A limited-angle CT image reconstruction algorithm based on a repair matrix

Abstract

The application relates to the technical field of CT imaging, in particular to a finite-angle CT image reconstruction algorithm based on a repair matrix, which comprises the following steps: constructing a repair matrix according to a prior information set; updating a landslide artifact image according to the repair matrix, a wavelet tight frame transformation operator, a preset reconstruction image, a preset landslide artifact image and a first preset auxiliary variable to obtain an updated landslide artifact image; and updating a reconstruction image according to a system matrix, the wavelet tight frame transformation operator, the updated landslide artifact image and a second preset auxiliary variable to obtain an updated reconstruction image. In this way, the preset landslide artifact image is updated through the repair matrix, and then the preset reconstruction image is updated according to the updated preset landslide artifact image, so that the details and edge information blurred and degraded by the landslide artifact in the image are repaired, and the quality of the finite-angle CT image is improved. Meanwhile, in the iteration process, the noise is suppressed through the wavelet tight frame transformation operator, and the quality of the finite-angle CT image is further improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of CT imaging technology, and particularly relates to a limited-angle CT image reconstruction algorithm based on a repair matrix. BACKGROUND

[0002] CT (Computed Tomography) technology is based on reconstructing internal structure information of an object without damaging the internal structure of the object, and has become one of indispensable imaging methods in modern radiology and has been widely applied to medical diagnosis, industrial non-destructive testing and other fields. In some important applications, due to the limitation of scanning environment and X-ray dose, the acquired projection data is usually angle-limited, and the result reconstructed from the acquired projection data will be affected by landslide artifacts. The details of the reconstructed image will be blurred and degraded at the edge where the projection data is not tangent, the more the angle is missing, the greater the blurring degree is, and for medical images, it will lead to false medical diagnosis; for industrial images, it will affect non-destructive testing.

[0003] The images obtained by the FBP (Filtered Back Projection Reconstruction Algorithm), FDK, SART (Simultaneous Algebraic Reconstruction Technique) and other image reconstruction algorithms in the prior art are of low quality due to the lack of consideration of the landslide artifacts caused by angle missing. SUMMARY

[0004] In view of the deficiencies in the prior art, the present application provides a limited-angle CT image reconstruction algorithm based on a repair matrix, which improves the quality of the limited-angle CT image.

[0005] The technical scheme adopted by the present application is a limited-angle CT image reconstruction algorithm based on a repair matrix.

[0006] In a first implementation manner, a limited-angle CT image reconstruction algorithm based on a repair matrix comprises:

[0007] Step S1, determining a prior information set, a system scanning parameter set and a wavelet tight frame transformation operator;

[0008] Step S2, constructing a repair matrix according to the prior information set, wherein an optimization model is used for modeling according to the prior information set, and the repair matrix is obtained by solving the model; a system matrix is obtained according to the system scanning parameter set, wherein the system coordinates of the target to be reconstructed are determined according to the scanning angle range of the target to be reconstructed, and the system scanning parameter set is obtained;

[0009] Step S3, updating the landslip artifact image according to the repair matrix, the wavelet tight frame transform operator, the preset reconstructed image, the preset landslip artifact image and the first preset auxiliary variable to obtain an updated landslip artifact image;

[0010] Step S4, updating the reconstructed image according to the system matrix, the wavelet tight frame transform operator, the updated landslip artifact image, the preset reconstructed image and the second preset auxiliary variable to obtain an updated reconstructed image;

[0011] Step S5, obtaining a first updated auxiliary variable according to the updated landslip artifact image and the first preset auxiliary variable;

[0012] Step S6, obtaining a second updated auxiliary variable according to the updated reconstructed image and the second preset auxiliary variable;

[0013] Step S7, taking the first updated auxiliary variable as the first preset auxiliary variable, taking the second updated auxiliary variable as the second preset auxiliary variable, taking the updated reconstructed image as the preset reconstructed image, and taking the updated landslip artifact image as the preset landslip artifact image, and repeating S3-S7 for several times until the iteration termination condition is met.

