A sparse CT image reconstruction method based on residual diffusion network
By using a sparse CT image reconstruction method based on residual diffusion networks, the reconstruction problem is decomposed into image and residual subproblems. The diffusion model and wavelet domain are used to process global and detail information, which solves the problems of image degradation and noise in sparse view CT reconstruction and achieves high-quality image restoration.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HUNAN UNIV OF SCI & TECH
- Filing Date
- 2026-04-27
- Publication Date
- 2026-07-14
AI Technical Summary
Sparse view CT reconstruction suffers from problems such as image degradation, noise, stripe artifacts, and loss of structural details. Existing methods are computationally intensive, sensitive to parameter selection, and produce overly smooth reconstruction results. Supervised deep learning methods lack robustness and are limited by dataset dependence, thus restricting their application.
A sparse CT image reconstruction method based on residual diffusion network is constructed. The reconstruction problem is decomposed into image subproblem and residual subproblem through joint optimization model. The global structure and detail information are processed by image domain diffusion model and wavelet domain residual diffusion model respectively. The results are gradually optimized by iterative optimization strategy.
It achieves high-quality reconstruction of sparse CT images, restores fine details and textures, improves the stability and robustness of reconstruction, and integrates image priors and residual priors to provide complementary guidance.
Smart Images
Figure CN122115744B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of image processing, and in particular to a sparse CT image reconstruction method based on residual diffusion networks. Background Technology
[0002] Computed tomography (CT) plays a vital role in modern medical diagnosis. Standard CT imaging protocols typically require a large number of X-ray projections to ensure high-fidelity reconstruction, inevitably exposing patients to high radiation doses and potentially posing health risks. To mitigate these risks, sparse-view CT (SVCT) has been developed as an alternative protocol, acquiring only a limited number of projections. Despite the clinical advantages of SVCT, its reconstruction remains a highly challenging pathological inverse problem, often leading to severe image degradation, including noise, streak artifacts, and loss of structural detail.
[0003] To address these issues, various reconstruction methods have been explored. Traditional analytical algorithms, such as filtered back projection (FBP), remain computationally attractive but are highly sensitive to artifacts and often fail to accurately recover fine structural details under sparse view conditions. To improve reconstruction quality, iterative reconstruction algorithms have been proposed. These algorithms formulate the task as an optimization problem, typically incorporating prior knowledge or regularization terms (such as total variation (TV), anisotropic total variation (ATV), low-rank, and dictionary learning) to stabilize the solution. While iterative methods offer improved performance with limited data, they are computationally expensive, sensitive to the choice of regularization parameters, and prone to over-smoothing reconstructions that obscure important anatomical structures.
[0004] In recent years, deep learning-based methods have gained increasing attention as a powerful technology in medical imaging. Typical supervised deep learning methods do not rely on raw projective measurement data, meaning the reconstruction process is no longer limited by specific imaging system protocols. Through end-to-end training, neural networks can directly map degraded input images to high-quality reconstructed images without additional input. Supervised deep learning methods offer advantages such as fast inference speed and flexible deployment. However, the application of supervised deep learning methods in computed tomography (CT) scans of lung nodules is limited because they require large-scale, high-quality training datasets, which are not easily obtained. Furthermore, the performance of supervised deep learning methods is highly sensitive to data distribution and lacks robustness under different acquisition protocols, which often limits their application in real-world scenarios.
[0005] Diffusion models have garnered significant attention due to their ability to accurately sample from complex data distributions. This advantage has been successfully applied to sparse-view computed tomography (CT) reconstruction. Diffusion modeling frameworks unify various generative paradigms, including fractional, likelihood-based, and energy-guided formulations, providing a general methodological foundation for image reconstruction and inverse problems. In particular, diffusion models exhibit unique advantages in unsupervised inverse problems, serving as powerful image priors. When only partial or degraded measurement data is available, a pre-trained diffusion model can act as a prior sampler, generating feasible solutions from an approximate posterior distribution and effectively guiding the solution space toward the true data manifold. This mechanism is especially effective for severely ill-posed or underposed inverse problems. However, diffusion models require the simultaneous reconstruction of both high-frequency and low-frequency information and do not explicitly utilize the frequency characteristics of CT images. Furthermore, most existing wavelet ensemble methods either operate only in the frequency domain or are applied globally, potentially failing to capture fine local structures during iterative generation. Summary of the Invention
[0006] To address the aforementioned technical problems, this invention provides a sparse CT image reconstruction method based on residual diffusion networks that features a simple algorithm and good reconstruction results.
