A sparse-angle CT reconstruction method based on sinespace and image space

Abstract

The present application belongs to the technical field of X-ray computed tomography, and particularly relates to a sparse-angle CT reconstruction method based on a sinusoidal domain and an image domain; the method comprises the following steps: collecting sparse-angle sinogram training data sets to train a sparse-angle CT reconstruction network model based on a sinusoidal domain and an image domain; inputting the sparse-angle sinogram into the trained sparse-angle CT reconstruction network model to obtain a repaired full-angle sinogram and a reconstructed CT image; constructing a CT image reconstruction objective equation, taking the repaired full-angle sinogram and the reconstructed CT image as a prior regular constraint of the CT image reconstruction objective equation, iteratively optimizing the CT image reconstruction objective equation, and solving the high-precision reconstructed CT image by using a least square method; in view of the network model generalization, robustness and data consistency problems, the present application integrates the network output as a deep prior into the iterative reconstruction, and further improves the quality of the reconstructed CT image.

Description

Technical Field

[0001] The present invention belongs to the technical field of X-ray computed tomography (CT), and in particular relates to a sparse angle CT reconstruction method based on the sine domain and the image domain. Background Art

[0002] Due to their high resolution and high sensitivity, CT images are widely used in clinical diagnosis, non-destructive testing, and biological research. With the continuous development of medical CT technology, people are demanding faster, safer, and more accurate CT technology. However, the high-dose radiation from CT may pose potential hazards to the human body, and long-term, high-frequency scanning further increases the hazard. Currently, the radiation dose can be reduced by reducing the current intensity (low-dose CT) and reducing the number of sampling times (sparse angle CT), but this destroys the integrity of the projection data, and the quality of images directly reconstructed by traditional reconstruction algorithms will be severely degraded. Therefore, how to reduce the radiation dose while ensuring the quality of the reconstructed image has become a hot topic in CT research in recent years.

[0003] In recent years, researchers have proposed data-driven sparse projection CT reconstruction techniques, which replace mathematical statistical models with data-driven or adaptive models (dictionary learning, sparse transformation, tensor transformation) to train model parameters using both real and undersampled data to reconstruct CT images. This type of technology is further divided into learning-based adaptive model techniques and deep learning techniques. The sparse projection CT reconstruction method based on deep learning first uses the filtered back projection algorithm (FBP) to generate a noisy image from the sparse sinusoidal image, and then compares it with the noise-free labeled image to learn the artifact distribution. The Image Science and Technology Laboratory of Southeast University proposed a sparse projection reconstruction hybrid neural network that uses deep learning to simultaneously denoise the projected sinusoidal data and the reconstructed image, ultimately obtaining a reconstructed image. Although this method fully considers streak artifacts in the image domain, it only considers image domain information and not the projected sinusoidal domain information. In the case of high noise or severe lack of projection data, it is difficult to obtain satisfactory reconstruction results. To address this issue, the Computer and Information Laboratory of Anhui University of Technology proposed a hybrid dual-domain reconstruction method for cone-beam CT sparse projections. This method considers both sinusoidal and image domain information, but it does not consider the consistency between the two domains, which can lead to secondary artifacts during the reconstruction process. Furthermore, this work lacks constraints on deep neural network feature generation, which can cause structural features outside the target CT image to appear in the reconstructed image, leading to extremely serious problems. Furthermore, the robustness and generalizability of this method remain to be verified. Summary of the Invention

[0004] To solve the above problems, the present invention provides a sparse angular CT reconstruction method based on the sine domain and image domain. The CT reconstruction method takes into account the introduction of sine domain and image domain priors in the iterative model, so as to obtain stable high-quality CT reconstruction results with good robustness and generalization.

[0005] The specific scheme of the present invention is:

[0006] S1. Collecting a sparse angle sinusoidal training data set, the sparse angle sinusoidal training data set includes a sparse angle sinusoidal atlas and its corresponding label data set;

[0007] S2. Construct a sparse angle CT reconstruction network model based on the sine domain and image domain, and train the sparse angle CT reconstruction network model using a sparse angle sinusoidal training dataset until the model converges;

[0008] S3. Input the sparse angle sinusoidal graph into the trained sparse angle CT reconstruction network model to obtain the repaired full angle sinusoidal graph and the reconstructed CT image;

[0009] S4. Construct the CT image reconstruction target equation, use the repaired full-angle sinusoidal image and reconstructed CT image as the prior regularization constraints of the CT image reconstruction target equation, iteratively optimize the CT image reconstruction target equation, and use the least squares method to solve it to obtain a high-precision reconstructed CT image.

