Method and system for finite angle CT image optimization reconstruction based on denoising diffusion regularization
By using a noise reduction diffusion regularization method, a pre-trained diffusion model, and a separable quadratic substitution algorithm, the problem of poor image quality in finite-angle CT scans was solved, achieving high-quality CT image reconstruction under low doses and improving reconstruction accuracy and detail preservation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Chinese People's Liberation Army Cyberspace Force Information Engineering University
- Filing Date
- 2026-03-17
- Publication Date
- 2026-07-03
Smart Images
Figure CN122336074A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of computed tomography imaging technology, and in particular to a finite-angle CT image optimization and reconstruction method and system based on noise reduction diffusion regularization. Background Technology
[0002] Computed tomography (CT) technology, with its high spatial resolution and rapid imaging capabilities, has become an indispensable medical diagnostic tool in clinical practice. However, in the field of medical CT, the ionizing radiation generated by X-rays poses a potential health risk to patients. Therefore, reducing the radiation dose from CT scans has become an important research direction in medical imaging. Reducing the number of projection angles is one effective way to reduce radiation dose, but it directly leads to incomplete projection data, affecting the quality of reconstructed images.
[0003] In medical chest CT scans, due to the complexity of human anatomy, especially with long shoulders or overlapping tissues in other parts of the chest, the X-ray penetration path may have some missing or overlapping projection data. This phenomenon can lead to limited angle problems during CT image reconstruction.
[0004] Currently, filtered back projection (FBP) algorithms still dominate commercial CT scans. Sidky et al. proposed the classic total variation (TV) algorithm, which uses a total variation regularization term to suppress noise and artifacts in images. However, these algorithms are prone to losing detailed information, affecting the early diagnosis of some diseases. In recent years, deep learning methods have made significant progress in medical CT reconstruction through data-driven feature extraction. However, these methods rely on large-scale labeled datasets, and obtaining high-quality labeled medical image datasets is costly and involves issues such as patient privacy protection.
[0005] Traditional generative models, such as Generative Adversarial Networks (GANs), are prone to problems such as training instability and mode collapse. Images generated by Variational Autoencoders (VAEs) generally suffer from blurred details. In recent years, diffusion models, with their accurate modeling ability for high-dimensional data distributions and powerful image generation and restoration performance, have provided a new technical path for solving the inverse problem of CT image reconstruction. In 2022, Wu et al. proposed the Wavelet Improved Score-Based Generative Model (WSGM), which transfers the diffusion process from the pixel space to the wavelet space, performing targeted diffusion denoising in the wavelet domain. This invention, based on a diffusion model, uses images generated by the diffusion model as implicit priors to achieve high-quality reconstruction of CT images from limited angles. Summary of the Invention
[0006] To address the issues of poor image quality in existing limited-angle CT scans due to reduced projection angles and incomplete projection data, as well as the tendency of traditional reconstruction algorithms to lose details and the reliance of deep learning methods on labeled data, this invention proposes a limited-angle CT image optimization reconstruction method and system based on noise reduction and diffusion regularization, achieving high-quality limited-angle CT image reconstruction under low dose conditions.
[0007] To achieve the above objectives, the technical solution adopted is:
[0008] This invention provides a finite-angle CT image optimization and reconstruction method based on noise reduction and diffusion regularization, comprising the following steps:
[0009] Step 1: Pre-train a diffusion model on a given CT image dataset and use it as an implicit image prior;
[0010] Step 2: Subtract the weighted noise predicted by the diffusion model from the reconstructed image of the current iteration to obtain the estimated image;
[0011] Step 3: Based on the observed projection data and the physical process of CT imaging, the estimated image is updated for data consistency using a separable quadratic substitution algorithm to obtain the physical update term;
[0012] Step 4: Using the first-order diffusion probability model solver, the physical update term and the predicted noise term output by the diffusion model are weighted and sampled to obtain the updated CT image, completing one iteration; repeat steps 2 to 4 until a finite-angle CT reconstruction image that meets the accuracy requirements is obtained.
[0013] According to the finite-angle CT image optimization and reconstruction method based on denoising diffusion regularization of the present invention, the diffusion model in step 1 further includes a forward diffusion process and a reverse denoising process, wherein the forward diffusion process gradually transforms the clean CT image into standard Gaussian noise through a T-step Markov chain, and the reverse denoising process predicts the noise and gradually recovers the image through a neural network.
