CN113034641B - Sparse angle CT reconstruction method based on wavelet multi-scale convolution feature coding - Google Patents

Abstract

The invention discloses a sparse angle CT reconstruction method based on wavelet multi-scale convolution feature coding, which belongs to the technical field of computed tomography. The method first performs wavelet transformation on high-quality CT sample images to obtain a high-frequency coefficient map, then performs multi-scale convolution feature learning on the high-frequency coefficient map to construct a multi-scale filter dictionary; and then introduces the constructed multi-scale filter dictionary, A sparse angle CT reconstruction model with wavelet multi-scale convolution feature coding constraints is established; the reconstruction model is decomposed into variables, which are divided into convolution feature learning update objective function and reconstructed image update objective function; A dictionary of scale filters to obtain the final reconstructed image. The invention can effectively reduce the stripe artifacts and the loss of details in the sparse angle CT reconstruction, improve the contrast of the reconstructed image, and promote the use of the sparse angle CT scan in the field of clinical diagnosis and treatment.

Description

A Sparse Angle CT Reconstruction Method Based on Wavelet Multiscale Convolutional Feature Coding

technical field

The invention relates to the technical field of computerized tomography, and more specifically, to a sparse-angle CT reconstruction method based on wavelet multi-scale convolution feature coding.

Background technique

Computed Tomography (CT) is an image technology that uses the X-ray attenuation difference of object components to present accurate structural information through reconstruction algorithms, and can realize non-invasive detection. CT imaging has a series of advantages such as high spatial resolution, low scanning cost, and short time. It is complementary to magnetic resonance imaging, ultrasound imaging, and positron emission tomography in clinical practice, and can provide imaging for disease screening, diagnosis, and treatment. The foundation is one of the indispensable medical equipment in hospitals at all levels. However, excessive X-ray exposure can damage tissue cells, increasing the risk of acquiring underlying diseases. According to the survey, in a conventional spiral CT scan, the examiner may be exposed to a radiation dose of 1.5-10 mSv, which is much higher than the dose of 0.2-0.5 mSv in ordinary chest X-ray examination. As the number of inspections increases, radiation also has a cumulative effect, prolonging the damage suffered by the examiner, and some special groups (such as children, pregnant women, the elderly, etc.) are more injured. Therefore, the X-ray dose should be reduced as much as possible without affecting the image diagnosis.

Using sparse angle scanning to reduce the number of projection data angles is an effective way to reduce X-ray exposure. However, reducing the sampling of rays will lead to the loss of acquired signals, which in turn will cause the degradation of the reconstructed image, especially the loss of tissue details and increase the streak artifacts of the reconstructed image, which will lead to missed diagnosis and misdiagnosis when doctors read the image. In order to improve the effect of sparse-angle CT imaging: On the one hand, from the perspective of CT images, researchers design professional image restoration and processing algorithms to suppress artifacts and enhance image details. However, under different scanning equipment, modes and reconstruction methods, the artifact representation of CT images varies greatly, which also leads to poor generalization ability of this method. On the other hand, from the perspective of CT projection data, the original data or the projection data after logarithmic transformation are repaired and restored to improve the consistency of the projection data, thereby improving the reconstruction effect. However, due to the high sensitivity of projection data, under-correction, over-correction and low data consistency are prone to occur during processing. In addition, improving the reconstruction algorithm is also a main way to improve the imaging effect. In recent years, a large number of iterative reconstruction algorithms have been proposed and achieved excellent results, especially the statistical iterative reconstruction algorithm based on prior information constraints. However, the main problems faced by this type of algorithm are: there are many hyperparameters, it is difficult to adaptively optimize; the algorithm complexity is high, and repeated iterative calculations are required; Reconstruction is difficult to give full play to its value in clinical application scenarios. Although there are still many problems in "sparse scanning imaging", these will be important indicators in the field of CT research in the future, and also the main direction of X-ray imaging development.