[0010] Furthermore, the process of collecting the sparse angle sinusoidal graph training data set in step S1 includes:

[0011] S11. For the object to be measured, fan beam geometry CT is used with 0, For a half-turn of the initial angle, 23,800 first sinusoidal images were collected, each containing 180 projections;

[0012] S12. Each first sinusoidal image is intercepted to obtain a corresponding sparse angle sinusoidal image, each sparse angle sinusoidal image contains 60 projections;

[0013] S13. The first sinusoidal graph is used as label data, and the label data is compared with the sparse angle sine graph. Figure 1 A sparse angular sinusoidal graph training dataset is obtained one by one, and the sparse angular sinusoidal graph training dataset is divided into a training set, a validation set, and a test set in a ratio of 7:2:1.

[0014] Furthermore, in step S2, the sparse angle CT reconstruction network model includes a projection recovery network, a filtered back projection reconstruction layer, and an image enhancement network. The training process of the sparse angle CT reconstruction network model based on the sine domain and the image domain includes the following steps:

[0015] S21. Interpolate the sparse angle sinusoidal graph S by linear interpolation method and use its corresponding label data S R Assign values ​​to the pixels at the interpolation position to obtain the interpolated and completed full-angle sinusoidal graph S L ;

[0016] S22. The full angle sinusoidal graph S L Input into the projection restoration network to obtain the restored full-angle sinusoidal graph S out ;

[0017] S23. Construct the first loss function and calculate the label data S R Compared with the repaired full angle sinogram S out Repair losses;

[0018] S24. The repaired full angle sinogram S out As input, the intermediate reconstructed CT image X is obtained through the filtered back projection reconstruction layer out ; Use FBP algorithm to label data S R Perform back projection to obtain the label CT image X label ;

[0019] S25. Construct the second loss function and calculate the intermediate reconstructed CT image X out CT image with label X label The filtered back-projection reconstruction loss;

[0020] S26. Reconstruct the intermediate CT image X out CT image with label X label Input them together into the image enhancement network for confrontation to obtain the enhanced reconstructed CT image X;

[0021] S27. Construct the third loss function and calculate the enhanced reconstructed CT image X and the label CT image X label The generation loss and adversarial loss between them.

[0022] Furthermore, the projection restoration network described in step S22 includes a sub-attention mechanism and a residual convolution block; the residual convolution block includes two convolution layers with a convolution kernel size of 3x3, a residual convolution layer with a kernel size of 1x1, two group normalization layers with a group number of 8 and an addition layer, and the activation function used in the residual convolution block is swish.

[0023] Furthermore, step S23 constructs a first loss function based on the sinogram label and the corresponding restored full-angle sinogram, which is expressed as:

[0024] L E =||S out -S R||1=||E ω (S L )-S R ||1

[0025] Among them, E ω () represents the projection recovery network.

[0026] Furthermore, in step S24, the intermediate reconstructed CT image X is obtained by filtering the back projection reconstruction layer. out The process includes:

[0027] S51. The full-angle sinusoidal graph X repaired in step S22. out The physical geometric information of the fan beam is converted into a parallel beam projection to obtain the first repaired full-angle sinusoidal graph S out1 ;

[0028] S52. Repair the first full angle sinusoidal diagram S out1 Perform two-dimensional Fourier transform to obtain the frequency domain image S out2 And the frequency domain image S is filtered by Ram-Lak out2 filtering;

[0029] S53. Use two-dimensional inverse Fourier transform to process the filtered frequency domain image S out2 Get the filtered sinusoidal graph S out3 ;

[0030] S54. Filtered sinusoidal graph S out3 Perform parallel beam back projection to obtain the intermediate reconstructed CT image X out .

