A method for simultaneously sparse angle CT reconstruction and high-precision correction of metal artifacts

Abstract

The application discloses a kind of simultaneously sparse angle CT reconstruction and metal artifact high-precision correction method, belong to medical imaging field, specifically: simulate the projection data under the influence of beam hardening under sparse angle sampling, obtain sparse sampling and the sinogram of containing metal trace;Interpolation processing is carried out to sparse sinogram, and the sinogram is obtained as the initial sinogram of sinogram domain;According to the additive property of artifact, preliminarily decompose the CT image containing a large number of artifacts, obtain the initial estimated image of image domain and the initial artifact image of artifact domain;A multi-domain optimization model is established, and the constructed multi-domain optimization problem is alternately iterated minimization solution;Iterative update is carried out to sinogram domain, image domain and artifact domain respectively;The high-precision CT image of reconstruction is output.The application can simulate the sinogram containing metal trace and sparse obtained by CT imaging equipment to carry out simultaneously sparse angle CT reconstruction and metal artifact correction, and the reconstruction effect is good and correction precision is high.

Description

Technical Field

[0001] This invention belongs to the field of medical imaging, and is specifically designed to simultaneously solve the problems of sparse angle CT reconstruction and metal artifact correction, and can be used in CT imaging systems. Background Technology

[0002] Computed tomography (CT) is a non-invasive imaging technique widely used in clinical, biological, and medical fields, allowing for direct observation of the internal structure of objects. CT images affected by metallic implants exhibit structured and non-localized metal artifacts. Furthermore, sparse-view CT (SVCT) scanning is commonly used clinically to reduce the risk of cancer and scan time; this involves obtaining projection data through a larger-than-normal viewing interval. This inevitably leads to severe streak artifacts and exacerbates metal artifacts, thus limiting subsequent clinical diagnosis and treatment. Therefore, with the widespread clinical application of metallic implants and the pursuit of reducing CT radiation dose, reconstructing high-precision CT images for patients with metallic implants under sparse-view conditions is a crucial issue in medical imaging.

[0003] Currently, research on simultaneously solving the sparse-view and metal artifact reduction (SVMAR) problem in sparse-angle CT reconstruction is in its early stages. Existing SVMAR methods fall into two categories: deep learning methods based on two domains and recursive network methods based on two domains and their data consistency layers. Although both attempts have achieved relatively satisfactory solutions to the SVMAR problem compared to existing standalone MAR and SVCT methods, the two-domain knowledge is not fully embedded in the network architecture and training, resulting in incomplete preservation of detailed information in the reconstructed image and room for improvement in correction performance. Theoretically, the two deep learning methods mentioned above focus on network architecture design. Due to the empirical design and black-box nature of data-driven networks, such network architectures lack model interpretability. In sparse-angle CT scanning, insufficient artifact correction and missing tissue structure information are technical bottlenecks limiting the application of existing SVMAR algorithms to practical CT imaging systems.

[0004] In summary, although there are numerous existing independent sparse angle CT reconstruction methods and CT metal artifact correction methods, each has its own limitations in simultaneously addressing these two tasks. Therefore, based on existing SVMAR methods, a high-precision sparse angle CT metal artifact correction method is proposed to achieve a significant improvement in image quality. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the existing technologies by proposing a deep unfolding method based on multi-domain knowledge to simultaneously solve the problems of sparse angle CT reconstruction and metal artifact correction, thereby improving artifact correction accuracy, restoring rich tissue detail information, and providing a model interpretability for the network architecture.

[0006] A method for simultaneous sparse angle CT reconstruction and high-precision correction of metal artifacts includes the following steps:

[0007] S1, simulates the projection data affected by beam hardening under sparse angle sampling, that is, obtains a sine pattern with sparse sampling and metal traces.

[0008] S2, interpolate the sparse sine graph to obtain a sine graph of the full sampling size, and use this sine graph as the initial sine graph of the sine domain;

[0009] S3. Based on the additivity property of artifacts, the CT image containing a large number of artifacts is initially decomposed to obtain the initial estimated image in the image domain and the initial artifact image in the artifact domain.