Sparse feature learning is used as a priori model to constitute a constraint item, which is widely used in sparse angle CT reconstruction. Sparse feature learning methods also exhibit superior performance, which greatly promotes the practicality of sparse-angle CT imaging algorithms. This type of method mainly constructs a dictionary through sample training, and uses the dictionary to sparsely encode the signal. It has received extensive attention in the fields of feature recognition, classification, and image restoration. However, the traditional sparse feature learning has limited a priori information extraction ability. How to expand and enhance its feature learning ability, how to design multi-scale feature encoding forms, so as to give full play to its advantages and better serve low-dose CT imaging , is a key issue in the development of clinical CT imaging.

The information disclosed in this Background section is only for enhancing the understanding of the general background of the present invention and should not be taken as an acknowledgment or any form of suggestion that the information constitutes the prior art that is already known to those skilled in the art.

Contents of the invention

1. The technical problem to be solved by the invention

The purpose of the present invention is to overcome the problems of low image quality, residual artifacts, loss of tissue details, and low contrast existing in the sparse angle CT reconstruction method in the prior art, and to provide a sparse angle CT reconstruction method based on wavelet multi-scale convolution feature coding The angle CT reconstruction method is called Wavelet domain Multi-Scale Convolutional sparse coding constrained Reconstruction (WMCR for short). This method is to improve feature information perception, encoding and decoding capabilities through multi-scale convolutional feature learning without changing the cost of existing CT hardware, obtain rich prior knowledge, and serve for high-quality reconstruction of sparse-angle CT . The present invention improves image quality of sparse-angle CT reconstruction by suppressing image artifacts and loss of details caused by missing scanning angles, and ultimately reduces extra radiation for patients and increases diagnosis and treatment benefits.

2. Technical solution

In order to achieve the above object, the technical scheme provided by the invention is:

A kind of sparse angle CT reconstruction method based on wavelet multi-scale convolution feature coding of the present invention comprises the following steps:

Step 1. Obtain the initial multi-scale filter dictionary atom;

和

分别为水平、垂直和对角三个方向的子带信号；对F⁰进行多尺度卷积特征学习，获取初始的多尺度滤波器字典原子

Perform wavelet transformation on a given high-quality CT sample image x ^s to obtain high-frequency and low-frequency wavelet coefficients, where the high-frequency coefficients are expressed as

and

are the sub-band signals in the horizontal, vertical and diagonal directions respectively; perform multi-scale convolution feature learning on F ⁰ to obtain the initial multi-scale filter dictionary atoms

The learning model is expressed as:

为对应原子的特征图，β为正则化参数；Where * is the convolution operator, K is the number of convolution kernel scales, and N is the number of convolution kernels at a single scale,

is the feature map of the corresponding atom, and β is the regularization parameter;

Step 2. Construct a sparse-angle CT reconstruction model constrained by wavelet multi-scale convolution feature coding;

Step 3. Reconstruction model decomposition: Decompose the reconstruction model with fixed variables to obtain the convolution feature learning update objective function and the image update objective function to be reconstructed;

Step 4. Alternately solve the convolution feature learning update objective function and the image to be reconstructed update objective function to obtain the final reconstruction result map.

Further, the reconstructed model constructed in step 2 is expressed as:

Where * is the convolution operator, K is the number of convolution kernel scales, N is the number of convolution kernels at a single scale, A is the projection matrix of the CT system, x is the image to be reconstructed, p is the sparse projection data, and W is the wavelet Transform the high-frequency coefficient extraction operator, λ and β are the regularization parameters, d _{n, k} are the multi-scale filter dictionary atoms, and M _{n, k} are the corresponding feature maps.

Furthermore, the convolutional feature learning update objective function obtained by decomposing in step 3 and the update objective function of the image to be reconstructed are respectively expressed as:

为第t次更新后的多尺度滤波器字典原子，

为第t次更新后对应原子的特征图。Where * is the convolution operator, K is the number of convolution kernel scales, N is the number of convolution kernels at a single scale, A is the projection matrix of the CT system, x is the image to be reconstructed, p is the sparse projection data, and W is the wavelet Transform the high-frequency coefficient extraction operator, λ and β are regularization parameters, x ^t is the image to be reconstructed after the tth (0≤t) update,

is the multi-scale filter dictionary atom after the tth update,

is the feature map of the corresponding atom after the tth update.