[0031] Furthermore, the image enhancement network eliminates the intermediate reconstructed CT image X based on adversarial learning. out stripe artifacts; the network structure of the generator of the image enhancement network is the same as that of the projection restoration network; the discriminator of the image enhancement network adopts a deep convolutional structure, consisting of 10 convolutional layers, 10 group normalization layers and 10 swish activation function layers; among them, the convolution kernel sizes of the 10 convolutional layers increase in sequence.

[0032] Further, step S27 is based on the enhanced reconstructed CT image X and the label CT image X label Construct the third loss function, expressed as:

[0033] L G =L Gan +αL pMSE

[0034]

[0035]

[0036] Among them, L Gan Denotes the adversarial loss, L pMSE represents pixel mean square loss, α represents weight coefficient, G θ represents a generator, represents the discriminator, W and H represent the width and height of the image respectively, X(x,y) represents the pixel (x,y) of the enhanced reconstructed CT image X, X label (x,y) represents the label CT image X label The pixel point (x,y).

[0037] Furthermore, the CT image reconstruction target equation constructed in step S3 is expressed as:

[0038]

[0039] Among them, ||SA(x i )|| 2 represents the data fidelity term, s represents the sparse angular sinusoidal graph, A represents the forward projection matrix, x i represents the target CT image reconstructed by the i-th iteration, ||x i -G θ (S)|| 2 、||SE ω (S)|| 2 represents the regularization term, G θ ,f R ,E ω Represent the trained image enhancement network, filtered back projection reconstruction layer, and projection recovery network respectively, and λ1 and λ2 represent the hyperparameters for balancing the fidelity term and the regularization term;

[0040] The iterative optimization CT image reconstruction objective equation is solved according to the least squares method and is expressed as:

[0041]

[0042] Among them, A T represents the transpose of the forward projection matrix, i=0,1,2,… represents the number of iterations.

[0043] Beneficial effects of the present invention:

[0044] 1. The present invention provides a sparse angle CT reconstruction method based on the sine domain and image domain. The sine domain and image domain outputs of the sparse angle sinusoid in the sparse angle CT reconstruction network model are used as deep priors and integrated into the optimization iterative process of the CT image reconstruction target equation. Compared with the traditional dual-domain reconstruction method that only uses neural networks, the present invention has more stable result output and higher robustness and generalization. The data fidelity term is introduced into the target equation, which can effectively maintain the feature consistency between the projected sine domain and the reconstructed image domain.

[0045] 2. This invention designs a filtered back-projection reconstruction layer that bridges the sinusoidal and image domains. This layer allows for gradient backpropagation. By introducing a Radon consistency loss for supervised training, it effectively suppresses secondary artifacts generated during the reconstruction process, improving reconstruction accuracy. The image enhancement network of this invention incorporates adversarial training between labeled CT images and intermediate reconstructed CT images, further improving image quality.

[0046] 3. By introducing the self-attention mechanism, the present invention can dynamically adjust its attention according to different areas of the image, thereby more accurately capturing the high-level features of the image. At the same time, this method uses an upsampling-downsampling network structure based on residual blocks. The residual blocks can skip some convolutional layers to reduce the complexity of the network, thereby reducing the degree of overfitting of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of the sparse angle CT reconstruction method based on the sine domain and image domain of the present invention;

[0048] Figure 2 This is a training flow chart of the sparse angle CT reconstruction network model based on the sine domain and image domain of the present invention;

[0049] Figure 3 This is a structural diagram of the sparse angle CT reconstruction model based on the sine domain and image domain of the present invention;

[0050] Figure 4 This is a comparison chart of the effects of the present invention and the traditional reconstruction method. DETAILED DESCRIPTION

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0052] In order to achieve high-precision reconstruction of sparse angle sinusoidal CT, the present invention provides a sparse angle CT reconstruction method based on the sinusoidal domain and the image domain, such as Figure 1 As shown, the following steps are included:

[0053] S1. Collecting a sparse angle sinusoidal training data set, the sparse angle sinusoidal training data set includes a sparse angle sinusoidal atlas and its corresponding label data set;

[0054] Specifically, fan-beam geometry CT was used to sample the object at equal intervals. The specific settings included: scanning voltage range of [100, 120] kV, scanning current range of [200, 500] mA, X-ray source distance from projection center of 950 cm, detector distance from projection center of 200 cm, and detector unit area of ​​1.2 x 1.09 mm. 2 , the slice thickness is 0.1mm.