[0014] According to the finite-angle CT image optimization and reconstruction method based on noise reduction diffusion regularization of the present invention, the transition probability of the forward diffusion process is further expressed as: Where t represents the diffusion step index, This represents the image at step t. This represents the image at step t-1, i.e., the image from the previous step. This indicates that the image from the previous step is known. Under these conditions, the current image The probability distribution, This is a noise scheduling parameter that increases with the number of diffusion steps t. It follows a Gaussian distribution. It is the identity matrix. Let be the mean of the Gaussian distribution at step t. Let be the variance of the Gaussian distribution at step t.
[0015] According to the finite-angle CT image optimization and reconstruction method based on noise reduction diffusion regularization of the present invention, the conditional probability of the reverse denoising process is further expressed as: ,in, Indicates that the current image is known. Under the condition that the previous image The probability distribution, Let be the mean of the Gaussian distribution at step t, which is given by the parameter . The noise predicted by the neural network Calculated Represents the magnitude of variance. It is the identity matrix. Let be the variance of the Gaussian distribution at step t.
[0016] According to the finite-angle CT image optimization and reconstruction method based on noise reduction diffusion regularization of the present invention, the neural network adopts a U-Net with residual connections, which is used as the noise predictor of the diffusion model, and the input of the noise predictor is the image of the current step. Given the diffusion step index t, the output is the predicted noise value. .
[0017] According to the finite-angle CT image optimization and reconstruction method based on noise reduction and diffusion regularization of the present invention, the calculation formula for the estimated image in step 2 is further as follows: Where k represents the iteration round index of CT image reconstruction, This represents the clean image estimate in the k-th iteration. This represents the current image input during the k-th iteration. Represents the cumulative image retention coefficient. , Characterizes the proportion of original structural features retained in the image from the previous step in the k-th iteration. The noise scheduling parameters for each iteration; This represents the noise weighting coefficient for the k-th iteration. This indicates the diffusion model for the current image in the k-th round. The predicted noise value.
[0018] According to the finite-angle CT image optimization and reconstruction method based on noise reduction and diffusion regularization of the present invention, the update formula of the separable quadratic substitution algorithm in step 3 is further as follows: in, This represents the final clean image estimate obtained after data consistency correction in the k-th iteration. This represents the clean image estimate given by the diffusion model prior in the k-th iteration. This represents the current image input during the k-th iteration. This represents the projection data actually measured by the CT scanner. As a relaxation factor, For the system matrix, This is the regularization parameter.
[0019] According to the finite-angle CT image optimization and reconstruction method based on noise reduction diffusion regularization of the present invention, the relaxation factor... The range of values is .
[0020] According to the finite-angle CT image optimization and reconstruction method based on noise reduction and diffusion regularization of the present invention, the weighted sampling update formula in step 4 is further as follows: .
[0021] Furthermore, the present invention also provides a finite-angle CT image optimization and reconstruction system based on noise reduction diffusion regularization, comprising:
[0022] The diffusion model pre-training module is used to pre-train a diffusion model on a given CT image dataset, using it as an implicit image prior.
[0023] An estimated image generation module is used to subtract the weighted noise predicted by the diffusion model from the reconstructed image of the current iteration to obtain an estimated image;
[0024] The physical update term calculation module is used to update the estimated image based on the observation projection data and the CT imaging physical process, and to obtain the physical update term by using a separable quadratic substitution algorithm.
[0025] The weighted sampling iteration module is used to use the first-order diffusion probability model solver to perform weighted sampling on the physical update term and the prediction noise term output by the diffusion model to obtain the updated CT image and complete one iteration.
[0026] The iterative control module is used to control the repeated execution of the estimated image generation module, the physical update term calculation module, and the weighted sampling iteration module until a finite-angle CT reconstruction image that meets the accuracy requirements is obtained.
[0027] The beneficial effects achieved by adopting the above technical solution are:
[0028] This invention introduces a diffusion model as a plug-and-play implicit prior into finite-angle CT image reconstruction, improving the reconstruction accuracy of finite-angle CT images. It can effectively preserve image details, suppress noise and artifacts, and achieve high-quality CT image reconstruction under low dose conditions. The prior term solution only relies on the diffusion model's inverse denoising process, without the need to redesign a complex optimization model, forming a deterministic diffusion posterior sampling reconstruction algorithm, which is more efficient. This invention broadens the practical application prospects of existing low-dose CT reconstruction and significantly improves the reconstruction effect of finite-angle CT images in real-world scenarios. Attached Figure Description
[0029] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments of the present invention will be briefly described below. The drawings are merely illustrative of some embodiments of the present invention and are not intended to limit the scope of the present invention to all embodiments.