[0014] According to the technical solution of the first implementation manner, the application has the following beneficial technical effects:

[0015] 1. The repair matrix is constructed according to the prior information set, the landslip artifact image is updated according to the repair matrix, the wavelet tight frame transform operator, the preset reconstructed image, the preset landslip artifact image and the first preset auxiliary variable to obtain an updated landslip artifact image, and the reconstructed image is updated according to the system matrix, the wavelet tight frame transform operator, the updated landslip artifact image and the second preset auxiliary variable to obtain an updated reconstructed image. In this way, the preset landslip artifact image is updated through the repair matrix, and then the preset reconstructed image is updated according to the updated preset landslip artifact image, the details and edge information blurred and degraded by the landslip artifact in the image are repaired, and the quality of the limited-angle CT image is improved.

[0016] 2. The updated landslip artifact image is obtained according to the wavelet tight frame transform operator, and the updated reconstructed image is obtained according to the wavelet tight frame transform operator and the updated landslip artifact image. In this way, in the iteration process, the noise is suppressed through the wavelet tight frame transform operator, and the quality of the limited-angle CT image is further improved.

[0017] In combination with the first implementation manner, in the second implementation manner, the iteration termination condition is that the difference between the preset reconstructed image and the updated reconstructed image is within a first preset range.

[0018] In combination with the first implementation manner, in the third implementation manner, the iteration termination condition is that the number of iterations is within a second preset range.

[0019] In the fourth implementation manner, the projection set is acquired by using limited-angle CT scanning.

[0020] In the fifth implementation manner, according to the repair matrix, the wavelet tight frame transform operator, the preset reconstructed image, the preset landslip artifact image and the first preset auxiliary variable, the landslip artifact image is updated to obtain an updated landslip artifact image, including:

[0021] The updated landslip artifact image is obtained by calculating The updated landslip artifact image is obtained by calculating (k+1) x is the updated landslip artifact image, B is the repair matrix, x is the updated landslip artifact image to be optimized, x (k) is the preset landslip artifact image, u (k) is the preset reconstructed image, β1 and γ2 are regularization parameters, W is the wavelet tight frame transform operator, is the first preset auxiliary variable, and x (k) is the kth updated landslip artifact image result, where the first time can be reconstructed by using a classical reconstruction algorithm according to the projection set to obtain; u (k) is the kth updated reconstructed image result, where the first time can be initialized to obtain, where each element in u (k) is 0; the first preset auxiliary variable is the kth first updated auxiliary variable, where the first time can be initialized to obtain, where each element in is 0.

[0022] In the sixth implementation manner, according to the system matrix, the wavelet tight frame transform operator, the updated landslip artifact image, the preset reconstructed image and the second preset auxiliary variable, the reconstructed image is updated to obtain an updated reconstructed image, including:

[0023] The updated reconstructed image is obtained by calculating

[0024]

[0025] The updated reconstructed image is obtained by calculating (k+1) u is the updated reconstructed image, A is the system matrix, u is the updated reconstructed image to be optimized, b is the projection set, B is the repair matrix, x (k+1) is the updated landslip artifact image, β2 and γ1 are regularization parameters, W is the wavelet tight frame transform operator, is the second preset auxiliary variable, and u (k) is the preset reconstructed image; the updated landslip artifact image x (k+1) is the kth updated landslip artifact image result; the preset reconstructed image u (k)obtained by setting each element in to 0; the second preset auxiliary variable (k) obtained by setting each element in to 0; the second preset auxiliary variable is the kth second update auxiliary variable, which can be initialized as the first time obtained by setting each element in to 0.

