Mobile C-shaped arm CT image reconstruction method based on anisotropic self-guided filtering

Abstract

The invention relates to a mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering, and belongs to the technical field of image reconstruction. The method comprises the following steps: S1, starting a CT system, and obtaining orthogonal limited angle projection data of a scanned object; s2: for an orthogonal finite angle CT reconstruction problem, proposing ASGIF to suppress shadow artifacts and protect an image structure by using image sparsity and scanning angle range priori; and S3, as the target function is non-convex and non-smooth, direct optimization is difficult. Introducing a proxy function for the target function; decomposing the target into three sub-problems by utilizing a splitting technology, and obtaining a three-step algorithm; solving the sub-problem by using an alternating direction iteration method to obtain a solution of the reconstruction model; and S4, outputting a reconstructed image. According to the method, CT reconstruction is guided by utilizing the structural features of the image, the noise and artifacts of the orthogonal finite angle CT reconstruction image are effectively inhibited, and the quality of the CT reconstruction image is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of image reconstruction, and relates to a mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering. Background Art

[0002] Mobile C-arm CT is an advanced medical imaging device, mainly composed of an X-ray generator, a flat-panel detector and a workbench. The device is easy to operate and powerful. During surgery, the ideal working position can be achieved by adjusting the C-arm sliding angle along the track, the axial rotation angle or the left and right swing angle. Among them, the working position refers to the C-arm angle required during surgery. However, the surgical environment may limit the scanning angle range, making the obtained projection data incomplete. For example, in order to avoid the C-arm colliding with the patient, projection data can only be collected at certain angles. In addition, X-ray radiation may cause cancer or genetic diseases. In order to adapt to the surgical environment or reduce the radiation dose, it is of great significance to study the use of the patient's projection data within a certain angle range for image reconstruction.

[0003] Sparse angle sampling, limited angle sampling and segmented limited angle sampling are three effective downsampling strategies that can obtain projection data of the object to be measured at some angles. Sparse angle sampling refers to scanning the object to be measured at equal intervals within a 360-degree range, which can reduce radiation dose or scanning time. However, in C-arm CT, sparse angle sampling requires frequent operation of the switch button, which is complicated to implement. Although there are some mature sparse angle CT reconstruction methods, the complexity of technical implementation has led to the fact that sparse angle CT has not been widely used. Limited angle sampling usually refers to scanning the object to be measured within a range of less than 180 degrees. Limited angle CT is easy to implement, but the projection data has a high data correlation and the reconstructed image has obvious artifacts. Segmented limited angle sampling refers to scanning the object to be measured in multiple segments within a 360-degree range. Segmented limited angle sampling has the characteristics of limited angle sampling and sparse angle sampling. When the number of segments is equal to 1, segmented limited angle sampling degenerates into traditional limited angle sampling. As the number of segments increases, segmented limited angle sampling gradually approaches sparse angle sampling. Orthogonal finite angle sampling is a piecewise finite angle sampling. The finite angle ranges covered by the two X-ray generator trajectories are α and 1 and α 2, and the bisectors of the two angle ranges are mutually orthogonal. In practical applications, CT reconstruction theory shows that edges and details tangent to the projection direction are easy to recover, and the artifact direction of the reconstructed image is directly related to the scanning angle range. Orthogonal finite angle sampling makes the edges and details in the object tangent to more projection directions, reducing the ill-posedness of the CT reconstruction problem. Nevertheless, due to incomplete projection data, orthogonal finite angle CT images still have shadow artifacts. At present, there are many methods for solving the problem of reconstruction of incomplete projection data. Traditional analytical reconstruction methods, such as filtered back projection methods, reconstruct images with obvious geometric distortion and shadow artifacts. Algebraic reconstruction technology and simultaneous algebraic reconstruction technology are more effective in suppressing artifacts and noise, but it is difficult to obtain high-quality reconstructed images. With the introduction of compressed sensing theory, regularized reconstruction methods have received widespread attention in solving the CT reconstruction problem of incomplete projection data. In addition, image filtering methods have been applied to CT image reconstruction. A good image filtering method can retain important image structure features while suppressing noise. The patent application with publication number CN 116843784A discloses "a CT image reconstruction method based on self-guided filtering". This method mainly uses image sparsity as prior information and uses the structural features of the reconstructed image itself as a reference to guide image reconstruction, which can effectively suppress shadow artifacts and protect image structure. However, the above patent does not take into account the impact of intensity changes in different directions on image quality. Summary of the invention