[0030] Figure 1 This is a flowchart illustrating the finite-angle CT image optimization and reconstruction method based on noise reduction diffusion regularization according to an embodiment of the present invention.
[0031] Figure 2 This is a diagram illustrating the effect of finite-angle CT image reconstruction according to an embodiment of the present invention;
[0032] Figure 3 Visual comparison of the method of this invention and the FBP method in a finite-angle CT image reconstruction scenario. Detailed Implementation
[0033] The exemplary solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art.
[0034] This invention discloses a finite-angle CT image optimization and reconstruction method based on noise reduction and diffusion regularization, such as... Figure 1 and Figure 2 As shown, it includes the following steps:
[0035] Step S1: Pre-train a diffusion model on a given CT image dataset and use it as an implicit image prior.
[0036] The diffusion model comprises two core processes: forward diffusion and backward denoising, both modeled as T-step Markov chains. The primary purpose of the forward diffusion process is to progressively transform the clean CT image into standard Gaussian noise. Let the clean CT image... ,in This represents the distribution of a clean image. During each diffusion step, the image from the previous step... Injecting Gaussian noise into the image yields the current image. The transition probability of the forward diffusion process is expressed as:
[0037]
[0038] Where t represents the diffusion step index, This represents the image at step t. This represents the image at step t-1, i.e., the image from the previous step. This indicates that the image from the previous step is known. Under these conditions, the current image The probability distribution, These are predefined noise scheduling parameters, and they satisfy... As the number of diffusion steps t increases, As the value gradually increases, the injected noise intensity also increases, and finally, when t=T, the image... Approximating pure Gaussian noise, its distribution Approximately ; It follows a Gaussian distribution. It is the identity matrix. Let be the mean of the Gaussian distribution at step t. Let be the variance of the Gaussian distribution at step t. Based on predefined noise scheduling parameters. Define the single-step image preservation coefficient. Its derivation formula is: , Characterizing the image from the previous step during the t-th step forward diffusion. The proportion of original structural features preserved; further, the cumulative image preservation coefficient is defined. Its derivation formula is: In subsequent iterative reconstruction processes, the diffusion step number index t corresponds to the iteration round index k.
[0039] The goal of the inverse denoising process is to learn the inverse of the forward diffusion process, i.e., to progressively recover the original clean image from Gaussian noise. In the inverse denoising process, it is necessary to estimate the noise level under given conditions. In this case, conditional probability distribution Since the transition probability of the forward diffusion process follows a Gaussian distribution, according to Bayes' theorem, It also approximates a Gaussian distribution, and the conditional probability of the reverse denoising process is expressed as:
[0040]
[0041] in, Indicates that the current image is known. Under the condition that the previous image The probability distribution; Let be the mean of the Gaussian distribution at step t, which is given by the parameter . The noise predicted by the neural network The formula for calculating the mean is as follows: ; Represents the magnitude of variance. It is the identity matrix. Let be the variance of the Gaussian distribution at step t.
[0042] In this embodiment, a U-Net with residual connections is used as the noise predictor in the diffusion model. The U-Net network structure has a symmetrical encoder-decoder structure, which can effectively capture multi-scale features of the image. The introduction of residual connections can alleviate the gradient vanishing problem during the training process of deep neural networks, improving the training stability and convergence speed of the network. The input to the noise predictor is the image of the current step. Given the diffusion step index t, the output is the predicted noise value. .
[0043] Step S2: Subtract the weighted noise predicted by the diffusion model from the reconstructed image of the current iteration to obtain the estimated image.
[0044] Modeling the finite-angle CT reconstruction problem as an optimization problem:
[0045]
[0046] in, For the unknown image to be reconstructed, For the system matrix, The projection data is obtained from actual measurements. For data fidelity, measure the current image. Through physical processes The generated projection and the actual measured projection The smaller the error, the better. The closer the results are to the actual scan results; This is a regularization term (prior term), which applies a constraint to filter out smooth images with clear edges.