Furthermore, in step 1, the wavelet transform adopts a layer 2 two-dimensional stationary wavelet transform, and the Haar wavelet base is selected.

Furthermore, the parameters of the multi-scale filter in step 1 are: the range of convolution kernel scales is 2≤K≤5, the value range of the number of convolution kernels at a single scale is 32≤N≤64, and the size of the convolution kernel can be The selection range is from 6×6×3 to 14×14×3.

Furthermore, in step 1, the learning model formula (1) is solved using the alternating direction multiplier algorithm to obtain the initial multi-scale filter dictionary atoms.

Furthermore, the operation steps of the wavelet transform high-frequency coefficient extraction operator W in step 2 are as follows: first, perform a 1-layer two-dimensional stationary wavelet transform on the image, and select the Haar wavelet base; then select the horizontal, vertical and The sub-band signals in three diagonal directions; finally, the sub-band signals in these three directions are superimposed and combined according to the order of the third dimension.

Furthermore, in step 3, when t=0 is the initial value, the initial multi-scale filter dictionary atom is obtained in step 1, and the initial image x ⁰ to be reconstructed is reconstructed by the filter back projection algorithm of the slope filter.

Furthermore, in step 4, the convolutional feature learning update objective function (3) is solved by the alternating direction multiplier algorithm, and the image update objective function (4) to be reconstructed is solved by the paraboloid substitution algorithm.

Furthermore, in step 4, stop when the image to be reconstructed before and after iteration satisfies RMSE(x ^t+1 -x ^t )≤30, and output the final reconstruction result map, where RMSE(·) is the mean square error calculation operator.

3. Beneficial effect

Compared with the prior art, the technical solution provided by the invention has the following beneficial effects:

A sparse-angle CT reconstruction method based on wavelet multi-scale convolution feature coding of the present invention, first, perform wavelet transformation on high-quality CT sample images to obtain high-frequency coefficient maps, and perform multi-scale convolution feature learning on high-frequency coefficient maps , to construct a multi-scale filter dictionary; then, with the constructed multi-scale filter dictionary as the initial value, a reconstruction model with the convolution feature coding constraints of high-frequency coefficients in the wavelet domain is established; next, the variable decomposition of the reconstruction model is divided into reconstruction Image update and multi-scale filter dictionary update; finally, the reconstructed image and the multi-scale filter dictionary are updated through an alternate iterative strategy to obtain the final reconstructed image. By introducing the wavelet-domain multi-scale convolutional feature coding prior into the reconstruction, the existing reconstruction methods can effectively improve the problems of strip artifacts and loss of details in the reconstruction of sparse scanning angles. The experimental results have verified that the method of the present invention (WMCR) can effectively suppress the reconstructed image compared with the traditional wavelet domain convolutional sparse coding reconstruction method (WCSC) under the scan data of various sparse angles. The reconstructed image has better visual effect and contrast due to the strip artifacts and loss of details caused by the lack of projection angle. The method of the present invention is expected to provide an advanced and practical sparse angle reconstruction framework for domestic hospital imaging departments and CT manufacturers, reduce additional radiation for patients, increase diagnosis and treatment benefits, and has high application and promotion prospects.

Description of drawings

Fig. 1 is the schematic flow chart of the sparse angle CT reconstruction method based on wavelet multi-scale convolution feature coding in the present invention;

Fig. 2 is the reconstructed image of projection data of 180 scanning angles of the abdomen in the embodiment (a: reference image; b: FBP reconstructed image; c: WCSC reconstructed image; d: WMCR reconstructed image);

Fig. 3 is the reconstructed image of projection data of 120 scan angles of the abdomen in the embodiment (a: reference image; b: FBP reconstructed image; c: WCSC reconstructed image; d: WMCR reconstructed image);

Fig. 4 is a schematic diagram of filter dictionary set after abdominal reconstruction in the embodiment (a: 180 angle scanning experiments; b: 120 angle scanning experiments);

Fig. 5 is the reconstructed figure of projection data of 180 scan angles of the chest in the embodiment (a: reference figure; b: FBP reconstructed figure; c: WCSC reconstructed image; d: WMCR reconstructed image);

Fig. 6 is the reconstructed figure of projection data of 120 scanning angles of the chest in the embodiment (a: reference figure; b: FBP reconstructed figure; c: WCSC reconstructed image; d: WMCR reconstructed image);

Fig. 7 is the Profile curve of the reconstruction image of the chest projection data in the embodiment (a: 180 scanning angles; b: 120 scanning angles).