[0007] The technical solution of this invention to solve the above-mentioned technical problems is: a sparse CT image reconstruction method based on residual diffusion networks, comprising the following steps:
[0008] Step 1: Analyze sparse-view CT images;
[0009] Step 2: Based on the results of the analysis in Step 1, construct a joint optimization model;
[0010] Step 3: Decompose the joint optimization objective of the joint optimization model into two independent sub-problems, namely the image sub-problem and the residual sub-problem;
[0011] Step 4: Solve the image subproblem using the image domain diffusion model to obtain intermediate reconstruction results;
[0012] Step 5: Solve the residual subproblem using the residual diffusion model in the wavelet domain to obtain the optimized residual;
[0013] Step 6: Fuse the intermediate reconstruction results with the optimized residuals to obtain the final reconstruction result.
[0014] In the above-described sparse CT image reconstruction method based on residual diffusion networks, step 1 describes the mathematical model of sparse-view CT imaging as a linear inverse problem:
[0015] (1);
[0016] In the formula, This represents the original, clean CT image. , This is the optimized output of the general model. It is the difference between the real image and the image reconstructed by the general model. Represents the projected data of the measurement; Represents the CT system matrix; This indicates noise in the measurement data.
[0017] In the above-mentioned sparse CT image reconstruction method based on residual diffusion networks, the joint optimization model constructed in step 2 is as follows:
[0018] (2);
[0019] In the formula, For data fidelity items; For regularization terms; For complementary regularization terms; To balance the hyperparameters of the regularization term; The hyperparameters for balancing complementary regularization terms; To minimize the parameter function; This is the output of the general model; The difference between the real image and the reconstructed image The optimal estimation result; The square of the L2 norm; In response to The prior regularization function; In response to The prior regularization function.
[0020] In the above-mentioned sparse CT image reconstruction method based on residual diffusion networks, step 3 employs a block coordinate descent algorithm to decompose the joint optimization objective into two independent sub-problems: the image sub-problem shown in equation (3) and the residual sub-problem shown in equation (4).
[0021] (3);
[0022] (4);
[0023] In the formula, Indicates the first The image variables are updated in each iteration; Indicates the first The residual variable obtained from the next iteration update; Indicates the first The residual variable is obtained from the next iteration update.
[0024] In the above-described sparse CT image reconstruction method based on residual diffusion networks, step 4 introduces a first auxiliary variable for the image sub-problem. Equation (3) can be decomposed into the following two parts:
[0025] (5);
[0026] (6);
[0027] In the formula, This represents the first auxiliary variable introduced for the image subproblem. In the The result obtained from the next iteration update; Indicates the first The image variables input in the next iteration; Indicates the penalty parameter; In response to The prior regularization function;
[0028] Equation (5) constructs a prior subproblem related to the variables, which is solved by using an image domain diffusion model. The iterative results generated by the image domain diffusion model are used to learn the relevant prior information. The value depends on Intermediate solutions obtained during the iteration process. and Both are affected by image domain diffusion model prediction and random perturbations; the learned prior information is used to guide the entire optimization process; the prior generation statement for each step is as follows:
[0029] (7);
[0030] In the formula, The first auxiliary variable introduced for the image subproblem In the The result obtained from the next iteration update; For the first The step size parameter corresponding to the next iteration; For parameters The image domain diffusion model scores the input using its score function. For parameters Image domain diffusion model in the first The next iteration is based on the input... The scoring function; Index for iteration count; This is a random perturbation term that follows a Gaussian distribution.
[0031] In the above-mentioned sparse CT image reconstruction method based on residual diffusion networks, in step 4, equation (6) is used as a data consistency constraint and solved using simultaneous iterative reconstruction technology to ensure that the intermediate results of each iteration are consistent with the initial sparse view projection; the iteration process is as follows:
[0032] (8);
[0033] in, Represents a diagonal matrix. ; This indicates an operation that constructs a diagonal matrix using the elements within the parentheses as diagonal elements; The second norm of a vector; Representing the CT system matrix The row vectors For row index, , Representing the CT system matrix number of rows; express The transpose of .