[0047] The original problem is decoupled into two subproblems. Subproblem 1 involves prior optimization and requires solving for auxiliary variables. The question takes the following form:
[0048]
[0049] in, This represents the clean image estimate in the k-th iteration. Represents auxiliary variables. This represents the current image input during the k-th iteration. Let denoise the noise reduction intensity in the k-th round of the diffusion denoising process. This is a regularization term. In this embodiment... The specific solution uses the following calculation formula:
[0050]
[0051] Where k represents the iteration round index of CT image reconstruction, This represents the clean image estimate in the k-th iteration. This represents the current image input in the k-th iteration, where... For an explanation, see the cumulative image retention coefficient in step S1. ; This represents the noise weighting coefficient for the k-th iteration. This indicates the diffusion model for the current image in the k-th round. The predicted noise value. This calculation process is based on the current image. The process of subtracting some of the predicted noise is also known as noise reduction for noisy images.
[0052] Step S3: Based on the observed projection data and the CT imaging physical process, the estimated image is updated for data consistency using a separable quadratic substitution algorithm to obtain the physical update term.
[0053] Given a prior estimate Based on the projection data By constraining the measurement data, a reconstructed image that better matches the measurement data can be obtained. The iterative solution is obtained using the Separable Quadratic Surrogate (SQS) algorithm, as shown in the following formula:
[0054]
[0055] in, This represents the final clean image estimate obtained after data consistency correction in the k-th iteration. This represents the clean image estimate given by the diffusion model prior in the k-th iteration. This represents the current image input during the k-th iteration. This represents the projection data actually measured by the CT scanner. The relaxation factor has a range of values of 1000. The preferred value is , For the system matrix, This is the regularization parameter. Calculate the current image Simulated projection and actual measured projection The difference between them, if the difference is large, indicates It does not yet conform to physical measurement; The difference between the current image and the clean image suggested by the diffusion model needs to be calculated, and adjustments need to be made in the direction of the diffusion model.
[0056] Step S4: Using the first-order diffusion probability model solver, the physical update term and the predicted noise term output by the diffusion model are weighted and sampled to obtain the updated CT image, completing one iteration; repeat steps S2 to S4 until a finite-angle CT reconstruction image that meets the accuracy requirements is obtained.
[0057] This embodiment employs a deterministic sampling method based on a first-order diffusion probability model solver (Diffusion Probabilistic Model-Solver, DPM-Solver), that is, it utilizes the physical update term during sampling. Based on the previous round Predicted noise The weighted sampling method, that is: This sampling method in latent space When the determination is made, deterministic reconstruction results will be obtained, which is of great value and significance for medical and industrial imaging.
[0058] Corresponding to the above method, embodiments of the present invention also disclose a finite-angle CT image optimization and reconstruction system based on noise reduction diffusion regularization, comprising:
[0059] The diffusion model pre-training module is used to pre-train a diffusion model on a given CT image dataset, using it as an implicit image prior.
[0060] An estimated image generation module is used to subtract the weighted noise predicted by the diffusion model from the reconstructed image of the current iteration to obtain an estimated image;
[0061] The physical update term calculation module is used to update the estimated image based on the observation projection data and the CT imaging physical process, and to obtain the physical update term by using a separable quadratic substitution algorithm.
[0062] The weighted sampling iteration module is used to use the first-order diffusion probability model solver to perform weighted sampling on the physical update term and the prediction noise term output by the diffusion model to obtain the updated CT image and complete one iteration.
[0063] The iterative control module is used to control the repeated execution of the estimated image generation module, the physical update term calculation module, and the weighted sampling iteration module until a finite-angle CT reconstruction image that meets the accuracy requirements is obtained.
[0064] Figure 3 To verify the feasibility and superiority of the proposed method in real CT limited-angle reconstruction, the CT images reconstructed by this method significantly outperform the comparative algorithms in terms of detail preservation, artifact suppression, and noise reduction. In typical limited-angle scanning scenarios such as 120° and 150°, the image texture is clear, with no obvious stripe artifacts or edge blurring problems, and is closer to the real GT (reference ground truth) image; while the images reconstructed by traditional algorithms such as FBP suffer from severe artifacts and loss of detail.
[0065] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A limited-angle CT image optimization reconstruction method based on denoising diffusion regularization, characterized in that, Includes the following steps: Step 1: Pre-train a diffusion model on a given CT image dataset and use it as an implicit image prior; Step 2: Subtract the weighted noise predicted by the diffusion model from the reconstructed image of the current iteration to obtain the estimated image; Step 3: Based on the observed projection data and the CT imaging physical process, the estimated image is updated for data consistency using a separable quadratic substitution algorithm to obtain the physical update term; Step 4: Using the first-order diffusion probability model solver, the physical update term and the predicted noise term output by the diffusion model are weighted and sampled to obtain the updated CT image, completing one iteration; repeat steps 2 to 4 until a finite-angle CT reconstruction image that meets the accuracy requirements is obtained.