Detailed ways

In order to further understand the content of the present invention, the present invention will be described in detail in conjunction with the accompanying drawings.

In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer" etc. The indicated orientation or positional relationship is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the referred device or element must have a specific orientation, or in a specific orientation. construction and operation, therefore, should not be construed as limiting the invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and should not be construed as indicating or implying relative importance.

The present invention will be further described below in conjunction with embodiment.

Example 1

A flow chart of a sparse angle CT reconstruction method based on wavelet multi-scale convolution feature coding in this embodiment is shown in Figure 1, and the specific steps are as follows:

Step 1. Obtain the initial multi-scale filter dictionary atom;

和

分别为水平、垂直和对角三个方向的子带信号；对F⁰进行多尺度卷积特征学习，获取初始的多尺度滤波器字典原子

学习模型可表示为：Perform wavelet transform on a given high-quality CT sample image x ^s to obtain high-frequency and low-frequency wavelet coefficients, where the high-frequency coefficients can be expressed as

and

are the sub-band signals in the horizontal, vertical and diagonal directions respectively; perform multi-scale convolution feature learning on F ⁰ to obtain the initial multi-scale filter dictionary atoms

The learning model can be expressed as:

为对应原子的特征图，β为正则化参数。Where * is the convolution operator, K is the number of convolution kernel scales, and N is the number of convolution kernels at a single scale,

is the feature map of the corresponding atom, and β is the regularization parameter.

Specifically, the given high-quality CT sample image x ^s is subjected to one-layer two-dimensional stationary wavelet transform, and the Haar wavelet base is selected. The multi-scale filter parameters are: the range of the number of convolution kernel scales is 2≤K≤5, the value range of the number of convolution kernels at a single scale is 32≤N≤64, and the optional range of convolution kernel size is 6×6 Between ×3 and 14×14×3, the specific size is manually selected based on factors such as the number of scanning angles, the size of computer storage space, and the quality of the image to be reconstructed. β is a regularization parameter that is manually adjusted according to specific data. After solving Equation (1) using the Alternating Direction Multiplier Algorithm, the initial multiscale filter dictionary atoms are obtained

Step 2. Construct a sparse-angle CT reconstruction model constrained by wavelet multi-scale convolution feature coding;

The constructed reconstruction model can be expressed as:

Where * is the convolution operator, K is the number of convolution kernel scales, N is the number of convolution kernels at a single scale, A is the projection matrix of the CT system, x is the image to be reconstructed, p is the sparse projection data, and W is the wavelet Transform the high-frequency coefficient extraction operator, λ and β are the regularization parameters, d _{n, k} are the multi-scale filter dictionary atoms, and M _{n, k} are the feature maps of the corresponding atoms.

Specifically, the operation steps of the wavelet transform high-frequency coefficient extraction operator W in the sparse angle CT reconstruction model are as follows: first, perform a two-dimensional stationary wavelet transform on the image, and select the Haar wavelet base; then select the level of the high-frequency coefficient part, The sub-band signals in three vertical and diagonal directions; finally, the sub-band signals in these three directions are superimposed and combined according to the order of the third dimension. After the operation of the operator W, the obtained data is three-dimensional data, in which the size of the first and second dimensions is equal to the image to be reconstructed, and the size of the third dimension is 3. The regularization parameter λ is selected empirically based on specific data.