[0034] In the aforementioned sparse CT image reconstruction method based on residual diffusion networks, step 5 introduces a second auxiliary variable to address the residual subproblem. Equation (4) can be decomposed into the following two parts:
[0035] (9);
[0036] (10);
[0037] In the formula, A second auxiliary variable introduced for the residual subproblem In the The result obtained from the next iteration update; It is the difference between the real image and the image reconstructed by the general model; Indicates the first The residual variable obtained from the next iteration update; Indicates the first The residual variable obtained from the next iteration update; This represents the penalty parameter used to constrain consistency between the residual variable and the second auxiliary variable; In response to The prior regularization function;
[0038] For equation (9), the residual is decomposed into the wavelet domain, and the high-frequency and low-frequency components are predicted respectively:
[0039] (11);
[0040] (12);
[0041] In the formula, express Low-frequency components obtained through wavelet decomposition; express High-frequency components obtained through wavelet decomposition; express Low-frequency components obtained through wavelet decomposition; express High-frequency components obtained through wavelet decomposition; express Low-frequency components obtained through wavelet decomposition; express High-frequency components obtained through wavelet decomposition; Indicates the first The retention coefficients corresponding to the next iteration; Indicates the first The noise scheduling parameters corresponding to the next iteration; Indicates as of the date The cumulative retention coefficient of the next iteration; Indicates by parameters The wavelet domain residual diffusion model characterized in the first... The prediction results of the next iteration for low-frequency components; Indicates by parameters The wavelet domain residual diffusion model characterized in the first... The prediction results of the next iteration for high-frequency components; Indicates the iteration count index; Indicates the first The random disturbance strength parameter corresponding to the next iteration; Represents random noise; in and Guided by this, the residual diffusion model in the wavelet domain predicts the relevant low-frequency and high-frequency residuals, respectively;
[0042] Then, the inverse wavelet transform is used to obtain the residual prior, expressed as:
[0043] (13);
[0044] In the formula, This represents the inverse wavelet transform.
[0045] In the above-mentioned sparse CT image reconstruction method based on residual diffusion networks, in step 5, for equation (10), the following is defined:
[0046] (14);
[0047] In the formula, Indicates about The objective function value is optimized.
[0048] Calculate the partial derivative of equation (14) to obtain:
[0049] (15);
[0050] In the formula, express transpose; Indicates about The gradient operator;
[0051] The gradient descent method is used to iteratively solve equation (15):
[0052] (16);
[0053] In the formula, This represents the step size parameter used to control the update magnitude in each iteration; Indicates about The objective function value is optimized.
[0054] Equation (16) simplifies to:
[0055] (17).
[0056] In the above-described sparse CT image reconstruction method based on residual diffusion networks, the final reconstruction result in step 6 is as follows:
[0057] (18);
[0058] In the formula, Indicates by and The reconstructed image obtained by overlay.
[0059] The beneficial effects of this invention are as follows:
[0060] 1. This invention constructs a joint optimization model that integrates image priors and residual priors. The image priors are designed to constrain the global structure, while the residual priors are used to refine fine details and textures, providing complementary prior guidance for SVCT reconstruction and achieving detail restoration and global consistency.
[0061] 2. This invention uses a residual diffusion model in the wavelet domain to realize residual priors, which can further enhance the reconstruction of fine details and textures.
[0062] 3. This invention develops an iterative optimization strategy that gradually optimizes the results by alternately updating the reconstructed image and residual components, thereby improving the stability and robustness of the reconstruction. Attached Figure Description
[0063] Figure 1 This is the overall flowchart of the present invention. Detailed Implementation
[0064] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0065] like Figure 1 As shown, a sparse CT image reconstruction method based on residual diffusion networks includes the following steps:
[0066] Step 1: Analyze sparse-view CT imaging.
[0067] The mathematical model of sparse-view CT imaging can be expressed as a linear inverse problem:
[0068] (1)
[0069] In the formula, This represents the original, clean CT image. , This is the optimized output of the general model. It is the difference between the real image and the image reconstructed by the general model. Represents the projected data of the measurement; Represents the CT system matrix; This indicates noise in the measurement data.
[0070] Step 2: Based on the results of the analysis in Step 1, construct a joint optimization model.