[0010] S4. Establish a multi-domain optimization model and solve the constructed multi-domain optimization problem by alternating iterative minimization.

[0011] S5 iteratively updates the sinusoidal domain, image domain, and artifact domain respectively;

[0012] S6 outputs reconstructed high-precision CT images.

[0013] A further improvement to the technical solution of this invention is as follows: In step S1, SVCT data acquisition is simulated. First, an X-ray beam is simulated to perform sparse angle scanning on the test object containing a metal implant. Second, the intensity of the radiation is attenuated to different degrees during the penetration process. Finally, the detector receives highly incomplete projection data. It is stipulated that projection data of size 360×641 is the full-sampled projection data, that is, 360 projection views are uniformly sampled between 0 and 360 degrees. Projection data with undersampling rates of ×6, ×4, and ×2 are obtained by downsampling, that is, the projection view sizes are 60×641, 90×641, and 180×641, respectively.

[0014] A further improvement of the technical solution of the present invention is that the main features of the projection data of the sparse angle CT equipment imaging system in step S1 are: the y-axis of the projection data represents the number of projection views, and the x-axis of the projection data represents the number of detector elements.

[0015] A further improvement of the technical solution of the present invention is that: step S2 obtains full-view acquisition data y by preprocessing the measured projection data y. a The interpolation model is described as y a=U(y), where U(·) increases the number of projection angles by zero-padding the input sine graph, restoring it to the size of the fully sampled sine graph. The metallic trace of the sine graph is corrected using the linear interpolation LI method to obtain the initial input sine graph. Its formula is

[0016] A further improvement to the technical solution of the present invention is that: step S3 uses filtered back projection (FBP) to obtain the sine graph y a Obtain CT images with severe artifacts x a , represented as x a =FBP(y a Based on the additive nature of metal artifacts, CT images affected by artifacts can be decomposed into underlying images and artifact images. Therefore, x a It can be further decomposed into its underlying CT image and artifact image; the CT image of a metallic implant has two regions: the metallic part and the non-metallic part. Since metal usually has a higher CT value than normal tissue, the decomposition model can be derived as follows: Where m is a binary non-metallic mask, with 0 for the metallic mask region and 1 for the other regions. It is an artifact-free CT image at the bottom layer. This is an artifact image, where ⊙ represents element-wise product. Through the above image preprocessing steps, initial input images in the sine domain, image domain, and artifact domain are obtained. and

[0017] A further improvement to the technical solution of this invention lies in: the establishment of the multi-domain optimization model in step S4: the normalized sine curve affected by the metal is uniform; a corrected normalized sine curve is selected, resulting in a clean sine curve. It can be written as in These are the normalized coefficients obtained from the previous sine curve. This is the normalized sine curve, and the multi-domain SVMAR optimization problem is formulated as follows:

[0018]

[0019] Where m is a binary metallic mask, with 0 for metallic regions and 1 for non-metallic regions; tr is a binary metallic trace mask, with 1 for metallic projection regions and 0 for non-metallic projection regions; P is the Radon transform, forward projection; and A is a binary sparse sampling matrix, where the sparsely sampled parts are 1 and the unsampled parts are 0. Let ||·||1 be the normalization coefficient, ||·||1 represent the l1 norm, and the compact frame W satisfies the compact property.

[0020] A further improvement to the technical solution of the present invention is that step S5 specifically involves the following process:

[0021] The defined multi-domain SVMAR optimization problem is solved using an alternating iterative method, and each subproblem is solved using a proximal operator. At the (t+1)th iteration, and Alternating updates are as follows:

[0022] fixed renew

[0023]

[0024] After performing a quadratic approximation on the above equation and expressing it using the proximal operator, we obtain:

[0025]

[0026] in For the proximal operator associated with the regularization term R1(·).

