Sparse angle CL image reconstruction method and device
By using a hybrid regularization and noise variance weighted image reconstruction model based on TGV-TV, combined with the Chambolle-Pock optimization algorithm, the problems of missing interlayer information and noise in sparse angle image reconstruction are solved, achieving detail preservation and artifact suppression, thus improving reconstruction quality.
Patent Information
- Application Number
- CN202511083041.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-04
- Publication Date
- 2025-11-18
AI Technical Summary
Existing sparse angle computed tomography techniques suffer from problems such as missing interlayer information, strip artifacts, and difficulty in preserving fine structures during reconstruction. Furthermore, traditional methods do not perform well in noisy environments.
An image reconstruction model based on TGV-TV hybrid regularization is adopted, which combines data fidelity term and Chambolle-Pock optimization algorithm. The TGV term is regularized in the XY plane and the TV term is regularized in the Z direction. The image reconstruction process is optimized by using noise variance weighting matrix.
It effectively improves the quality of sparse angle image reconstruction, preserves the detailed information of complex structures, and suppresses noise and artifacts, thereby enhancing the reconstruction effect.
Smart Images
Figure CN120976342A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method and apparatus for reconstructing sparse angular CL images. Background Technology
[0002] Currently, computed tomography (CL) technology faces the challenge of reconstructing sparse-view projection data in applications such as medical diagnostics and industrial non-destructive testing. Sparse-view scanning has attracted significant attention due to its ability to significantly reduce radiation dose (in medical settings) or shorten detection time (in industrial settings). However, oblique scanning may not cover the complete projection angle of all cross-sections, resulting in projection data that does not meet the Tuy sampling condition (requiring coverage of 180°+ cone angle) in the z-axis direction, leading to missing inter-layer information during reconstruction. Furthermore, during oblique scanning, projection data in certain areas (especially object edges) may be obscured by other layers, exacerbating data sparsity in the z-axis direction and introducing striping artifacts during reconstruction.
[0003] Iterative reconstruction algorithms based on sparse regularization (such as TV minimization and dictionary learning) have improved the reconstruction quality of sparse viewpoints to some extent, but existing methods still have significant limitations: TV (Total Variation) regularization has inherent flaws: TV minimization forces image sparsity through first-order derivative constraints, which can suppress noise but is difficult to preserve fine structures (such as microvessels in medical images or fine cracks in industrial inspection), and is prone to producing "staircase effects" or blocky artifacts in high-noise scenes. The main limitation of traditional geometric modeling lies in its insufficient attention to the physical basis of the noise characteristics of projected data. Existing reconstruction methods generally ignore key physical factors: the difference in ray path length with viewpoint leads to a non-uniform distribution of accumulated noise on the penetration path. Summary of the Invention
[0004] The purpose of this invention is to provide a reconstruction method and apparatus based on sparse angle CL images, which can effectively improve the reconstruction effect of sparse angle CL images.
[0005] Based on the same inventive concept, this invention has two independent technical solutions:
[0006] 1. A method for reconstructing a sparse angle CL image, which reconstructs the image based on an image reconstruction model. The image reconstruction model includes a TGV term and a TV term. The TGV term is used to perform TGV regularization on the XY-axis plane of the image, and the TV term is used to perform TV regularization on the Z-axis direction of the image.
[0007] Furthermore, the image reconstruction model includes a data fidelity term, which comprises a weighted matrix based on the image noise variance.
[0008] Furthermore, the image reconstruction model is shown below.
[0009]
[0010] In the formula, Let g be the data fidelity term, u be the projected data, A be the image to be reconstructed, and A be the system matrix of dimension M*N. The weighted matrix based on the image noise variance is ∑. -1 It is a diagonal matrix with dimensions M*M; M is the total number of projected data, and N is the total number of voxels in the image to be reconstructed; It is the XY-axis plane gradient operator; ν is the gradient operator in the Z direction; ε is the symmetric derivative operator; ν is the first-order gradient dual variable; α1, α0 and α z These are the parameters for the TGV and TV items, respectively.