[0071] The constructed joint optimization model is as follows:
[0072] (2)
[0073] In the formula, For data fidelity items; For regularization terms; For complementary regularization terms; To balance the hyperparameters of the regularization term; The hyperparameters for balancing complementary regularization terms; To minimize the parameter function; Optimization output of the general model The optimal estimation result; Differences between real images and images reconstructed using a general model The optimal estimation result; The square of the L2 norm; In response to The prior regularization function; In response to The prior regularization function.
[0074] Step 3: Decompose the joint optimization objective of the joint optimization model into two independent sub-problems, namely the image sub-problem and the residual sub-problem.
[0075] Using the block coordinate descent algorithm, the joint optimization objective is decomposed into two independent sub-problems, namely the image sub-problem shown in equation (3) and the residual sub-problem shown in equation (4):
[0076] (3)
[0077] (4)
[0078] In the formula, Indicates the first The image variables are updated in each iteration; Indicates the first The residual variable obtained from the next iteration update; Indicates the first The residual variable is obtained from the next iteration update.
[0079] Step 4: Solve the image subproblem using the image domain diffusion model to obtain intermediate reconstruction results.
[0080] For the image subproblem, a first auxiliary variable is introduced. Equation (3) can be decomposed into the following two parts:
[0081] (5)
[0082] (6)
[0083] In the formula, This represents the first auxiliary variable introduced for the image subproblem. In the The result obtained from the next iteration update; Indicates the first The image variables input in the next iteration; Indicates the penalty parameter; In response to The prior regularization function;
[0084] Equation (5) constructs a prior subproblem related to the variables, which is solved by using an image domain diffusion model. The iterative results generated by the image domain diffusion model are used to learn the relevant prior information. The value depends on Intermediate solutions obtained during the iteration process. and Both are affected by image domain diffusion model prediction and random perturbations; the learned prior information is used to guide the entire optimization process; the prior generation statement for each step is as follows:
[0085] (7)
[0086] In the formula, The first auxiliary variable introduced for the image subproblem In the The result obtained from the next iteration update; For the first The step size parameter corresponding to the next iteration; For parameters The image domain diffusion model scores the input using its score function. For parameters Image domain diffusion model in the first The next iteration is based on the input... The scoring function; Index for iteration count; This is a random perturbation term that follows a Gaussian distribution.
[0087] Equation (6) serves as a data consistency constraint and is solved using the simultaneous iterative reconstruction technique to ensure that the intermediate results of each iteration remain consistent with the initial sparse view projection; the iterative process is as follows:
[0088] (8)
[0089] in, Represents a diagonal matrix. ; This indicates an operation that constructs a diagonal matrix using the elements within the parentheses as diagonal elements; The second norm of a vector; Representing the CT system matrix The row vectors For row index, , Representing the CT system matrix number of rows; express The transpose of .
[0090] Step 5: Solve the residual subproblem using the residual diffusion model in the wavelet domain to obtain the optimized residual.
[0091] To address the residual problem, a second auxiliary variable is introduced. Equation (4) can be decomposed into the following two parts:
[0092] (9)
[0093] (10)
[0094] In the formula, A second auxiliary variable introduced for the residual subproblem In the The result obtained from the next iteration update; It is the difference between the real image and the image reconstructed by the general model; Indicates the first The residual variable obtained from the next iteration update; Indicates the first The residual variable obtained from the next iteration update; This represents the penalty parameter used to constrain consistency between the residual variable and the second auxiliary variable; In response to The prior regularization function;
[0095] For equation (9), the residual is decomposed into the wavelet domain, and the high-frequency and low-frequency components are predicted respectively:
[0096] (11)
[0097] (12)
[0098] In the formula, express Low-frequency components obtained through wavelet decomposition; express High-frequency components obtained through wavelet decomposition; express Low-frequency components obtained through wavelet decomposition; express High-frequency components obtained through wavelet decomposition; express Low-frequency components obtained through wavelet decomposition; express High-frequency components obtained through wavelet decomposition; Indicates the first The retention coefficients corresponding to the next iteration; Indicates the first The noise scheduling parameters corresponding to the next iteration; Indicates as of the date The cumulative retention coefficient of the next iteration; Indicates by parameters The wavelet domain residual diffusion model characterized in the first... The prediction results of the next iteration for low-frequency components; Indicates by parameters The wavelet domain residual diffusion model characterized in the first... The prediction results of the next iteration for high-frequency components; Indicates the iteration count index; Indicates the first The random disturbance strength parameter corresponding to the next iteration; Represents random noise; in and Guided by this, the residual diffusion model in the wavelet domain predicts the relevant low-frequency and high-frequency residuals, respectively;
[0099] Then, the inverse wavelet transform is used to obtain the residual prior, expressed as:
[0100] (13)
[0101] In the formula, This represents the inverse wavelet transform.