[0027] fixed renew

[0028]

[0029] Similarly, The update rule is written as

[0030]

[0031] in The tight frame W satisfies the tight property Therefore, equation (5) can be expressed as

[0032]

[0033] Where soft(u,ε)=sign(u)max(|u|-ε,0) is the soft thresholding function, and ε=γ2η2 is the threshold. In this invention, a deep thresholding network (DTN) is used to adaptively determine the threshold from the coefficients of the artifact image, i.e. f(·) represents the proposed DTN.

[0034] fixed renew

[0035]

[0036] Similarly, The update rule is written as

[0037]

[0038] in

[0039] A further improvement to the technical solution of this invention lies in: embedding multi-domain knowledge, including the sine domain, image domain, artifact domain, and coding domain, into the multi-domain optimization model and network training, and designing a loss function based on multi-domain knowledge as follows:

[0040]

[0041] Where y gt It is a clean sine graph, x gt It is a real CT image, and the artifact baseline image is e. gt =x a -x gt Meanwhile, ω1, ω2, ω3, ω4, and ω5 are five trade-off parameters. To learn the compact frame W, the first term imposes compactness on the frame to be learned, while the second term imposes coding domain constraints to promote sparsity of artifact images on the compact frame. The third and fourth terms use the L2 and L1 losses between the network output and the clean image as image domain constraints. Furthermore, the fifth and sixth terms use L1 and L2 losses as artifact domain constraints and sinusoidal domain constraints, respectively. By combining knowledge from the image domain, artifact domain, and sinusoidal domain, high-quality CT images are reconstructed. In the artifact domain, a compact frame network with adaptive thresholding is used, and the coding domain constraints are used to recover detailed structural information of artifacts to achieve high-quality reconstruction.

[0042] A further improvement of the technical solution of the present invention is that: in step S4, the constructed multi-domain optimization problem is solved. An important feature of this step is that the problem is solved by an alternating iterative algorithm and decomposed into three sub-problems. The constructed optimization sub-problems are solved by using quadratic approximation and proximal operators. In view of the interpretability of traditional iterative algorithms and the good learning ability of deep learning, the iterative algorithm is expanded into a deep neural network. Each expansion corresponds to each iteration of the traditional iterative algorithm. At the same time, each layer is constructed by a deep neural network. In the sinusoidal domain and the image domain, multiple residual blocks are stacked. The artifact domain adopts a compact frame representation model with adaptive threshold. The above alternating iterative algorithm is expanded into a network. The network consists of T stages, corresponding to the T iterations of the iterative algorithm. Each stage includes Y-Net, E-Net and X-Net.

[0043] in, and The Y-Net, E-Net, and X-Net are updated based on Equations (3), (5), and (8), respectively. Y-Net and X-Net contain multiple residual blocks, and E-Net is a tight frame representation network that includes a depth thresholding network derived from an adaptively determined threshold.

[0044] Due to the adoption of the above technical solution, the technical effects achieved by the present invention are as follows:

[0045] A multi-domain optimization model is constructed based on simulated, highly incomplete projection data for simultaneous sparse-view and metal artifact reduction (SVMAR). The constructed optimization model is an optimization problem based on knowledge from the sinusoidal, image, and artifact domains. This method uses an alternating iterative minimization method to solve the constructed optimization model and unfolds the iterations into a network, constructing a deep unfolded SVMAR network. In the artifact domain, a compact frame representation model with stronger representational capabilities is used, and the representational capability is further improved and the network convergence speed is accelerated by constructing an encoding domain, fully utilizing multi-domain knowledge for high-precision artifact correction. Because the knowledge from the sinusoidal, image, artifact, and encoding domains is fully utilized and embedded in the network training process, the method of this invention can utilize multi-domain information and the rich structural characteristics of artifact images to perform simultaneous sparse-view CT reconstruction and high-precision metal artifact correction. Attached Figure Description

[0046] Figure 1 This is the overall flowchart of the depth unfolding method of the present invention based on multi-domain knowledge for simultaneous sparse angle CT reconstruction and metal artifact correction.