Step 3, reconstruction model decomposition:

By decomposing the fixed variables of the reconstruction model formula (2), the convolutional feature learning update objective function and the image update objective function to be reconstructed can be obtained, which are expressed as:

为第t次更新后的多尺度滤波器字典原子，

为第t次更新后对应原子的特征图。Among them, * is the convolution operator, K is the number of convolution kernel scales, N is the number of scale convolution kernels, A is the projection matrix, p is the projection data, W is the wavelet transform high-frequency coefficient extraction operator, λ and β are Regularization parameters, x ^t is the image to be reconstructed after the tth (0≤t) update,

is the multi-scale filter dictionary atom after the tth update,

is the feature map of the corresponding atom after the tth update.

Specifically, in the convolutional feature learning update objective function and the image update objective function to be reconstructed, when t=0 is the initial value, the initial multi-scale filter dictionary atoms and feature maps are obtained by step 1, and the initial image to be reconstructed x ⁰ It is reconstructed by the filter back projection (Filter Back Projection, FBP) algorithm.

Step 4. Alternately solve the convolution feature learning update objective function and the image to be reconstructed update objective function to obtain the final reconstructed image.

可简化表示为矩阵相乘DM(其中矩阵元素之间仍然是卷积运算)，并为向量化的特征图集合M与滤波器字典D添加辅助变量C和F，则式(3)的求解可包括以下式：Specifically, the convolutional feature learning update objective function formula (3) is solved by an alternating direction multiplier algorithm. Let D=(d _1,1 ,d _1,2 ,…,d _n,k ) be a vectorized filter dictionary, and M=(M _1,1 ,M _1,2 ,…,M _n,k ) be Vectorized feature map set, then

It can be simplified as matrix multiplication DM (where the matrix elements are still convolution operations), and add auxiliary variables C and F to the vectorized feature map set M and filter dictionary D, then the solution of formula (3) can be Include the following formulas:

u ^t+1 ＝u ^t +M ^t+1 -C ^t+1 (3-3)

h ^t+1 ＝h ^t +D ^t+1 -F ^t+1 (3-6)

where u and h are scaled dual auxiliary variables in the solution, ρ ₁ and ρ ₂ are Lagrangian multipliers, the size can be set as ρ ₁ =50β+1, ρ ₂ =1, Proj(·) is the projection truncation The operation is to ensure that the encoding size is the same as the size of the image data to be reconstructed through the truncation operation of the filter. After initialization, F ⁰ =D ⁰ , C ⁰ =M ⁰ , h ⁰ =0, u ⁰ =0. Equation (3-1) is the update of the feature map, and Equation (3-4) is the update of the filter dictionary. The solutions of Equation (3-1) and Equation (3-4) can be obtained by solving the three-dimensional Fourier transform row , Equation (3-2) can be obtained by the soft threshold shrinkage algorithm, and Equation (3-5) can be obtained by three-dimensional Fourier transform and projection truncation. The update objective function formula (4) of the image to be reconstructed is solved by the paraboloid substitution algorithm, which can be specifically expressed as:

x ^t+1 ＝x ^t -[ ^AT (Ax ^t -p)+λW ^T (DM-Wx ^t )]/[ ^AT AI+λ] (4-1)

Among them, ^{AT is the back projection operator of the CT system, W T is} the wavelet high-frequency coefficient inverse transform operation, and I is a vector with all 1s. Finally, formula (3-1), formula (3-2), formula (3-3), formula (3-4), formula (3-5), formula (3-6) and formula ( 4-1), repeat the iteration until the image to be reconstructed before and after the iteration satisfies RMSE(x ^t+1 -x ^t )≤30 and stop, and output the final reconstruction result map, where RMSE( ) is the mean square error calculation operator.

Effect Evaluation Criteria

In the experiment, we simulated high-quality abdominal and chest image data, obtained simulated projection data from different scanning angles, and carried out corresponding reconstruction. The parameters used in the simulation scan are: the detector size is 960, the detector unit size is 0.78mm, the distances from the ray source to the center of the object and the center of the detector are 50cm and 100cm respectively, and the scan collects 180 projection data and 120 projection data respectively , and other parameters adopt the default values. The regularization parameters λ and β in the reconstruction of 180 abdominal projection data are 0.02 and 0.016 respectively, the parameters in the reconstruction of 120 abdominal projection data are 0.025 and 0.018; the regularization parameters λ and β in the reconstruction of 180 chest projection data are 0.022 and 0.018 respectively , the parameters in the reconstruction of 120 chest projection data are 0.026 and 0.021. In the experiment, the number of convolution kernels at a single scale is 32, the number of convolution kernel scales is 3, and the sizes of convolution kernels are 8×8×3, 10×10×3, and 12×12×3.

