruction method based on a total variational regularized diffusion model provided in Embodiment 1 of this invention has the following advantages: Significantly improves computational efficiency in image processing: This invention completely eliminates the cumbersome step of injecting additional Gaussian noise into the input data in traditional diffusion models by directly using low-dose PET images as the initial state for backdiffusion during the inference stage. This greatly shortens the backdiffusion trajectory. Combined with the TV regularization module, the model requires only a very small number of sampling iterations (only 25 steps) to complete high-quality reconstruction, processing a single PET slice in only about 1 second. This completely breaks through the computational bottleneck of traditional diffusion models, which are time-consuming to infer and cannot meet the needs of real-time clinical applications. A theoretically supported accelerated convergence mechanism: This invention integrates the TV minimization operation depth into the iterative sampling of PC, and uses the TV prior as a strict mathematical constraint to significantly improve the Poincaré constant of the target data distribution from a theoretical perspective. This optimization of the underlying energy landscape ensures that Langevin dynamics can achieve a faster convergence speed in the back sampling process. Excellent denoising and artifact suppression: By continuously introducing the TV denoising module in the iterative loop of the predictor and corrector, this method can effectively suppress statistical noise and stripe artifacts common in low-dose PET imaging while greatly reducing the number of iterations. It performs particularly well in high-noise environments, significantly improving the average signal-to-noise ratio and structural similarity of the reconstructed image and reducing the normalized root mean square error.

[0057] Precise preservation of structural details and high lesion contrast: The conditional constraint mechanism of this invention effectively balances the data fidelity term and the TV prior term, successfully overcoming the problems of excessive image smoothing and texture distortion that are easily caused by traditional deep learning denoising methods. While effectively reducing noise, this method can sharply preserve the boundaries of complex anatomical structures and significantly improve the contrast of lesion areas, providing a more accurate diagnostic basis for clinical tumor detection and quantitative analysis.

[0058] Strong robustness and cross-dose generalization ability: Thanks to the powerful gradient distribution learning ability and unsupervised training mechanism of the fractional diffusion model, this invention not only performs well in conventional low-dose scenarios, but also maintains excellent and stable reconstruction performance in the face of more stringent ultra-low-dose conditions and cross-motif validation. This characteristic of not depending on specific degradation modes gives the method strong clinical generalization potential and adaptability.

[0059] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0060] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A low-dose PET reconstruction method based on total variation regularized diffusion model, characterized in that, include: Fully sampled normal dose PET images are acquired, Gaussian noise is injected through a forward stochastic differential equation, and a fraction-based diffusion model is obtained through denoised fractional matching training. Acquire the low-dose PET image to be reconstructed, use the low-dose PET image directly as the initial state for backdiffusion, and do not inject additional Gaussian noise into the low-dose PET image at the corresponding starting point, including: Directly utilizing acquired low dose PET images As the initial state of the inverse diffusion process, its initialization formula is expressed as: ； In the formula, represents the image state of the starting point of the reverse diffusion sampling process in the i-th iteration step, step, and is a preset total iteration step number. setting a final noise parameter of the inverse diffusion process using a noise scheduling strategy satisfies so that the entire denoising process is numerically stable in the last step and maintains the denoising ability; The reverse diffusion process is simulated by iterating the image state using the fractional diffusion model and the prediction-correction sampler, including: The predictor in the prediction-correction sampler is used as a numerical solver for the inverse stochastic differential equation. The next image state is derived in each outer loop, where the update formula for the outer loop prediction step is: ； In the formula, is a score function predicted based on a fractional diffusion model; Conditional constraints are integrated into the predictor, and the update formula for the outer loop prediction step is expressed as: ； wherein are the image states of the first , the image state of the step, , are the image states of the first , the noise schedule parameters of the step, is a gradient operator on the image states , is a data fidelity term based on the low-dose PET image, is a regularization term encoding a TV prior; performing a single prediction result on the inner loop through the corrector secondary Langrangian dynamics iterations to integrate the set of conditional constraints of the low dose PET image into the sampling, so that the generated image samples are more proximate to the target posterior distribution wherein an update formula of the corrector is: ； wherein are the image states after the first, second, third, fourth, and fifth inner loop at the first time step, are the image states after the first, second, third, fourth, and fifth inner loop at the first time step, are the image states after the first, second, third, fourth, and fifth inner loop at the first time step, are the image states after the first, second, third, fourth, and fifth inner loop at the first time step, is the step size of the first time step, is the step size of the first time step, is the injected random Gaussian perturbation; A total variation minimization operation is applied to the image state during the reverse diffusion process until the preset number of iterations is reached, and the reconstructed PET image is output.

2. The low-dose PET reconstruction method based on the total variation regularized diffusion model according to claim 1, characterized in that, In the step of injecting Gaussian noise through a forward stochastic differential equation and obtaining a score-based diffusion model through denoising score matching, the forward stochastic differential equation is used to describe the evolution of the image from the original data distribution to the noise distribution. The forward stochastic differential equation is: ； In the formula, The drift coefficient, Where is the diffusion coefficient. For the smallest positive time step, For Brownian motion, Image status; The objective function for training and optimizing the score-based diffusion model is: ； In the formula, This represents the parameters after network optimization. Represents a positive weighting function. Indicates in The time variable of uniform sampling within the interior, This represents the initial normal dose PET image data. Indicates time Image data after being perturbed by noise, This indicates a score-based diffusion model that needs to be trained. Indicates The Gaussian perturbation kernel centered on the center, For mathematical expectation, It is the square of the L2 norm.

3. The low-dose PET reconstruction method based on the total variation regularized diffusion model according to claim 1, characterized in that, In the step of applying a total variation minimization operation to the image state during the reverse diffusion process until the preset number of iterations is reached, and then outputting the reconstructed PET image, the total variation minimization operation is integrated into the iterative update process of the prediction-correction sampler. The regularization objective function of the total variation minimization operation is: ； In the formula, The first , The image state of the step, For low-dose PET images, This is a priori for TV regularization.

4. The low-dose PET reconstruction method based on the total variation regularized diffusion model according to claim 1, characterized in that, In the step of applying a total variation minimization operation to the image state during the reverse diffusion process until the preset number of iterations is reached, and then outputting the reconstructed PET image, the total variation minimization operation satisfies the following: ； In the formula, This is the image state after TV regularization processing. The first , The image state of the step, This is the gradient descent step size. The change in image state. For TV norms about gradient, For gradient operators, It is a 2-norm.

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