[0055] The process of collecting a sparse angular sinusoidal graph training data set in step S1 includes:

[0056] S11. For the object to be measured, fan beam geometry CT is used with 0, The initial angle is rotated half a circle, and a total of 23,800 first sinusoidal images containing 180 angles are collected, and each first sinusoidal image contains 180 projections;

[0057] S12. For each first sinusoidal graph, 60 angles are intercepted to obtain the corresponding sparse angle sinusoidal graph, each sparse angle sinusoidal graph contains 60 projections;

[0058] S13. The first sinusoidal graph is used as label data, and the label data is compared with the sparse angle sine graph. Figure 1 A sparse angular sinusoidal graph training dataset is obtained one by one, and the sparse angular sinusoidal graph training dataset is divided into a training set, a validation set, and a test set in a ratio of 7:2:1.

[0059] S2. Construct a sparse angle CT reconstruction network model based on the sine domain and image domain, and train the sparse angle CT reconstruction network model using a sparse angle sinusoidal training dataset until the model converges;

[0060] S3. Input the sparse angle sinusoidal graph into the trained sparse angle CT reconstruction network model to obtain the repaired full angle sinusoidal graph and the reconstructed CT image;

[0061] S4. Construct the CT image reconstruction target equation, use the repaired full-angle sinusoidal image and reconstructed CT image as the prior regularization constraints of the CT image reconstruction target equation, iteratively optimize the CT image reconstruction target equation, and use the least squares method to solve it to obtain a high-precision reconstructed CT image.

[0062] In one embodiment, if Figure 3As shown in FIG, the sparse angle CT reconstruction network model includes a projection restoration network (Sinogram Enhancement network), a filtered back projection reconstruction layer (Radon Inversion module) and an image enhancement network (Image Generative network and Image Discriminative network). The training process of the sparse angle CT reconstruction network model based on the sinusoidal domain and the image domain is as follows: Figure 2 As shown, the following steps are included:

[0063] S21. Interpolate the sparse angle sinusoidal graph S through the linear interpolation method and use its corresponding label data S R Assign values ​​to the pixels at the interpolation position to obtain the interpolation-completed full-angle sinusoidal graph S with an image resolution of (180×624) L ;

[0064] S22. The full angle sinusoidal graph S L Input into the projection restoration network to obtain the restored full-angle sinusoidal graph S out ;

[0065] Specifically, if Figure 3 As shown, the projection restoration network includes a sub-attention mechanism and a residual convolution block; the residual convolution block includes two convolution layers with a convolution kernel size of 3x3, a residual convolution layer with a kernel size of 1x1, two group normalization layers with a group number of 8, and an addition layer, and the activation function used by the residual convolution block is swish. The residual convolution block uses convolution and residual connection to achieve enhanced processing of the input image to ensure that its features are not lost. The sub-attention mechanism calculates the inner product of the query (Query) and the key (Value) using the Softmax function to calculate the attention weight, and applies different weights to each pixel of the input image, thereby controlling the network model's attention to the image, better retaining the useful information in the image, and reducing errors in the image restoration process.

[0066] The projection restoration network takes as input (10, 180, 624, 1) and outputs (10, 180, 624, 1). It can be divided into a downsampling phase and an upsampling phase. First, the residual convolution block in the downsampling phase extracts features from the input image and weights the extracted features using a sub-attention mechanism. Then, the upsampling phase performs a deconvolution operation, ultimately yielding the restored sinusoidal image.

[0067] S23. Construct the first loss function and calculate the label data S R Compared with the repaired full angle sinogram Sout repair loss;

[0068] Specifically, the first loss function L E is represented as:

[0069] L E =||S out -S R ||1=||E ω (S L )-S R ||1

[0070] wherein E ω () represents the projection restoration network.