[0011] Furthermore, The definition is as follows:
[0012]
[0013] v is close to Dual variables:
[0014]
[0015] The symmetric derivative operator ε is defined as follows:
[0016]
[0017] Furthermore, ∑ -1 Let be a diagonal matrix, where the element value of each element is defined as:
[0018]
[0019] Then ∑ -1 A diagonal matrix is represented as:
[0020]
[0021] Let ∑ -1 =W T If W, then the weight W is defined as:
[0022]
[0023] Furthermore, the image reconstruction model is solved based on the Chambolle-Pock primal dual optimization algorithm to obtain the reconstructed image u.
[0024] Furthermore, when solving the image reconstruction model formula (1) based on the Chambolle-Pock primal dual optimization algorithm, the linear operator K is first defined.
[0025]
[0026] Furthermore, when solving the image reconstruction model formula (1) based on the Chambolle-Pock primal dual optimization algorithm,
[0027] Formula (1) has two original variables that need to be updated, namely u and v, which can be used to obtain the following equation:
[0028] F(y,e,h,o)=F1(y)+F2(e)+F3(h)+F4(o).
[0029]
[0030] The primal and dual problems are linked to a general saddle point optimization problem, which takes the following form:
[0031]
[0032] In the objective function of formula (1), the original variables are According to equation (11), the objective function is transformed into the following saddle point:
[0033]
[0034] The conjugate function is represented as follows:
[0035]
[0036] Where p, q, r, t are the dual variables of y, e, h, o, respectively, and p is updated as follows:
[0037]
[0038] The dual variable q is updated as follows:
[0039]
[0040] The dual variable r is updated as follows:
[0041]
[0042] The dual variable t is updated as follows:
[0043]
[0044] Where δ=τ=1 / L is the iteration step size,
[0045] The original variable u is updated as follows:
[0046]
[0047] The original variable v is updated as follows:
[0048] v k+1 =v k -τ(-q k+1 +ε T (r k+1 )) (twenty two)
[0049]
[0050] Furthermore, the parameter L takes the maximum singular value of the linear operator matrix K.
[0051] 2. A sparse angle CL image reconstruction apparatus for performing the above method.
[0052] The beneficial effects of this invention are as follows:
[0053] This invention reconstructs images based on an image reconstruction model, which includes a TGV (Generalized Total Variation, TGV) term and a TV (Total Variation, TV) term. The TGV term is used for TGV regularization of the image's XY-axis plane, and the TV term is used for TV regularization of the image's Z-axis direction. This invention proposes a sparse angle CL image reconstruction method based on TGV-TV hybrid regularization, overcoming the limitations of traditional TV methods in detail preservation and artifact suppression. Compared to the isotropic constraints of traditional TV, this method introduces TGV regularization (combining first-order gradient and second-order curvature constraints) in the XY-plane to accurately model complex texture structures, retains TV regularization in the Z-axis direction, and forces a smooth transition of interlayer anatomical structures through sparse gradient constraints, suppressing interlayer aliasing in CL image reconstruction, improving the detection capability of complex structures (such as textures and edges), and effectively improving the reconstruction effect of sparse angle CL images.
[0054] The image reconstruction model of this invention includes a data fidelity term, which comprises a weighted matrix based on the image noise variance. This weighted matrix reflects the statistical characteristics of the noise and directly affects the reliability of the measurement data. By assigning adaptive weights to the fidelity term for different projection data, this invention enables the reconstruction algorithm to place greater trust in low-noise data while suppressing high-noise data, thereby achieving optimal estimation in a statistical sense and further improving the image reconstruction effect.
[0055] This invention solves the image reconstruction model based on the Chambolle-Pock primal-dual optimization algorithm to obtain the reconstructed image u; when solving the image reconstruction model formula (1) based on the Chambolle-Pock primal-dual optimization algorithm,
[0056] Formula (1) has two original variables that need to be updated, namely u and v, which can be used to obtain the following equation:
[0057] F(y,e,h,o)=F1(y)+F2(e)+F3(h)+F4(o).