In the accompanying drawings, all reconstructed CT images show a window width of 400HU (Housfield Units, HU) and a window level of 50HU. The experiment will adopt the methods of subjective evaluation and objective evaluation to verify the validity of the algorithm of the present invention. Subjective evaluation: by comparing the FBP reconstruction figure, WCSC reconstruction figure and WMCR reconstruction figure of sparse angle hypogastric region and chest data, analyze the average reconstruction effect of the present invention (as Fig. 2, Fig. 3, Fig. 5 and Fig. 6); By selecting For the region of interest, draw the profile curve of the fixed area of the reconstruction map (as shown in Figure 4 and Figure 7, the area marked by the white line segment), so that the deviation of the details of the reconstructed tissue can be carefully observed. Objective evaluation: The experiment will use reference evaluation indicators, such as Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index (SSIM), to quantitatively compare the experimental results.

subjective evaluation

By observing and comparing the stripe artifact intensity, artifact distribution, tissue details, contrast between different tissues, reconstructed image texture and other characteristics of CT reconstruction images in Fig. 2, Fig. 3, Fig. 5 and Fig. 6, it can be seen that the present invention can Obtain higher quality reconstructed images. At the same time, we can see from the reconstruction results that when the number of scanning angles is reduced, the FBP reconstruction image is severely disturbed by noise, and tissue details cannot be distinguished. The noise artifacts in the WCSC reconstruction image and WMCR reconstruction image are significantly suppressed, and WMCR Compared with the WCSC reconstruction method, the reconstruction method can better maintain the image details and improve the contrast. As the number of angles decreases, the more artifacts, the quality of the reconstructed image gradually decreases, but the WMCR method still brings better reconstruction results, which is obviously better than that of the WCSC algorithm.

objective comment

While subjectively evaluating the effectiveness of the method of the present invention in sparse angle scanning CT reconstruction, the experiment will further use two quantitative indicators of PSNR and SSIM to evaluate the reconstructed image to quantitatively confirm the effectiveness of the method of the present invention. PSNR and SSIM are calculated as follows:

where x ^T is the last updated image to be reconstructed, x ^r is the high-quality reference image used for simulation, N is the total number of image pixels; H _max is the maximum value of x ^r , μ _xT and μ _xr respectively represent the CT image x ^T and the mean value of the total pixel CT values in x ^r ; σ _xT and σ _xr respectively represent the standard deviation of the total pixel CT values in CT images x ^T and x ^r , σ _xTr is the covariance of CT images x ^T and x ^r , Constants C ₁ =(0.01×H _max ) ² , C ₂ =(0.03×H _max ) ² . Taking the high-quality image used for simulation as a reference image, calculate the PSNR and SSIM values of the reconstructed images with different data, and the results are shown in Table 1.

Table 1

It can be seen from Table 1 that in the data reconstruction of the lower abdomen and chest at simulated sparse angles, the quantitative index of the FBP reconstruction image is the worst, and the WCSC reconstruction results have been improved to a certain extent, and the WMCR method of the present invention can obtain a higher SSIM With PSNR value (WMCR method of the present invention compares with WCSC method result, in 180 angle scan data experiments, PSNR about 1.4dB higher, SSIM about 0.01 higher, in 120 angle scan data experiments, PSNR about about .9dB higher and SSIM about 0.01 higher). It can be seen from Fig. 4 and Fig. 7 that in the selected pixels (in Fig. 4(a) and Fig. 7(a), the white line segment mark area of the image, Ref is the reference image), the tissue boundary pixel value jumps in the WMCR reconstruction map It is more obvious, the tissue boundary is sharper, and the curve trend is closer to the reference image. It can be seen from the above experiments that under the same sparse angle scanning condition, the method of the present invention can obtain a CT reconstruction image with fewer artifacts, and has high stability, which has a certain application prospect.