[0071] S24. Taking the repaired full-angle sinogram S out as input, the intermediate reconstructed CT image X out is obtained by filtered back-projection reconstruction layer; the label CT image X R is obtained by back-projection of the label data S label using FBP algorithm;

[0072] Specifically, the process of obtaining the intermediate reconstructed CT image X out by filtered back-projection reconstruction layer includes:

[0073] S51. According to the physical geometric information of the full-angle sinogram S out repaired in step S22, the fan-beam geometry projection is converted into parallel-beam projection to obtain the first repaired full-angle sinogram S out1 ; the physical geometric information includes the size of the full-angle sinogram S out , the number of detectors, the pixel size, the distance from the X-ray source to the projection center, the distance from the detector to the projection center, and the detector size; the conversion process is represented as:

[0074]

[0075] wherein (γ,β) represents the fan-beam geometry projection coordinates, (t,θ) represents the parallel-beam projection coordinates, and d represents the distance from the projection center to the detector.

[0076] S52. The two-dimensional Fourier transform is performed on the first repaired full-angle sinogram S out1 to obtain the frequency domain image S out2 , and the frequency domain image S out2 is filtered by a Ram-Lak filter;

[0077] S53. The filtered back-projection reconstruction layer is adopted to process the filtered frequency domain image S out2 to obtain the filtered sinogram S out3 ;

[0078] S54. Filtered sinusoidal graph S out3 Perform parallel beam back projection to obtain the intermediate reconstructed CT image X out .

[0079] Specifically, the intermediate reconstructed CT image X out Find the gradient of the parallel beam projection operator F, backpropagate the gradient, and associate the intermediate reconstructed CT image X in the image domain out The restored full-angle sinogram S in the sine domain out .

[0080] Preferably, according to the restored full angle sinusoidal graph S out The reconstructed image can be expressed as:

[0081]

[0082]

[0083] in, represents the two-dimensional Fourier transform, represents the two-dimensional inverse Fourier transform, S para (t,θ) represents the restored projection sinogram converted to parallel beam projection, ω represents the filter, and θ represents the projection angle.

[0084] S25. Construct the second loss function and calculate the intermediate reconstructed CT image X out CT image with label X label The filtered back-projection reconstruction loss;

[0085] Specifically, the second loss function L R , expressed as:

[0086] L R =||X out -X||1=||f R (S out )-X||1

[0087] Among them, f R () represents the filtered back projection reconstruction layer.

[0088] S26. Reconstruct the intermediate CT image X out CT image with label X label Input them together into the image enhancement network for confrontation to obtain the enhanced reconstructed CT image X;

[0089] Specifically, the image enhancement network eliminates the stripe artifacts of the intermediate reconstructed CT image based on adversarial learning, enhances the detailed texture features, and obtains the enhanced reconstructed CT image. The network structure of the generator of the image enhancement network is the same as that of the projection restoration network, such as Figure 3As shown in Figure 2, the discriminator of the image enhancement network adopts a deep convolutional structure consisting of 10 convolutional layers, 10 group normalization layers, and 10 swish activation function layers. The convolution kernels of the 10 convolutional layers increase in size to achieve layer-by-layer enhancement of the CT image feature map. Finally, global average pooling is performed and connected to a linear layer to achieve true and false discrimination of the reconstructed CT image.

[0090] S27. Construct the third loss function and calculate the enhanced reconstructed CT image X and the label CT image X label Specifically, according to the enhanced reconstructed CT image X and the label CT image X label Construct the third loss function, expressed as:

[0091] L G =L Gan +αL pMSE

[0092]

[0093]

[0094] Among them, L Gan Denotes the adversarial loss, L pMSE represents pixel mean square loss, α represents weight coefficient, G θ represents a generator, represents the discriminator, W and H represent the width and height of the image respectively, X(x,y) represents the pixel (x,y) of the enhanced reconstructed CT image X, X label (x,y) represents the label CT image X label The pixel point (x,y).

[0095] Specifically, the total loss is expressed as:

[0096] L=L G +λL R +γL E

[0097] Among them, L G Represents the third loss function, L R Represents the second loss function, L E represents the first loss function, λ and γ represent weight coefficients.

[0098] In one embodiment, the CT image reconstruction objective equation is expressed as:

[0099]

[0100] Among them, ||SA(x i )|| 2represents the data fidelity term, s represents the sparse angular sinusoidal graph, A represents the forward projection matrix, x i represents the target CT image reconstructed by the i-th iteration, ||x i -G θ (S)|| 2 、||SE ω (S)|| 2 represents the regularization term, G θ ,f R ,E ω Represent the trained image enhancement network, filtered back projection reconstruction layer, and projection recovery network respectively, and λ1 and λ2 represent the hyperparameters for balancing the fidelity term and the regularization term;

[0101] The iterative optimization CT image reconstruction objective equation is solved according to the least squares method and is expressed as:

[0102]

[0103] Among them, A T represents the transpose of the forward projection matrix, i=0,1,2,… represents the number of iterations.