[0058]
[0059] The primal and dual problems are linked to a general saddle point optimization problem, which takes the following form:
[0060]
[0061] In the objective function of formula (1), the original variables are According to equation (11), the objective function is transformed into the following saddle point:
[0062]
[0063] The conjugate function is represented as follows:
[0064]
[0065] Where p, q, r, t are the dual variables of y, e, h, and o, respectively.
[0066] The dual variable p is updated as follows:
[0067]
[0068] The dual variable q is updated as follows:
[0069]
[0070] The dual variable r is updated as follows:
[0071]
[0072] The dual variable t is updated as follows:
[0073]
[0074] Where δ=τ=1 / L is the iteration step size,
[0075] The original variable u is updated as follows:
[0076]
[0077] The original variable v is updated as follows:
[0078] v k+1 =vk -τ(-q k+1 +ε T (r k+1 )) (twenty two)
[0079]
[0080] The parameter L takes the largest singular value of the linear operator K matrix.
[0081] This invention solves for the regularization term and the geometrically weighted fidelity term using the Chambolle-Pock algorithm described above, ensuring the convergence reliability of the algorithm and effectively guaranteeing the image reconstruction effect.
[0082] Extensive experiments were conducted using simulated and real CL image data to verify the effectiveness of the image reconstruction method proposed in this invention. Experiments demonstrate that the method effectively preserves image edge details while removing noise during image reconstruction, successfully reconstructing sparse angular CL images with complex noise types and artifacts. Attached Figure Description
[0083] Figure 1 This is a schematic diagram illustrating the solution of the image reconstruction model based on the Chambolle-Pock primal dual optimization algorithm of this invention. Detailed Implementation
[0084] The present invention will now be described in detail with reference to the embodiments shown in the accompanying drawings. However, it should be noted that these embodiments are not intended to limit the present invention. Equivalent changes or substitutions in function, method, or structure made by those skilled in the art based on these embodiments are all within the scope of protection of the present invention.
[0085] Example 1:
[0086] Reconstruction methods for sparse angle CL images
[0087] The image is reconstructed based on an image reconstruction model, which includes TGV and TV terms. The TGV term is used for TGV regularization of the image in the XY plane, and the TV term is used for TV regularization of the image in the Z-axis direction. The image reconstruction model also includes a data fidelity term, which comprises a weighted matrix based on the image noise variance.
[0088] The image reconstruction model is shown below.
[0089]
[0090] In the formula, Let g be the data fidelity term, u be the projected data, A be the image to be reconstructed, and A be the system matrix of dimension M*N. The weighted matrix based on the image noise variance is ∑. -1 It is a diagonal matrix with dimensions M*M; M is the total number of projected data, and N is the total number of voxels in the image to be reconstructed; It is the XY-axis plane gradient operator; ν is the gradient operator in the Z direction; ε is the symmetric derivative operator; ν is the first-order gradient dual variable; α1, α0 and α z These are the parameters for the TGV and TV items, respectively.
[0091] The definition is as follows:
[0092]
[0093] v is close to Dual variables:
[0094]
[0095] The symmetric derivative operator ε is defined as follows:
[0096]
[0097] ∑ -1 Let be a diagonal matrix, where the element value of each element is defined as:
[0098]
[0099] Then ∑ -1 A diagonal matrix is represented as:
[0100]
[0101] Let ∑ -1 =W T If W, then the weight W is defined as:
[0102]
[0103] The image reconstruction model is solved based on the Chambolle-Pock primal dual optimization algorithm to obtain the reconstructed image u.
[0104] When solving the image reconstruction model formula (1) based on the Chambolle-Pock primal dual optimization algorithm, the linear operator K is first defined.
[0105]
[0106] When solving the image reconstruction model formula (1) based on the Chambolle-Pock primal dual optimization algorithm,
[0107] Formula (1) has two original variables that need to be updated, namely u and v, which can be used to obtain the following equation:
[0108] F(y,e,h,o)=F1(y)+F2(e)+F3(h)+F4(o).