[0026] In the seventh implementable manner, in combination with the first implementable manner, the first update auxiliary variable is obtained according to the updated landslide pseudo-image and the first preset auxiliary variable, and the method comprises the following steps:

[0027] obtained by setting each element in to 0. obtained by setting each element in to 0. is the k+1th first update auxiliary variable, β1, λ1 and d1 are regularization parameters, W is a wavelet tight frame transform operator, x (k+1) is the updated landslide pseudo-image, v1 is the first update auxiliary variable to be optimized, is the first preset auxiliary variable, ‖·‖0 is an l0 quasi-norm, i.e., the number of non-zero elements; the updated landslide pseudo-image x (k+1) is the k+1th updated landslide pseudo-image result; the first preset auxiliary variable is the kth first update auxiliary variable result, which can be initialized as the first time obtained by setting each element in to 0.

[0028] In the eighth implementable manner, in combination with the first implementable manner, the second update auxiliary variable is obtained according to the updated reconstruction image and the second preset auxiliary variable, and the method comprises the following steps:

[0029] obtained by setting each element in to 0. obtained by setting each element in to 0. is the second update auxiliary variable, β2, λ2 and d2 are regularization parameters, W is a wavelet tight frame transform operator, u (k+1) is the updated reconstruction image, v2 is the second update auxiliary variable to be optimized, is the second preset auxiliary variable, ‖·‖0 is an l0 quasi-norm, i.e., the number of non-zero elements; the updated reconstruction image u (k+1) is the k+1th updated reconstruction image result; the second preset auxiliary variable is the kth second update auxiliary variable, which can be initialized as the first time obtained by setting each element in to 0.

[0030] According to the technical solutions of the seventh and eighth implementation manners, the application has the beneficial technical effects as follows: the first preset auxiliary variable and the second preset auxiliary variable are updated according to the l0 pseudo norm, the updated landslide artifact image is obtained according to the first preset auxiliary variable, and the updated reconstruction image is obtained according to the second preset auxiliary variable and the updated landslide artifact image. In this way, in the iteration process, the noise is suppressed by the l0 pseudo norm, and the quality of the limited-angle CT image is further improved.

[0031] In combination with the fourth, sixth, seventh and eighth implementation manners, in a ninth implementation manner, the adjustment range of the regularization parameter is (0, 1). BRIEF DESCRIPTION OF DRAWINGS

[0032] In order to more clearly illustrate the technical solutions of the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. In all the drawings, similar elements or parts are generally identified by similar reference signs. In the drawings, the elements or parts are not necessarily drawn according to the actual proportions.

[0033] Figure 1 An example of a limited-angle CT image reconstruction algorithm based on a repair matrix is provided for the embodiments of the application. DETAILED DESCRIPTION

[0034] The embodiments of the technical solutions of the application will be described in detail below with reference to the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the application, and therefore only serve as examples, and cannot limit the protection scope of the application.

[0035] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in the present application should be understood as the usual meanings understood by the skilled person in the field of the application.

[0036] In combination Figure 1 As shown in the drawings, the embodiments of the application provide a limited-angle CT image reconstruction algorithm based on a repair matrix, which comprises:

[0037] Step S1, determining a set of prior information, a set of system scanning parameters and a wavelet tight frame transformation operator;

[0038] Step S2, constructing a repair matrix according to the set of prior information, wherein the set of prior information is modeled by using an optimization model, and the repair matrix is obtained by solving the model; and a system matrix is obtained according to the set of system scanning parameters, wherein the system scanning parameter set is obtained according to the scanning angle range of the target to be reconstructed, the system coordinates of the target to be reconstructed are determined, and the system scanning parameter set is obtained;

[0039] Step S3, updating the landside artifact image according to the repair matrix, the wavelet tight frame transform operator, the preset reconstructed image, the preset landside artifact image and the first preset auxiliary variable, to obtain an updated landside artifact image;

[0040] Step S4, updating the reconstructed image according to the system matrix, the wavelet tight frame transform operator, the updated landside artifact image, the preset reconstructed image and the second preset auxiliary variable, to obtain an updated reconstructed image;

[0041] Step S5, obtaining a first updated auxiliary variable according to the updated landside artifact image and the first preset auxiliary variable;

[0042] Step S6, obtaining a second updated auxiliary variable according to the updated reconstructed image and the second preset auxiliary variable;

[0043] Step S7, taking the first updated auxiliary variable as the first preset auxiliary variable, taking the second updated auxiliary variable as the second preset auxiliary variable, taking the updated reconstructed image as the preset reconstructed image, taking the updated landside artifact image as the preset landside artifact image, repeating S3-S7 for several times until the iteration termination condition is met.