[0004] In view of this, the purpose of the present invention is to provide a mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering. Aiming at the problem of orthogonal limited-angle CT reconstruction, the method takes image sparsity and scanning angle range as prior information and designs an anisotropic self-guided image filter to guide CT reconstruction.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering, the method comprising the following steps:

[0007] S1: Start the computed tomography (CT) system to obtain orthogonal limited angle projection data of the scanned object;

[0008] S2: Aiming at the orthogonal limited-angle CT reconstruction problem, a mobile C-arm CT image reconstruction model ASGIF (Anisotropic Self-Guided Image Filtering) based on anisotropic self-guided filtering is proposed to suppress shadow artifacts and protect image structure by utilizing image sparsity and scanning angle range priors.

[0009] S3: Since the objective function is non-convex and non-smooth, it is difficult to optimize directly. To simplify the solution process, a proxy function is first introduced for the objective function. Then, the objective is decomposed into three sub-problems using the splitting technique, and a three-step algorithm is obtained. Finally, the alternating direction iteration method is used to solve the sub-problems to obtain the solution of the reconstruction model.

[0010] S4: Output the reconstructed image.

[0011] Furthermore, in S1, the X-ray source and the detector are rotated around the object to collect orthogonal projection data.

[0012] Furthermore, in S2, the ASGIF model is:

[0013]

[0014] The first term is the data fidelity term, and the second term is the regularization term; the matrix A is the projection matrix of the CT system, p is the projection data, f is the image to be reconstructed, ε is a non-negative positive number, and λ is the regularization parameter; |·| represents the absolute value operator; d∈{x,y}, where x represents the horizontal direction and y represents the vertical direction; w d is the weight parameter in direction d; D d f i Represents the difference of image f at pixel i along direction d.

[0015] Further, in S3, solving the ASGIF model specifically includes the following steps:

[0016] S31: Introduce a proxy function for the objective function;

[0017] S32: Decompose the goal into three sub-problems and obtain a three-step algorithm;

[0018] S33: Use the alternating direction iteration method to solve the subproblems to obtain the solution of the ASGIF model.

[0019] Further, in S31, the regularization term of the objective function is recorded as:

[0020]

[0021] The following relationship holds:

[0022]

[0023] Only when |D d f i |<ε, the inequality holds, and the difference between them is very small; As a proxy function of the R(f,ε) term; solving the ASGIF model becomes solving the following problem (4):

[0024]

[0025] Further, the S32 includes the following steps:

[0026] S321: Introduce auxiliary variable u and reconstruct model (4) as follows:

[0027]

[0028] S322: Use the augmented Lagrangian method to transform the optimization problem (5) into:

[0029]

[0030] Among them, α is a positive parameter, b is a Lagrange multiplier; the model (6) to be solved is the optimization model about f,u,b;

[0031] S323: Problem (6) is divided into three sub-problems about variables f, u, and b, as follows:

[0032] Sub-question 1:

[0033] Sub-question 2:

[0034] Subproblem 3: b←b-f+u;

[0035] Finally, the above three sub-problems are solved alternately to obtain the reconstructed image.

[0036] Further, the S33 specifically includes the following steps:

[0037] S331: Sub-questions about f:

[0038]

[0039] Wherein, (7) consists of two terms; SART is used to minimize the first term to obtain the intermediate image f (k+1 / 2) ; Subproblem 1 becomes the following problem (8):

[0040]

[0041] Get the analytical solution to the problem:

[0042]

[0043] S332: Sub-problems about u:

[0044]

[0045] Observed is the quadratic term and (D d u i ) 2 The objective (10) is reformulated as the following optimization problem (11):

[0046]

[0047] Where L d is the Toeplitz matrix in the d direction, used to calculate the forward difference of image u; Q d (d∈{x,y}) means that the i-th diagonal element is diagonal matrix; use the iterative method to solve the above problem (11);

[0048] S333: Update Lagrange multiplier b:

[0049] b←b-f+u(12)

[0050] Further, in S4, when the iterative algorithm in S3 stops iterating, the reconstructed image is output.