[0109]
[0110] The primal and dual problems are linked to a general saddle point optimization problem, which takes the following form:
[0111]
[0112] In the objective function of formula (1), the original variables are According to equation (11), the objective function is transformed into the following saddle point:
[0113]
[0114] The conjugate function is represented as follows:
[0115]
[0116] Where p, q, r, t are the dual variables of y, e, h, and o, respectively.
[0117] The dual variable p is updated as follows:
[0118]
[0119] The dual variable q is updated as follows:
[0120]
[0121] The dual variable r is updated as follows:
[0122]
[0123] The dual variable t is updated as follows:
[0124]
[0125] Where δ=τ=1 / L is the iteration step size,
[0126] The original variable u is updated as follows:
[0127]
[0128] The original variable v is updated as follows:
[0129] v k+1 =vk -τ(-q k+1 +ε T (r k+1 )) (twenty two)
[0130]
[0131] The parameter L takes the largest singular value of the linear operator K matrix.
[0132] In specific implementation, such as Figure 1 As shown, the image reconstruction model is solved based on the Chambolle-Pock primal dual optimization algorithm.
[0133] (I) Constructing the noise weight matrix of the projection data
[0134] (1) In the projected image, a 3x3 local window is used to calculate the noise variance of the region, which is then used as the noise variance corresponding to each pixel g(i,j) in the projected data. Assume that the local window is a 3x3 matrix centered at pixel g(i,j), and its 9 pixels are:
[0135]
[0136] (2) Calculate the mean: First, calculate the mean of all pixel values in this 3x3 window, where g k This represents the value of each pixel in a 3x3 matrix.
[0137]
[0138] (3) Calculate the variance of pixel g(i,j) That is, the average of the sum of the squares of the differences between all pixel values and the mean.
[0139]
[0140] (4) Generate the weighted matrix
[0141]
[0142] (II) Initialization of Reconstruction-Related Parameters
[0143] (1) Parameter initialization of TGV and TV terms: Apply TGV regularization in the xy plane, with parameter α1 = 0.01 for the first-order term and parameter α0 = 3 for the second-order term. Apply TV regularization in the z direction, with parameter α z =0.0001.
[0144] (2) Parameter optimization: Initialize the step size parameters δ and τ of the Chambolle-Pock algorithm to satisfy the following conditions: The specific algorithm for solving L is as follows:
[0145] 1: Intticialize x0=(u,v) T ∈I to a non-zero image
[0146] 2:k←0
[0147] 3:x k+1 ←K T Kx k
[0148] 4:
[0149] 5:L←||Kx k+1 ||2
[0150] 6:k←k+1
[0151] 7: until k≥N
[0152] Where u is the image to be reconstructed, ν is the first-order gradient dual variable, and K is a linear operator, defined as follows:
[0153]
[0154] In the formula, A represents a system matrix of size M*N, M is the total number of projection data, and N is the total number of voxels in the image to be reconstructed; It is the XY-axis plane gradient operator; ε is the gradient operator in the Z direction; ε is the symmetric derivative operator.
[0155] (III) Initialization of original variables (image to be reconstructed) and dual variables: Set the initial values of original variables u0 = 0 (image to be reconstructed), ν0 = 0, and dual variables p0 = q0 = r0 = t0 = 0 to zero.
[0156] (iv) Updating the original and dual variables during the iterative reconstruction process:
[0157] (1) Update the dual variable p as follows:
[0158]
[0159] (2) Update the dual variable q as follows:
[0160]
[0161] (3) Update the dual variable r as follows:
[0162]
[0163] (4) Update the dual variable t as follows:
[0164]
[0165] (5) Update of the original variable u (the image to be reconstructed):
[0166]
[0167] (6) Update of the original variable v:
[0168] v k+1 =v k -τ(-q k+1 +ε T (r k+1 (35)
[0169]
[0170] (7) Convergence judgment: The reconstruction quality index RMSE is calculated and output every 3 iterations. When the number of iterations is 2000, the RMSE value reaches stability, which proves that the algorithm has converged.