The above schematically describes the present invention and its implementation, which is not restrictive, and what is shown in the drawings is only one of the implementations of the present invention, and the actual structure is not limited thereto. Therefore, if a person of ordinary skill in the art is inspired by it, without departing from the inventive concept of the present invention, without creatively designing a structural mode and embodiment similar to the technical solution, it shall all belong to the protection scope of the present invention .

Claims (1)

1. A sparse angle CT reconstruction method based on wavelet multi-scale convolution feature coding, characterized in that, comprising the following steps: Step 1. Obtain the initial multi-scale filter dictionary atom; Carry out wavelet transform on a given high-quality CT sample image x ^s to obtain high-frequency and low-frequency wavelet coefficients, where the wavelet transform uses a two-dimensional stationary wavelet transform with a layer of Haar wavelet basis; the high-frequency coefficient part is expressed as

f _v ⁰ and

are the sub-band signals in the horizontal, vertical and diagonal directions respectively; perform multi-scale convolution feature learning on F ⁰ to obtain the initial multi-scale filter dictionary atoms

The learning model is expressed as:

Where * is the convolution operator, K is the number of convolution kernel scales, and N is the number of convolution kernels at a single scale,

is the feature map corresponding to the atom, and β is the regularization parameter; the learning model formula (1) is solved by the alternate direction multiplier algorithm to obtain the initial multi-scale filter dictionary atoms; the multi-scale filter parameters are: the range of the convolution kernel scale number 2≤K≤5, the value range of the number of convolution kernels under a single scale is 32≤N≤64, and the optional range of convolution kernel size is 6×6×3 to 14×14×3; Step 2. Construct a sparse angle CT reconstruction model constrained by wavelet multi-scale convolution feature coding; the constructed reconstruction model is expressed as:

Where * is the convolution operator, K is the number of convolution kernel scales, N is the number of convolution kernels at a single scale, A is the projection matrix of the CT system, x is the image to be reconstructed, p is the sparse projection data, and W is the wavelet Transform the high-frequency coefficient extraction operator, λ and β are regularization parameters, d _{n, k} are the multi-scale filter dictionary atoms, M _{n, k} are the corresponding feature maps; the operation of the wavelet transform high-frequency coefficient extraction operator W The steps are as follows: firstly carry out 1-layer two-dimensional stationary wavelet transform on the image, and select the Haar wavelet base; then select the sub-band signals in the horizontal, vertical and diagonal directions of the high-frequency coefficient part; finally, the sub-band signals in the three directions The band signals are superimposed and combined according to the order of the third dimension; after the operation of the operator W, the obtained data is three-dimensional data, in which the size of the first dimension and the second dimension are equal to the image to be reconstructed, and the size of the third dimension is 3; Step 3. Reconstruction model decomposition: Decompose the reconstruction model with fixed variables to obtain the convolution feature learning update objective function and the image update objective function to be reconstructed; respectively expressed as:

Where * is the convolution operator, K is the number of convolution kernel scales, N is the number of convolution kernels at a single scale, A is the projection matrix of the CT system, x is the image to be reconstructed, p is the sparse projection data, and W is the wavelet Transform the high-frequency coefficient extraction operator, λ and β are regularization parameters, x ^t is the image to be reconstructed after the tth (0≤t) update,

is the multi-scale filter dictionary atom after the tth update,

is the feature map of the corresponding atom after the t-th update; where t=0 is the initial value, the initial multi-scale filter dictionary atom is obtained from step 1, and the initial image x ⁰ to be reconstructed is reconstructed by the filter back projection algorithm of the slope filter get; Step 4. Alternately solve the convolutional feature learning update objective function and the image update objective function to be reconstructed to obtain the final reconstruction result graph; where the convolution feature learning update objective function formula (3) is solved by the alternate direction multiplier algorithm, and the image to be reconstructed Image update objective function formula (4) is solved by paraboloid substitution algorithm; stop when the image to be reconstructed before and after iteration satisfies RMSE(x ^t+1 -x ^t )≤30, and output the final reconstruction result map, where RMSE( ) is mean Square error calculation operator.

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