[0102] For equation (10), define:
[0103] (14)
[0104] In the formula, Indicates about The objective function value is optimized.
[0105] Calculate the partial derivative of equation (14) to obtain:
[0106] (15);
[0107] In the formula, express transpose; Indicates about The gradient operator;
[0108] The gradient descent method is used to iteratively solve equation (15):
[0109] (16);
[0110] In the formula, This represents the step size parameter used to control the update magnitude in each iteration; Indicates about The objective function value is optimized.
[0111] Equation (16) simplifies to:
[0112] (17).
[0113] Step 6: Fuse the intermediate reconstruction results with the optimized residuals to obtain the final reconstruction result. The final reconstruction result is as follows:
[0114] (18)
[0115] In the formula, Indicates by and The reconstructed image obtained by overlay.
[0116] This invention provides a comprehensive evaluation of three publicly available computed tomography (CT) datasets: AAPM, Lung-PET-CT-Dx, and CQ500. Under sparse view conditions of 30 views, 45 views, and 90 views, the method of this invention was compared with existing state-of-the-art sparse view CT reconstruction methods. Peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) were used as evaluation metrics. The comparison results are shown in Table 1.
[0117] Table 1. Results obtained from testing on the CQ500 dataset.
[0118]
[0119] In Table 1, FBP is the filtered back projection algorithm, FBPConvNet is the FBP algorithm based on convolutional neural network, LEARN is the reconstruction network based on expert evaluation learning, WSG is the score generation model based on wavelet improvement, WISM is the multi-channel score diffusion model based on wavelet inspiration, and DCDS is the diffusion sampling method based on dual-domain collaboration. The bold data in Table 1 represents the optimal value of the evaluation index. The test results show that under different datasets and different sparse perspectives, the PSNR and SSIM of the reconstruction results obtained by the method of this invention are better than the comparison methods. The overall quantitative evaluation results are optimal, showing better PSNR and SSIM, and the overall results are optimal.
Claims
1. A sparse CT image reconstruction method based on residual diffusion networks, characterized in that, Includes the following steps: Step 1: Analyze sparse-view CT images; Step 2: Based on the results of the analysis in Step 1, construct a joint optimization model; Step 3: Decompose the joint optimization objective of the joint optimization model into two independent sub-problems, namely the image sub-problem and the residual sub-problem; Step 4: Solve the image subproblem using the image domain diffusion model to obtain intermediate reconstruction results; For the image subproblem, a first auxiliary variable is introduced. The image subproblem is decomposed into the following two parts: （5）； （6）； In the formula, This represents the first auxiliary variable introduced for the image subproblem. In the The result obtained from the next iteration update; Indicates the first The image variables input in the next iteration; Indicates the penalty parameter; In response to The prior regularization function; Indicates the first The image variables are updated in each iteration; To minimize the parameter function; The square of the L2 norm; Represents the CT system matrix; It is the optimized output of the general model; Represents the projected data of the measurement; To balance the hyperparameters of the regularization term; Indicates the first The residual variable obtained from the next iteration update; Equation (5) constructs a prior subproblem related to the variables, which is solved by using an image domain diffusion model. The iterative results generated by the image domain diffusion model are used to learn the relevant prior information. The value depends on Intermediate solutions obtained during the iteration process. and Both are affected by image domain diffusion model prediction and random perturbations; the learned prior information is used to guide the entire optimization process; the prior generation statement for each step is as follows: （7）； In the formula, The first auxiliary variable introduced for the image subproblem In the The result obtained from the next iteration update; For the first The step size parameter corresponding to the next iteration; For parameters The image domain diffusion model scores the input using its score function. For parameters Image domain diffusion model in the first The next iteration is based on the input... The scoring function; Index for iteration count; For random perturbation terms that follow a Gaussian distribution; Equation (6) serves as a data consistency constraint and is solved using a simultaneous iterative reconstruction technique to ensure that the intermediate results of each iteration remain consistent with the initial sparse view projection; the iterative process is as follows: （8）； in, Represents a diagonal matrix. ; This indicates an operation that constructs a diagonal matrix using the elements within the parentheses as diagonal elements; The second norm of a vector; Representing the CT system matrix The row vectors For row index, , Representing the CT system matrix number of rows; express Transpose of; Step 