[0051] The beneficial effect of the present invention is that the method uses image sparsity and scanning angle range as prior information to guide CT reconstruction, which can effectively suppress noise and artifacts of the reconstructed image, thereby improving the quality of the CT reconstructed image.

[0052] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0054] Figure 1 It is a flow chart of the present invention;

[0055] Figure 2 This is a schematic diagram of a mobile C-arm CT according to the present invention;

[0056] Figure 3 This is a schematic diagram of orthogonal limited angle sampling of the present invention;

[0057] Figure 4 This is a reference image of the FORBILD head digital phantom of the present invention;

[0058] Figure 5The reconstructed images of the FORBILD head phantom obtained by the present invention using projection data within the scanning range of [105°, 165°] ∪ [195°, 255°]; (a) is the reconstructed image obtained by the TV method; (b) is the reconstructed image obtained by the ATV method; (c) is the reconstructed image obtained by the ADM-L0 method; (d) is the reconstructed image obtained by the ASGIF method; (e) is the residual image of the reconstructed image obtained by the TV method; (f) is the residual image of the reconstructed image obtained by the ATV method; (g) is the residual image of the reconstructed image obtained by the ADM-L0 method; (h) is the residual image of the reconstructed image obtained by the ASGIF method. DETAILED DESCRIPTION

[0059] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0060] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0061] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0062] The present invention provides a mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering, which uses image sparsity and scanning angle range as prior information to guide CT reconstruction, and can effectively improve the quality of CT reconstructed images from incomplete projection data.

[0063] Reference Figure 1 The main steps of the present invention are:

[0064] Step 1) Start the CT system, rotate the X-ray source and detector around the object, and obtain orthogonal limited angle projection data of the scanned object.

[0065] Step 2) According to the CT imaging principle, the ASGIF model is established as follows:

[0066]

[0067] The first term is the data fidelity term, and the second term is the regularization term; the matrix A is the projection matrix of the CT system, p is the projection data, f is the image to be reconstructed, ε is a non-negative positive number, and λ is the regularization parameter; |·| represents the absolute value operator; d∈{x,y}, where x represents the horizontal direction and y represents the vertical direction; w d is the weight parameter in direction d; D d f i Represents the difference of image f at pixel i along direction d.

[0068] Step 3) According to the model established in step 2), firstly introduce a proxy function for the objective function; then, use the splitting technique to decompose the objective into three sub-problems and obtain a three-step algorithm; finally, use the alternating direction iteration method to solve the sub-problems to obtain the solution of the ASGIF model.

[0069] Step 3-1) introduce a proxy function for the objective function;

[0070] The regularization term in the objective function (1) is denoted as R(f,ε), that is:

[0071]

[0072] The following relationship holds:

[0073]

[0074] Only when |D d f i |<ε, the inequality will hold, and the difference between them is very small; As a proxy function of the R(f,ε) term; solving the ASGIF model becomes solving the following problem (4):

[0075]

[0076] Step 3-2) Based on step 3-1), the objective function is decomposed into three sub-problems to obtain a three-step algorithm;

[0077] Step 3-2-1) introduces the auxiliary variable u, and the reconstruction model (4) can be expressed as follows:

[0078]

[0079] Step 3-2-2) Use the augmented Lagrangian method to transform the optimization problem (5) into:

[0080]

[0081] Among them, α is a positive parameter, b is a Lagrange multiplier. The model (6) to be solved is the optimization model of f,u,b.

[0082] Step 3-2-3) Problem (6) can be divided into three sub-problems about variables f, u, and b, as follows:

[0083] Sub-question 1:

[0084] Sub-question 2:

[0085] Subproblem 3: b←b-f+u.