2. The method of finite-angle CT image optimization reconstruction based on denoising diffusion regularization according to claim 1, characterized in that, The diffusion model described in step 1 includes a forward diffusion process and a reverse denoising process. The forward diffusion process uses a T-step Markov chain to gradually convert the clean CT image into standard Gaussian noise, while the reverse denoising process uses a neural network to predict the noise and gradually restore the image.
3. The method of finite-angle CT image optimization reconstruction based on denoising diffusion regularization of claim 2, wherein, The transition probability of the forward diffusion process is expressed as: Where t represents the diffusion step index, This represents the image at step t. This represents the image at step t-1, i.e., the image from the previous step. This indicates that the image from the previous step is known. Under these conditions, the current image The probability distribution, This is a noise scheduling parameter that increases with the number of diffusion steps t. It follows a Gaussian distribution. It is the identity matrix. Let be the mean of the Gaussian distribution at step t. Let be the variance of the Gaussian distribution at step t.
4. The method of finite-angle CT image optimization reconstruction based on denoising diffusion regularization of claim 2, wherein, The conditional probability of the reverse denoising process is expressed as: ,in, Indicates that the current image is known. Under the condition that the previous image The probability distribution, Let be the mean of the Gaussian distribution at step t, which is given by the parameter . The noise predicted by the neural network Calculated Represents the magnitude of variance. It is the identity matrix. Let be the variance of the Gaussian distribution at step t.
5. The method of finite-angle CT image optimization reconstruction based on denoising diffusion regularization of claim 4, wherein, The neural network adopts a U-Net with residual connection, taking it as a noise predictor of the diffusion model, the input of the noise predictor being the image of the current step and the diffusion step index t, and the output being the predicted noise value .
6. The method of finite-angle CT image optimization reconstruction based on denoising diffusion regularization of claim 5, wherein, The formula for calculating the estimated image in step 2 is: Where k represents the iteration round index of CT image reconstruction, This represents the clean image estimate in the k-th iteration. This represents the current image input during the k-th iteration. Represents the cumulative image retention coefficient. , Characterizes the proportion of original structural features retained in the image from the previous step in the k-th iteration. The noise scheduling parameters for each iteration; This represents the noise weighting coefficient for the k-th iteration. This indicates the diffusion model for the current image in the k-th round. The predicted noise value.
7. The method of finite-angle CT image optimization reconstruction based on denoising diffusion regularization of claim 6, wherein, The update formula for the separable quadratic substitution algorithm described in step 3 is: in, This represents the final clean image estimate obtained after data consistency correction in the k-th iteration. This represents the clean image estimate given by the diffusion model prior in the k-th iteration. This represents the current image input during the k-th iteration. This represents the projection data actually measured by the CT scanner. As a relaxation factor, For the system matrix, This is the regularization parameter.
8. The method of finite-angle CT image optimization reconstruction based on denoising diffusion regularization of claim 7, wherein, The relaxation factor is in the range .
9. The method of finite-angle CT image optimization reconstruction based on denoising diffusion regularization of claim 7, wherein, The weighted sampling update formula in Step 4 is: .
10. A finite-angle CT image optimization and reconstruction system based on noise reduction and diffusion regularization, characterized in that, include: The diffusion model pre-training module is used to pre-train a diffusion model on a given CT image dataset, using it as an implicit image prior. An estimated image generation module is used to subtract the weighted noise predicted by the diffusion model from the reconstructed image of the current iteration to obtain an estimated image; The physical update term calculation module is used to update the estimated image based on the observation projection data and the CT imaging physical process, and to obtain the physical update term by using a separable quadratic substitution algorithm. The weighted sampling iteration module is used to use the first-order diffusion probability model solver to perform weighted sampling on the physical update term and the prediction noise term output by the diffusion model to obtain the updated CT image and complete one iteration. The iterative control module is used to control the repeated execution of the estimated image generation module, the physical update term calculation module, and the weighted sampling iteration module until a finite-angle CT reconstruction image that meets the accuracy requirements is obtained.