[0047] Figure 2 This is a schematic diagram of the CT sampling device for simulating the presence of metal implants and sparse angles according to the present invention;

[0048] Figure 3 This is a schematic diagram of the analog data sampling device of the present invention obtaining sparsely sampled projection data containing metallic traces;

[0049] Figure 4 This is a schematic diagram of the preprocessing operation of the highly incomplete sine curve in this invention;

[0050] Figure 5 This is a flowchart of the high-precision artifact correction depth unfolding algorithm based on multi-domain knowledge in this invention;

[0051] Figure 6 The figure shows the simulation results obtained by the high-precision artifact correction algorithm according to the present invention. Detailed Implementation

[0052] The following, in conjunction with the accompanying drawings, clearly and completely describes the implementation steps of the present invention's method for simultaneous sparse angle CT reconstruction and high-precision correction of metal artifacts based on multi-domain knowledge, as well as the depth unfolding algorithm. Experimental simulation diagrams illustrate the effectiveness of the method. See also... Figure 1 The specific steps of the present invention for a method of simultaneous sparse angle CT reconstruction and high-precision correction of metal artifacts using multi-domain knowledge are as follows:

[0053] S1. Simulating Sparsely Sampling Projection Data: Using the DeepLesion dataset, we simulate projection data affected by beam hardening under sparse angular sampling. We define 360×641 pixels as the full-sample projection data, meaning 360 projection views are uniformly sampled between 0 and 360 degrees. We obtain projection data with undersampling rates of ×6, ×4, and ×2 through downsampling, resulting in projection view sizes of 60×641, 90×641, and 180×641 pixels, respectively.

[0054] The acquisition principle of sparse angle CT is as follows Figure 2 As shown, the main components include an X-ray source, the object to be observed (containing metal, marked in red), and a detector. Sparse angle sampling involves uniform sampling at intervals greater than the normal view interval to accelerate acquisition and reduce radiation dose. Using the traditional FBP algorithm to directly reconstruct the measurement data results in CT images with severe metal artifacts and numerous stripe artifacts. Our goal is to design a reconstruction network to obtain high-precision artifact-corrected images. Figure 3 The simulation process of sparse projection data is shown. Figure 3 The left-hand image shows a highly imperfect sine curve y obtained by uniformly sampling a fully sampled sine curve. Figure 3 As shown in the diagram on the right.

[0055] S2, Image preprocessing steps (such as...) Figure 4 (As shown): First, the measured sparse view projection data is preprocessed by interpolating the measured projection data y to obtain the full-view acquisition data y. a The interpolation model can be described as y a =U(y), where U(·) expands the number of projection angles by zero-padding the input sine graph, restoring it to the size of a fully sampled sine graph. Then, the metallic traces of the sine graph are corrected using a linear interpolation (LI) method to obtain the sine graph of the initial input. Its formula is

[0056] On the other hand, filtered back projection (FBP) is used to extract the sine curve y a Obtain CT images with severe artifacts x a Mathematically speaking, this can be represented as x a =FBP(ya Based on the additive nature of metal artifacts, CT images affected by artifacts can be decomposed into a sub-image and an artifact image. Based on this definition, x a It can be further decomposed into its underlying CT image and artifact image. CT images of metallic implants are observed to have two regions: the metallic portion and the non-metallic portion. Since metal typically has a higher CT value than normal tissue, this invention focuses on the non-metallic region. Therefore, the decomposition model can be derived as follows: Where m is a binary non-metallic mask (metallic mask regions are equal to 0, other regions are equal to 1), It is an artifact-free CT image at the bottom layer. This is an artifact image, and ⊙ represents element-wise product. Through the above image preprocessing steps, initial input images in the sine domain, image domain, and artifact domain are initially obtained. and

[0057] S3. Establishment of the Multi-Domain Optimization Model: Typically, the normalized sine curve affected by metals is uniform; therefore, this invention chooses a corrected normalized sine curve instead of the original sine curve. Formally, a clean sine curve... It can be written as in These are the normalized coefficients obtained from the previous sine curve. This is a normalized sine wave. To obtain a better solution, this invention applies a regularization term representing prior knowledge. Therefore, the multi-domain SVMAR optimization problem can be formulated as follows:

[0058]

[0059] Where m is a binary metallic mask (where metallic regions are 0 and non-metallic regions are 1), tr is a binary metallic trace mask (where metallic projection regions are 1 and non-metallic projection regions are 0), P is the Radon transform (forward projection), and A is a binary sparse sampling matrix (where the sparsely sampled parts are 1 and the unsampled parts are 0). Let ||·||1 be the normalization coefficient, ||·||1 represent the l1 norm, and the compact frame W satisfies the compact property.