[0044] In some embodiments, the target to be reconstructed is determined first, and then the prior information set of the target to be reconstructed is determined; the repair matrix is constructed according to the prior information set of the target to be reconstructed, and the repair matrix remains unchanged in the iteration process.

[0045] In some embodiments, the system scanning parameter set is obtained by using limited angle CT scanning, and the system matrix is obtained according to the system scanning parameter set.

[0046] Optionally, the iteration termination condition is that the difference between the preset reconstructed image and the updated reconstructed image is within a first preset range.

[0047] In some embodiments, the first preset range is [-ε, +ε], that is, -ε≤ the difference between the preset reconstructed image and the updated reconstructed image ≤+ε, or, in the case of ||u (k+1) -u (k)) ||≤ε, that is, the absolute value of the difference between the preset reconstructed image u (k) and the updated reconstructed image u (k+1) is less than or equal to the error ε, the limited angle CT image reconstruction algorithm based on the repair matrix stops iteration.

[0048] Optionally, the iteration termination condition is that the number of iterations is within a second preset range.

[0049] In some embodiments, the second preset range is [1, N], N is a positive integer, that is, in the case of 1≤ the number of iterations ≤N, the limited angle CT image reconstruction algorithm based on the repair matrix stops iteration.

[0050] Optionally, it also includes: acquiring a projection set using finite-angle CT scanning.

[0051] Optionally, the landslide artifact image is updated based on the repair matrix, wavelet tight frame transform operator, preset reconstructed image, preset landslide artifact image, and first preset auxiliary variable to obtain the updated landslide artifact image. The (k+1)th iteration includes:

[0052] Through calculation Obtain updated landslide artifact images; where x (k+1) To update the landslide artifact image, B is the instigation matrix, and x is the updated landslide artifact image to be optimized. (k) To pre-define the landslide artifact image, u (k) For the pre-defined reconstructed image, β1 and γ2 are regularization parameters, and W is the wavelet compact frame transform operator. The first preset auxiliary variable; the preset landslide artifact image u (k) The result of the landslide artifact image is updated for the kth time. The first time, a classic reconstruction algorithm (such as FBP) can be used to reconstruct the image based on the projection set. The preset reconstructed image u is... (k) The result of the k-th update of the reconstructed image is given, where u can be initialized in the 1st update. (k) Each element in the variable is 0; the first preset auxiliary variable is obtained. This is the first update auxiliary variable in the k-th iteration, where the first iteration is initializeable. Each element in the array is 0.

[0053] Optionally, determining the system scanning parameter set includes: obtaining the system scanning parameter set using finite angle CT scanning.

[0054] Optionally, by calculation Obtain the updated landslide artifact image; where RP1 represents the image reconstruction operator based on the system scan parameter set P related to the landslide artifact image. Optionally, RP1 is obtained through... The definition of the optimization problem.

[0055] Optionally, the reconstructed image is updated based on the system matrix, the wavelet compact frame transform operator, the updated landslide artifact image, and the second preset auxiliary variable to obtain the updated reconstructed image, including:

[0056] Through calculation

[0057] Obtain the updated reconstructed image; where u (k+1) To update the reconstructed image, A is the system matrix, u is the updated and reconstructed image to be optimized, b is the projection set, B is the instigation matrix, and x... (k+1) To update the landslide artifact image, β2 and γ1 are both regularization parameters, and W is the wavelet compact frame transform operator. is a second preset auxiliary variable, u (k) is a preset reconstructed image.