[0086] Finally, the reconstructed image can be obtained by alternately solving the above three sub-problems.

[0087] Step 3-3) Based on step 3-2), the solution of the ASGIF model is obtained by solving the sub-problems.

[0088] Step 3-3-1) Sub-problems about f:

[0089]

[0090] In theory, the analytical solution can be obtained by solving the derivative of problem (7). Let:

[0091]

[0092] but

[0093]

[0094] The analytical solution of problem (7) is obtained by calculation as f = (A T A+αI) -1 (A T p+α(u+b)), where I is the identity matrix. Observe that we can directly find A T The inverse calculation of A+αI is large and difficult to implement. The present invention uses SART reconstruction to obtain an intermediate result, denoted as f (k+1 / 2) ; Then, the approximate problem of subproblem (7) is as follows:

[0095]

[0096] Finally, the analytical solution to the problem is obtained by calculation:

[0097]

[0098] Step 3-3-2) Sub-problem about u:

[0099]

[0100] Observed is the quadratic term and (D d u i ) 2 Then the objective (12) can be rewritten as the following optimization problem:

[0101]

[0102] Where L d is the Toeplitz matrix in the d direction, used to calculate the forward difference of image u; Q d (d∈{x,y}) means that the i-th diagonal element is Theoretically, the analytical solution can be easily obtained by solving the derivative of problem (13). Here, the objective function in equation (13) is denoted as s(u), then:

[0103]

[0104] By calculating the derivative of s(u) and setting it to 0, we can obtain the following system of equations:

[0105]

[0106] Observing the system of equations (15), the most direct solution is to calculate the target matrix However, the direct inversion is computationally intensive and difficult to implement. In addition, considering that the target matrix is ​​a symmetric positive definite Laplace matrix, the present invention tends to use an iterative method to solve problem (13).

[0107] Step 3-3-3) Update the Lagrange multiplier b:

[0108] b←b-f+u(16)

[0109] Further, step 3) can be summarized as the following algorithm:

[0110]

[0111] Step 4) When the iterative algorithm in step 3) stops iterating, the reconstructed image is output.

[0112] Combine the following Figure 2 , Figure 3 , Figure 4 and Figure 5 The specific implementation modes of the present invention are described in detail.

[0113] Reference Figure 2 After the mobile C-arm CT system is started, the X-ray generator emits X-rays; then, the flat-panel detector collects the projection data of the patient at different angles and sends it to the computer on the workbench for CT reconstruction; finally, the tomographic images of different parts of the patient are displayed to provide assistance for medical diagnosis.

[0114] Reference Figure 3 Orthogonal finite angle sampling is a piecewise finite angle sampling. The finite angle ranges covered by the two X-ray generator trajectories are α 1 and α 2 , and the angular bisectors of the two angle ranges are orthogonal to each other. The total scanning angle range is recorded as α τ (α τ =α 1 +α 2 <180°). For a given α τ , multiple 1 and α 2 Orthogonal trajectory configuration. In C-arm CT, orthogonal finite angle sampling is easy to implement. For example, the X-ray generator is along Figure 3 The orthogonal trajectory shown can be sampled without frequent operation of the switch button.