[0060] S4. Solving the optimization problem:

[0061] The defined multi-domain SVMAR optimization problem is solved using an alternating iterative method, and each subproblem is solved using the proximal operator. In the (t+1)th iteration, and Alternating updates are as follows:

[0062] <1> fixed renew

[0063]

[0064] After performing a quadratic approximation on the above equation and expressing it using the proximal operator, we obtain:

[0065]

[0066] in For the proximal operator associated with the regularization term R1(·).

[0067] <2> fixed renew

[0068]

[0069] Similarly, The update rule is written as

[0070]

[0071] in The tight frame W satisfies the tight property Therefore, equation (5) can be expressed as

[0072]

[0073] Where soft(u,ε)=sign(u)max(|u|-ε,0) is the soft thresholding function, and ε=γ2η2 is the threshold. In this invention, a deep thresholding network (DTN) is used to adaptively determine the threshold from the coefficients of the artifact image, i.e. f(·) represents the proposed DTN.

[0074] <3> fixed renew

[0075]

[0076] Similarly, The update rule is written as

[0077]

[0078] in

[0079] Loss Function: Based on the aforementioned method for simultaneous sparse angular CT reconstruction and high-precision correction of metal artifacts using multi-domain knowledge, a tight-frame representation model with stronger representation capabilities is utilized in the artifact domain. Furthermore, the representation capability is enhanced and the network convergence speed is accelerated by constructing an encoding domain, fully leveraging multi-domain knowledge for high-precision artifact correction. To embed multi-domain (sine domain, image domain, artifact domain, and encoding domain) knowledge into the network architecture and training, a loss function based on multi-domain knowledge is carefully designed as follows:

[0080]

[0081] Where y gt It is a clean sine graph, x gt It is a real CT image, and the artifact baseline image is e. gt =x a -x gt Meanwhile, ω1, ω2, ω3, ω4, and ω5 are five trade-off parameters. To learn the compact frame W, the first term imposes compactness properties on the frame to be learned, while the second term imposes coding domain constraints to promote sparsity of artifact images on the compact frame. The third and fourth terms use the l2 and l1 losses between the network output and the clean image as image domain constraints. Furthermore, the fifth and sixth terms use l1 and l2 losses as artifact domain constraints and sine domain constraints, respectively. High-quality CT images are reconstructed by combining knowledge from the image domain, artifact domain, and sine domain, where a compact frame network with adaptive thresholding is used in the artifact domain, and detailed structural information of artifacts is recovered using coding domain constraints to achieve high-quality reconstruction. Due to the full utilization and embedding of knowledge from the sine domain, image domain, artifact domain, and coding domain into the network training process, the method of this invention can utilize information from multiple domains and the rich structural characteristics of artifact images for simultaneous sparse angular CT reconstruction and high-precision correction of metal artifacts.