[0058] is an updated landslip artifact image x (k+1) is a k+1th updated landslip artifact image result; a preset reconstructed image u (k) is a kth updated reconstructed image result, where the 1st can be initialized as u (k) each element in is obtained as 0; a second preset auxiliary variable is a kth second updated auxiliary variable, where the 1st can be initialized as each element in is obtained as 0.

[0059] Optionally, the updated reconstructed image is obtained by calculating ; where RP2represents an image reconstruction operator related to the reconstructed image based on a system scanning parameter set P. Optionally, RP2is defined by an optimization problem of

[0060] Optionally, a first updated auxiliary variable is obtained according to the updated landslip artifact image and a first preset auxiliary variable, comprising: the first updated auxiliary variable is obtained by calculating ; where is a k+1th first updated auxiliary variable, β1, λ1and d1are regularization parameters, W is a wavelet tight frame transform operator, x (k+1) is an updated landslip artifact image, v1is a first updated auxiliary variable to be optimized, is a first preset auxiliary variable, ‖·‖0is an l0quasi-norm, i.e., the number of non-zero elements.

[0061] is an updated landslip artifact image x (k+1) is a k+1th updated landslip artifact image result; a first preset auxiliary variable is a kth first updated auxiliary variable result, where the 1st can be initialized as each element in is obtained as 0.

[0062] Optionally, the first updated auxiliary variable is obtained by calculating ; where HT1represents a hard thresholding operator related to regularization parameters β1, λ1and d1. Optionally, HT1is defined by an optimization problem of

[0063] Optionally, a second updated auxiliary variable is obtained according to the updated reconstructed image and a second preset auxiliary variable, comprising:

[0064] the second updated auxiliary variable is obtained by calculating ; where ​​where β 2, λ 2 and d 2 are regularization parameters, W is a wavelet tight frame transform operator, u (k+1) where v 2 is the second update auxiliary variable to be optimized, where ||·|| 0 is the l 0 pseudo-norm, i.e., the number of non-zero elements.

[0065] update the reconstructed image u (k+1) where v 2 is the second update auxiliary variable to be optimized, where v 2 is the second update auxiliary variable to be optimized, where each element in v 2 is 0.

[0066] Optionally, the second update auxiliary variable v 2 is obtained by calculating where HT 2 denotes a hard thresholding operator with respect to the regularization parameters β 2, λ 2 and d 2. Optionally, HT 2 is defined by where the optimization problem is defined by

[0067] Optionally, the regularization parameters β 1, β 2, λ 1, λ 2, d 1, d 2, γ 1 and γ 2 are adjusted in the range of (0, 1).

[0068] In some embodiments, the FBP algorithm, the SART algorithm, the TV regularization algorithm, the gradient l 0 regularization algorithm, and the wavelet tight frame l 0 regularization algorithm used in the prior art are used to reconstruct an image from projection data acquired by limited angle scanning. In the limited angle CT image reconstruction algorithm based on the repair matrix of the present application, a repair matrix is constructed according to a set of prior information, the first preset auxiliary variable and the second preset auxiliary variable are updated according to the l 0 pseudo-norm, the landslip artifact image is updated according to the repair matrix, the wavelet tight frame transform operator, the preset reconstructed image, the preset landslip artifact image and the first preset auxiliary variable, an updated landslip artifact image is obtained, and the reconstructed image is updated according to the system matrix, the wavelet tight frame transform operator, the updated landslip artifact image and the second preset auxiliary variable, and an updated reconstructed image is obtained. By using the repair matrix to repair the details and edges under limited angle artifacts, and by using the wavelet tight frame transform operator and the l 0 pseudo-norm to suppress noise, the quality and usability of the limited angle CT image are improved.

[0069] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can still be modified, or some or all of the technical features can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application, and they should be covered in the scope of the claims and the specification of the present application.