[0171] Example 2:
[0172] Reconstruction apparatus for sparse angle CL images
[0173] The sparse angle CL image reconstruction apparatus is used to perform the sparse angle CL image reconstruction method described above.
[0174] The detailed descriptions listed above are merely specific descriptions of feasible embodiments of the present invention, and are not intended to limit the scope of protection of the present invention. All equivalent embodiments or modifications made without departing from the spirit of the present invention should be included within the scope of protection of the present invention.
[0175] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.
Claims
1. A method for reconstructing a sparse angular CL image, reconstructing an image based on an image reconstruction model, characterized in that: The image reconstruction model includes a TGV term and a TV term. The TGV term is used to perform TGV regularization on the XY plane of the image, and the TV term is used to perform TV regularization on the Z-axis direction of the image.
2. The method of reconstruction of a sparse angular CL image according to claim 1, characterized in that The image reconstruction model includes a data fidelity term, which comprises a weighted matrix based on the image noise variance.
3. The method of reconstruction of a sparse angular CL image according to claim 2, characterized in that: The image reconstruction model is shown below. wherein, is the data fidelity term, g is the projection data, u is the image to be reconstructed, A is a system matrix of dimension M*N, and ∑ is a weighting matrix based on the variance of the image noise -1 is a diagonal matrix of dimension M*M; M is the total number of projection data, and N is the total number of voxels of the image to be reconstructed; is the X-Y axial plane gradient operator; is the Z-direction gradient operator; ε is the symmetric derivative operator; ν is the first-order gradient dual variable; a1, a0 and a z are parameters of the TGV term and the TV term, respectively.
4. The method for reconstructing a sparse angle CL image according to claim 3, characterized in that: The definition is as follows: v is close to Dual variables: The symmetric derivative operator ε is defined as follows:
5. The method for reconstructing a sparse angle CL image according to claim 4, characterized in that: ∑ -1 is a diagonal matrix, where each element of the diagonal is defined as: Let be the variance of the current pixel value, i∈M, j∈M, and M be the total number of projected data; Then ∑ -1 The diagonal matrix is represented as: Let ∑ -1 = W T W, the weight W is defined as:
6. The method for reconstructing a sparse angle CL image according to claim 5, characterized in that: The image reconstruction model is solved based on the Chambolle-Pock primal dual optimization algorithm to obtain the reconstructed image u.
7. The method for reconstructing a sparse angular CL image according to claim 6, characterized in that: When solving the image reconstruction model formula (1) based on the Chambolle-Pock primal dual optimization algorithm, the linear operator K is first defined. In the formula, K is a linear operator, W is a weight matrix of size M*M, A represents a system matrix of size M*N, M is the total number of projection data, and N is the total number of voxels in the image to be reconstructed. It is the XY-axis plane gradient operator; It is the gradient operator in the Z direction; ε is a symmetric derivative operator, and I is a matrix with all values of 1.
8. The method for reconstructing a sparse angle CL image according to claim 7, characterized in that: When solving the image reconstruction model formula (1) based on the Chambolle-Pock primal dual optimization algorithm, Two original variables, u and v, need to be updated, which leads to the following equation: F(y,e,h,o)=F1(y)+F2(e)+F3(h)+F4(o). The primal and dual problems are linked to a general saddle point optimization problem, which takes the following form: In the objective function of formula (1), the original variables are According to equation (11), the objective function is transformed into the following saddle point: The conjugate function is represented as follows: Where p, q, r, t are the dual variables of y, e, h, and o, respectively. The dual variable p is updated as follows: The dual variable q is updated as follows: The dual variable r is updated as follows: The dual variable t is updated as follows: Where δ = τ = 1 / L is the iteration step size, and the parameter L takes the maximum singular value of the linear operator K matrix. The original variable u is updated as follows: The original variable v is updated as follows:
9. The method for reconstructing a sparse angle CL image according to claim 8, characterized in that: The parameter L takes the largest singular value of the linear operator K matrix.
10. A device for reconstructing sparse angular CL images, characterized in that, Used to perform the method according to any one of claims 1-9.