5: Solve the residual subproblem using the residual diffusion model in the wavelet domain to obtain the optimized residual; To address the residual problem, a second auxiliary variable is introduced. The residual subproblem is decomposed into the following two parts: （9）； （10）； In the formula, A second auxiliary variable introduced for the residual subproblem In the The result obtained from the next iteration update; It is the difference between the real image and the image reconstructed by the general model; Indicates the first The residual variable obtained from the next iteration update; Indicates the first The residual variable obtained from the next iteration update; This represents the penalty parameter used to constrain consistency between the residual variable and the second auxiliary variable; In response to The prior regularization function; For equation (9), the residual is decomposed into the wavelet domain, and the high-frequency and low-frequency components are predicted respectively: （11）； （12）； In the formula, express Low-frequency components obtained through wavelet decomposition; express High-frequency components obtained through wavelet decomposition; express Low-frequency components obtained through wavelet decomposition; express High-frequency components obtained through wavelet decomposition; express Low-frequency components obtained through wavelet decomposition; express High-frequency components obtained through wavelet decomposition; Indicates the first The retention coefficients corresponding to the next iteration; Indicates the first The noise scheduling parameters corresponding to the next iteration; Indicates as of the date The cumulative retention coefficient of the next iteration; Indicates by parameters The wavelet domain residual diffusion model characterized in the first... The prediction results of the next iteration for low-frequency components; Indicates by parameters The wavelet domain residual diffusion model characterized in the first... The prediction results of the next iteration for high-frequency components; Indicates the iteration count index; Indicates the first The random disturbance strength parameter corresponding to the next iteration; Represents random noise; in and Guided by this, the residual diffusion model in the wavelet domain predicts the relevant low-frequency and high-frequency residuals, respectively; Then, the inverse wavelet transform is used to obtain the residual prior, expressed as: （13）； In the formula, Indicates inverse wavelet transform; For equation (10), define: （14）； In the formula, Indicates about The objective function value is optimized. Calculate the partial derivative of equation (14) to obtain: （15）； In the formula, express Transpose of; Indicates about The gradient operator; The gradient descent method is used to iteratively solve equation (15): （16）； In the formula, This represents the step size parameter used to control the update magnitude in each iteration; Indicates about The objective function value is optimized. Equation (16) simplifies to: （17）； Step 6: Fuse the intermediate reconstruction results with the optimized residuals to obtain the final reconstruction result.
2. The sparse CT image reconstruction method based on residual diffusion networks according to claim 1, characterized in that, In step 1, the mathematical model of sparse-view CT imaging is expressed as a linear inverse problem: （1）； In the formula, This represents the original, clean CT image. , This is the optimized output of the general model. It is the difference between the real image and the image reconstructed by the general model. Represents the projected data of the measurement; Represents the CT system matrix; This indicates noise in the measurement data.
3. The sparse CT image reconstruction method based on residual diffusion networks according to claim 1, characterized in that, In step 2, the constructed joint optimization model is as follows: （2）； In the formula, For data fidelity items; For regularization terms; For complementary regularization terms; To balance the hyperparameters of the regularization term; The hyperparameters for balancing complementary regularization terms; To minimize the parameter function; This is the output of the general model; The difference between the real image and the reconstructed image The optimal estimation result; The square of the L2 norm; In response to The prior regularization function; In response to The prior regularization function.
4. The sparse CT image reconstruction method based on residual diffusion networks according to claim 3, characterized in that, In step 3, the block coordinate descent algorithm is used to decompose the joint optimization objective into two independent sub-problems, namely the image sub-problem shown in equation (3) and the residual sub-problem shown in equation (4): （3）； （4）； In the formula, Indicates the first The image variables are updated in each iteration; Indicates the first The residual variable obtained from the next iteration update; Indicates the first The residual variable is obtained from the next iteration update.
5. The sparse CT image reconstruction method based on residual diffusion networks according to claim 4, characterized in that, In step 6, the final reconstruction result is: （18）； In the formula, Indicates by and The reconstructed image obtained by overlay.