Claims

1. A limited-angle CT image reconstruction algorithm based on a repair matrix, characterized in that, The method comprises the following steps: Step S1, determining a prior information set, a system scanning parameter set and a wavelet tight frame transformation operator, obtaining a projection set by using limited angle CT scanning; Step S2, constructing a repair matrix according to the prior information set, wherein the repair matrix is obtained by solving a model established by using an optimization model according to the prior information set; obtaining a system matrix according to the system scanning parameter set, wherein the system scanning parameter set is obtained according to a scanning angle range of the target to be reconstructed; Step S3, updating a landslide artifact image according to the repair matrix, the wavelet tight frame transformation operator, a preset reconstructed image, a preset landslide artifact image and a first preset auxiliary variable, obtaining an updated landslide artifact image, comprising: obtained by calculating an updated landslip artifact image; wherein, is the updated landslip artifact image, B is a repair matrix, x is the updated landslip artifact image to be optimized, is the preset landslip artifact image, is the preset reconstructed image, and are regularization parameters, and W is a wavelet tight frame transform operator, is a first preset auxiliary variable; the preset landslip artifact image is the kth updated landslip artifact image result; the preset reconstructed image is the kth updated reconstructed image result, wherein the 1st is initialized by each element in is 0; the first preset auxiliary variable is the kth first updated auxiliary variable, wherein the 1st is initialized by each element in is 0; Step S4, updating a reconstructed image according to the system matrix, the wavelet tight frame transformation operator, the updated landslide artifact image, the preset reconstructed image and a second preset auxiliary variable, obtaining an updated reconstructed image, comprising: calculating obtaining an updated reconstructed image; wherein for updating the reconstructed image, A is a system matrix, u is the updated reconstructed image to be optimized, b is a set of projections, B is a repair matrix, for updating the landslide artifact image, and are regularization parameters, W is a wavelet tight frame transform operator, is a second predetermined auxiliary variable, is a predetermined reconstructed image; the updated landslide artifact image is a k+1th updated landslide artifact image result; the predetermined reconstructed image is a kth updated reconstructed image result, wherein the 1st is initialized by each element in is obtained as 0; the second predetermined auxiliary variable is a kth second updated auxiliary variable, wherein the 1st is initialized by each element in is obtained as 0; Step S5, obtaining a first updated auxiliary variable according to the updated landslide artifact image and the first preset auxiliary variable, comprising: obtaining the first updated auxiliary variable by calculating obtaining the first updated auxiliary variable; wherein, is the k+1th first updated auxiliary variable, , and are regularization parameters, W is a wavelet tight frame transform operator, is the updated landslide artifact image, the first updated auxiliary variable to be optimized, is the first preset auxiliary variable, is the pseudo norm, i.e. the number of non-zero elements; the updated landslide artifact image is the k+1th updated landslide artifact image result; the first preset auxiliary variable is the kth first updated auxiliary variable result, wherein the first time is obtained by initializing each element in the formula is 0. Step S6, obtaining a second updated auxiliary variable according to the updated reconstructed image and the second preset auxiliary variable, comprising: obtained by calculation obtaining a second update auxiliary variable; wherein, is a second update auxiliary variable, , and are regularization parameters, W is a wavelet tight frame transform operator, is an update reconstructed image, is a second update auxiliary variable to be optimized, is a second preset auxiliary variable, is a quasi-norm, i.e., the number of non-zero elements; the update reconstructed image is a k+1th update reconstructed image result; the second preset auxiliary variable is a kth second update auxiliary variable, wherein the 1st is obtained by initialization each element in is 0 Step S7, repeating steps S3-S7 for several times until an iteration termination condition is met, wherein the first updated auxiliary variable is taken as the first preset auxiliary variable, the second updated auxiliary variable is taken as the second preset auxiliary variable, the updated reconstructed image is taken as the preset reconstructed image, and the updated landslide artifact image is taken as the preset landslide artifact image.

2. The algorithm of claim 1, wherein, The iteration termination condition is that a difference between the preset reconstructed image and the updated reconstructed image is within a first preset range.

3. The algorithm of claim 1, wherein, The iteration termination condition is that an iteration number is within a second preset range.

4. The algorithm of claim 1, wherein, The regularization parameter is within a range of (0, 1).

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