[0104] In one embodiment, in order to measure the model performance, the reconstruction method of the present invention is compared with a traditional CT reconstruction method (FBP). Figure 4 The images are shown in Figure 1. A real CT image, a CT image reconstructed using FBP at 60 projection angles, a CT image reconstructed using FBP at 180 projection angles, and a CT image reconstructed using the method of the present invention at 60 projection angles. The results show that FBP can reconstruct CT images at 60 projection angles, but the reconstruction quality is poor, with numerous artifacts and unclear image details. Compared to the FBP method, the method of the present invention achieves better reconstruction results, with clearer edges and structures, the ability to display fine-grained features and details, and less noise and distortion.

[0105] In the present invention, unless otherwise clearly stipulated and limited, the terms "installation", "setting", "connection", "fixation", "rotation" and the like should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be the internal connection of two elements or the interaction relationship between two elements. Unless otherwise clearly defined, ordinary technicians in this field can understand the specific meanings of the above terms in the present invention according to the specific circumstances.

[0106] While embodiments of the application have been shown and described, it is to be understood that the embodiments described are merely exemplary of the principles and application of the present application. Numerous modifications and adaptions can be effected without departing from the spirit and scope of the present application, which is not limited to the exact construction and arrangement described. It is intended, therefore, to cover all modifications and adaptions that fall within the scope of the claims and their equivalents.

Claims

1. A sparse angular CT reconstruction method based on the sine domain and the image domain, characterized in that: The following steps are involved: S1. Collecting a sparse angle sinusoidal training data set, the sparse angle sinusoidal training data set includes a sparse angle sinusoidal atlas and its corresponding label data set; S2. Construct a sparse angle CT reconstruction network model based on the sine domain and image domain, and train the sparse angle CT reconstruction network model using a sparse angle sinusoidal training dataset until the model converges; In step S2, the sparse angle CT reconstruction network model includes a projection recovery network, a filtered back projection reconstruction layer, and an image enhancement network. The training process of the sparse angle CT reconstruction network model based on the sine domain and the image domain includes the following steps: S21. Interpolate the sparse angle sinusoidal graph S by linear interpolation method and use its corresponding label data S R Assign values ​​to the pixels at the interpolation position to obtain the interpolated and completed full-angle sinusoidal graph S L ; S22. The full angle sinusoidal graph S L Input into the projection restoration network to obtain the restored full-angle sinusoidal graph S out ; S23. Construct the first loss function and calculate the label data S R Compared with the repaired full angle sinogram S out Repair losses; S24. The repaired full angle sinusoidal graph S out As input, the intermediate reconstructed CT image X is obtained through the filtered back projection reconstruction layer out ; Use FBP algorithm to label data S R Perform back projection to obtain the label CT image X label ; S25. Construct the second loss function and calculate the intermediate reconstructed CT image X out CT image with label X label The filtered back-projection reconstruction loss; S26. Reconstruct the intermediate CT image X out CT image with label X label Input them together into the image enhancement network for confrontation to obtain the enhanced reconstructed CT image X; S27. Construct the third loss function and calculate the enhanced reconstructed CT image X and the label CT image X label Generative loss and adversarial loss between them; S3. Input the sparse angle sinusoidal graph into the trained sparse angle CT reconstruction network model to obtain the repaired full angle sinusoidal graph and the reconstructed CT image; The CT image reconstruction target equation constructed in step S3 is expressed as: Among them, ||SA(x i )|| 2 represents the data fidelity term, s represents the sparse angular sinusoidal graph, A represents the forward projection matrix, x i represents the target CT image reconstructed by the i-th iteration, ||x i -G θ (f R (E ω (S)))|| 2 、||A(x i )-E ω (S)|| 2 represents the regularization term, G θ ,f R ,E ω Represent the trained image enhancement network, filtered back projection reconstruction layer, and projection recovery network respectively, λ1 and λ2 represent the hyperparameters for balancing the fidelity term and the regularization term; The iterative optimization CT image reconstruction objective equation is solved according to the least squares method and is expressed as: Among them, A T represents the transpose of the forward projection matrix, i = 0, 1, 2, ... represents the number of iterations; S4. Construct the CT image reconstruction target equation, use the repaired full-angle sinusoidal image and reconstructed CT image as the prior regularization constraints of the CT image reconstruction target equation, iteratively optimize the CT image reconstruction target equation, and use the least squares method to solve it to obtain a high-precision reconstructed CT image.