[0082] Network Architecture Construction: In step S4, the constructed multi-domain optimization problem is solved. A key feature of this step is the use of an alternating iterative algorithm to solve the problem and decompose it into three sub-problems. Quadratic approximation and proximal operators are then used to solve the constructed optimization sub-problems. Simultaneously, considering the interpretability of traditional iterative algorithms and the strong learning capabilities of deep learning, the iterative algorithm is unfolded into a deep neural network. Each unfolding corresponds to each iteration of the traditional iterative algorithm, and each layer is constructed using a deep neural network. Therefore, the deep unfolded network of this invention not only inherits the interpretability of traditional model-based algorithms but also benefits from the powerful learning capabilities of deep neural networks. Specifically, the sine domain and image domain use multiple stacked residual blocks, and the artifact domain uses a compact frame representation model with adaptive thresholds. The alternating iterative algorithm is unfolded into a network consisting of T stages, corresponding to the T iterations of the iterative algorithm. Each stage includes a Y-Net, an E-Net, and an X-Net. Figure 5 A flowchart of the high-precision artifact correction algorithm based on multi-domain knowledge proposed in this invention is presented, showing the data flow within and between each stage. Multi-domain information is transferred between and within each stage, enabling features from multiple domains to interact and mutually reinforce each other. This interaction of multi-domain information facilitates the reconstruction of valuable details. and The Y-Net, E-Net, and X-Net are updated based on Equations (3), (5), and (8), respectively. Y-Net and X-Net contain multiple residual blocks, and E-Net is a tight frame representation network that includes a depth thresholding network derived from an adaptively determined threshold.

[0083] The following simulation results illustrate the effectiveness of the proposed method for simultaneous sparse angle CT reconstruction and high-precision correction of metal artifacts based on multi-domain knowledge.

[0084] Figure 6 The results demonstrate the visual reconstruction using the method of this invention with sparse views at sparse sampling rates of ×4 and ×6, employing metal implants from large to small. Generally, large metal implants are more difficult to repair than small ones. This invention achieves excellent results in repairing metal implants of different sizes. The reconstructed images remove a significant number of artifacts while still clearly preserving tissue information and bone structure, facilitating clinical diagnosis and treatment. The simulation results clearly demonstrate that the artifact correction method for SVMAR tasks provided by this invention can achieve high-precision artifact correction even with sparse angular sampling and the presence of metal implants.

[0085] To accurately analyze the effectiveness of the proposed method, peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and root mean square error (RMSE) were used to qualitatively evaluate the method. Table 1 lists the PSNR, SSIM, and RMSE values ​​for the sparse-angle CT metal artifact correction algorithm under three different sparse view settings, with undersampling rates of ×6, ×4, and ×2, respectively. The best results are highlighted in bold. It can be seen that the proposed method achieves the best PSNR, SSIM, and RMSE under all three different sparse view settings, demonstrating its feasibility and versatility. Furthermore, we can observe that the deep learning-based dual-domain SVMAR method significantly outperforms the single-domain correction method, illustrating the importance of domain knowledge mining for simultaneously solving sparse view and metal artifact correction tasks. In contrast, the deep unfolding multi-domain method proposed in this invention fully utilizes multi-domain knowledge and shows advantages in the SVMAR task.

[0086] Table 1

[0087]

[0088] Compared with the prior art, the present invention has the following advantages:

[0089] 1) Based on the principle of sparse angle CT imaging, this invention designs a multi-domain knowledge-based SVMAR system. Compared with existing SVMAR systems, this invention can reconstruct CT images with better accuracy and richer details from highly incomplete sine waves using multi-domain knowledge. It should be emphasized that this invention is the first to apply depth unfolding technology to the field of SVMAR, and the network model designed in this invention is interpretable.

[0090] 2) This invention addresses the simultaneous problems of sparse angle CT reconstruction and metal artifact correction. It leverages multi-domain knowledge to achieve high-precision artifact correction through an iteratively optimized algorithm. Compared to deep learning-based SVMAR methods, it can reconstruct the detailed structure of the image, improving reconstruction quality and achieving high-precision artifact correction.

[0091] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and detail without departing from the principles and structure of the present invention; however, these modifications and changes based on the spirit of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A method for simultaneous sparse angle CT reconstruction and high-precision correction of metal artifacts, characterized in that... Includes the following steps: S1, simulates the projection data affected by beam hardening under sparse angle sampling, that is, obtains a sine pattern with sparse sampling and metal traces. S2, interpolate the sine pattern to obtain a sine pattern of the full sampling size, and use this sine pattern as the initial sine pattern of the sine domain; S3. Based on the additivity property of artifacts, the CT image containing a large number of artifacts is initially decomposed to obtain the initial estimated image in the image domain and the initial artifact image in the artifact domain. S4. Establish a multi-domain optimization model and solve the constructed multi-domain optimization problem by alternating iterative minimization. Establishment of the multi-domain optimization model: The normalized sine curve affected by the metal is uniform. A corrected normalized sine curve is selected, resulting in a clean sine curve. Written ,in These are the normalized coefficients obtained from the previous sine curve. This is the normalized sine curve, and the multi-domain SVMAR optimization problem is formulated as follows: （1） in This is a binary metallic trace mask, where the metallic projection area is 1 and the non-metallic projection area is 0. This is the Radon transformation, also known as forward projection. This is a binary sparse sampling matrix, where the sparsely sampled portions are represented by 1s and the unsampled portions by 0s. The normalization coefficient is... Describe the l1 norm and the tight frame Satisfy tight property ; S5 iteratively updates the sinusoidal domain, image domain, and artifact domain respectively; The specific process is as follows: The defined multi-domain SVMAR optimization problem is solved using an alternating iterative method, and each subproblem is solved using the proximal operator. At the (t+1)th iteration, , and Alternating updates are as follows: fixed , ,renew : （2） After performing a quadratic approximation on the above equation and expressing it using the proximal operator, we obtain: （3） in , To be consistent with regularization terms Related proximal operators; fixed , ,renew : （4） The update rule is written as: （5） in The tight frame W satisfies the tight property. Therefore, equation (5) can be expressed as: （6） in It is a soft threshold function. It is a threshold; a deep thresholding network is used to adaptively determine the threshold from the coefficients of the artifact image, i.e. , This represents the proposed deep thresholding network; fixed , ,renew : （7） The update rule is written as: （8） in ; S6 outputs reconstructed high-precision CT images.

2. The method for simultaneous sparse angle CT reconstruction and high-precision correction of metal artifacts according to claim 1, characterized in that: In step S1, SVCT data acquisition is simulated. First, the X-ray beam is simulated to perform sparse angle scanning on the test object containing the metal implant. Second, the intensity of the X-ray is attenuated to different degrees during the penetration process. Finally, the detector receives highly incomplete projection data. It is stipulated that the projection data of size 360×641 is the full sampling projection data, that is, 360 projection views are uniformly sampled between 0 and 360 degrees. The undersampling rate of ×6, ×4 and ×2 is obtained by downsampling, that is, the projection view sizes are 60×641, 90×641 and 180×641 respectively.

3. The method for simultaneous sparse angle CT reconstruction and high-precision correction of metal artifacts according to claim 2, characterized in that: The main features of the projection data based on the sparse angle CT imaging system in step S1 are: the y-axis of the projection data represents the number of projection views, and the x-axis of the projection data represents the number of detector elements.

4. The method for simultaneous sparse angle CT reconstruction and high-precision correction of metal artifacts according to claim 1, characterized in that: Step S2 involves preprocessing the measured projection data to obtain full-view acquisition data. The interpolation model is described as follows: ,in The number of projection angles is increased by zero-padding the input sine curve to restore it to the size of a fully sampled sine curve. The metallic traces in the sine curve are then corrected using the linear interpolation LI method to obtain the sine curve of the initial input. Its formula is .

5. The method for simultaneous sparse angle CT reconstruction and high-precision correction of metal artifacts according to claim 4, characterized in that: Step S3 uses filtered back projection (FBP) to obtain a CT image with severe artifacts from the sine wave. , represented as Based on the additivity property of metal artifacts, CT images affected by artifacts can be decomposed into underlying images and artifact images. The decomposition process involves the underlying CT image and artifact images. The CT image of a metallic implant has two regions: the metallic portion and the non-metallic portion. Since metal has a higher CT value than normal tissue, the decomposition model is derived as follows: ,in It is a binary non-metallic mask, where the metallic mask area is equal to 0, and the other areas are equal to 1. It is an artifact-free CT image at the bottom layer. It is an artifact image. Representing element-wise product, the above image preprocessing steps yield the initial input images in the sine domain, image domain, and artifact domain.

Images