2. The sparse angular CT reconstruction method based on the sine domain and the image domain according to claim 1, characterized in that: The process of collecting a sparse angular sinusoidal graph training data set in step S1 includes: S11. For the object to be measured, fan beam geometry CT is used with 0, For a half-turn of the initial angle, 23,800 first sinusoidal images were collected, each containing 180 projections; S12. Each first sinusoidal image is intercepted to obtain a corresponding sparse angle sinusoidal image, each sparse angle sinusoidal image contains 60 projections; S13. The first sinusoidal graph is used as label data, and the label data is matched one-to-one with the sparse angle sinusoidal graph to obtain a sparse angle sinusoidal graph training data set, and the sparse angle sinusoidal graph training data set is divided into a training set, a validation set, and a test set in a ratio of 7:2:

1.

3. The sparse angular CT reconstruction method based on the sine domain and the image domain according to claim 1, characterized in that: The projection restoration network described in step S22 includes a sub-attention mechanism and a residual convolution block; the residual convolution block includes two convolution layers with a convolution kernel size of 3x3, a residual convolution layer with a kernel size of 1x1, two group normalization layers with a group number of 8 and an addition layer, and the activation function used in the residual convolution block is swish.

4. The sparse angular CT reconstruction method based on the sine domain and the image domain according to claim 1, characterized in that: In step S24, the intermediate reconstructed CT image X is obtained by filtering back projection reconstruction layer out The process includes: S51. The full-angle sinusoidal graph S repaired according to step S22 out The physical geometric information of the fan beam is converted into a parallel beam projection to obtain the first repaired full-angle sinusoidal graph S out1 ; S52. Repair the first full angle sinusoidal diagram S out1 Perform two-dimensional Fourier transform to obtain the frequency domain image S out2 And the frequency domain image S is filtered by Ram-Lak out2 filtering; S53. Use two-dimensional inverse Fourier transform to process the filtered frequency domain image S out2 Get the filtered sinusoidal graph S out3 ; S54. Filtered sinusoidal graph S out3 Perform parallel beam back projection to obtain the intermediate reconstructed CT image X out .

5. The sparse angular CT reconstruction method based on the sine domain and image domain according to claim 1, characterized in that: The image enhancement network eliminates the intermediate reconstructed CT image X based on adversarial learning. out stripe artifacts; the network structure of the generator of the image enhancement network is the same as that of the projection restoration network; the discriminator of the image enhancement network adopts a deep convolutional structure, consisting of 10 convolutional layers, 10 group normalization layers and 10 swish activation function layers; among them, the convolution kernel sizes of the 10 convolutional layers increase in sequence.

6. The sparse angular CT reconstruction method based on the sine domain and the image domain according to claim 1, characterized in that: Step S23 is based on the tag data S R Compared with the repaired full angle sinogram S out Construct the first loss function L E , expressed as: L E =||S out -S R ||1=||E ω (S L )-S R ||1 Among them, E ω () represents the projection recovery network; Step S25 reconstructs the CT image X according to the intermediate out The corresponding label CT map X constructs the second loss function L R , expressed as: L R =||X out -X||1=||f R (S out )-X||1 Among them, f R () represents the filtered back-projection reconstruction layer; Step S27 is based on the enhanced reconstructed CT image X and the label CT image X label Construct the third loss function, expressed as: L G =L Gan +αL pMSE Among them, L Gan Denotes the adversarial loss, L pMSE represents pixel mean square loss, α represents weight coefficient, G θ represents a generator, represents the discriminator, W and H represent the width and height of the image respectively, X(x,y) represents the pixel (x,y) of the enhanced reconstructed CT image X, X label (x,y) represents the label CT image X label The pixel point (x,y).

Images