[0115] In order to better demonstrate the advantages of the mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering in the reconstruction effect, the method of the present invention is compared with the existing TV method, ATV method and ADM-L0 method in combination with specific embodiments. The present invention mainly uses the FORBILD head digital phantom for simulation experiments, and the reference image is as follows: Figure 4 As shown. In this experiment, the orthogonal limited angle CT scanning angle range is selected as [105°, 165°] ∪ [195°, 255°]. The number of iterations N is set to 2000 times, the number of detector units is 512, the distance from the ray source to the rotation center is 210.66mm, the distance to the detector is 553.74mm, and the angle increment between adjacent projection angles is 2°. The reconstructed image and residual image are shown in Figure 5 shown. Figure 5The reconstructed images of the FORBILD head phantom obtained by the present invention using projection data within the scanning range of [105°, 165°] ∪ [195°, 255°]; (a) is the reconstructed image obtained using the TV method; (b) is the reconstructed image obtained using the ATV method; (c) is the reconstructed image obtained using the ADM-L0 method; (d) is the reconstructed image obtained using the ASGIF method; (e) is the residual image of the reconstructed image obtained using the TV method; (f) is the residual image of the reconstructed image obtained using the ATV method; (g) is the residual image of the reconstructed image obtained using the ADM-L0 method; (h) is the residual image of the reconstructed image obtained using the ASGIF method. The display windows of the first and second rows are [0.5, 1.5] and [-0.2, 0.2], respectively. The images reconstructed by the TV method and the ATV method have obvious shadow artifacts; both the ADM-L0 method and the ASGIF method can well suppress shadow artifacts and protect image structures, but the residual image of the ASGIF method is closer to the reference image and has better reconstruction performance. Comparative experiments have confirmed that the method described in the present invention can effectively improve the quality of orthogonal limited-angle CT reconstructed images.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering, characterized in that: The method comprises the following steps: S1: Start the computed tomography (CT) system to obtain orthogonal limited angle projection data of the scanned object; S2: Aiming at the orthogonal limited-angle CT reconstruction problem, a mobile C-arm CT image reconstruction model ASGIF (Anisotropic Self-Guided Image Filtering) based on anisotropic self-guided filtering is proposed to suppress shadow artifacts and protect image structure by utilizing image sparsity and scanning angle range priors. S3: Since the objective function is non-convex and non-smooth, it is difficult to optimize directly. To simplify the solution process, a proxy function is first introduced for the objective function. Then, the objective is decomposed into three sub-problems using the splitting technique, and a three-step algorithm is obtained. Finally, the alternating direction iteration method is used to solve the sub-problems to obtain the solution of the reconstruction model. S4: Output the reconstructed image.

2. The mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering according to claim 1, characterized in that: In S1, the X-ray source and the detector are rotated around the object to collect orthogonal projection data.

3. The mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering according to claim 1, characterized in that: In S2, the ASGIF model is: The first term is the data fidelity term, and the second term is the regularization term; the matrix A is the projection matrix of the CT system, p is the projection data, f is the image to be reconstructed, ε is a non-negative positive number, and λ is the regularization parameter; |·| represents the absolute value operator; d∈{x,y}, where x represents the horizontal direction and y represents the vertical direction; w d is the weight parameter in direction d; D d f i Represents the difference of image f at pixel i along direction d.

4. The mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering according to claim 1, characterized in that: In S3, solving the ASGIF model specifically includes the following steps: S31: Introduce a proxy function for the objective function; S32: Decompose the goal into three sub-problems and obtain a three-step algorithm; S33: Use the alternating direction iteration method to solve the subproblems to obtain the solution of the ASGIF model.

5. The method for mobile C-arm CT image reconstruction based on anisotropic self-guided filtering according to claim 4, characterized in that: In S31, the regularization term of the objective function is recorded as: The following relationship holds: Only when |D d f i |<ε, the inequality holds, and the difference between them is very small; As a proxy function of the R(f,ε) term; solving the ASGIF model becomes solving the following problem (4):

6. The mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering according to claim 4, characterized in that: The S32 includes the following steps: S321: Introduce auxiliary variable u and reconstruct model (4) as follows: S322: Use the augmented Lagrangian method to transform the optimization problem (5) into: Among them, α is a positive parameter, b is a Lagrange multiplier; the model (6) to be solved is the optimization model about f,u,b; S323: Problem (6) is divided into three sub-problems about variables f, u, and b, as follows: Sub-question 1: Sub-question 2: Sub-problem 3: b←b-f+u; Finally, the above three sub-problems are solved alternately to obtain the reconstructed image.

7. The mobile C-arm CT image reconstruction method based on anisotropic self-guided filtering according to claim 4, characterized in that: The S33 specifically includes the following steps: S331: Sub-questions about f: Wherein, (7) consists of two terms; SART is used to minimize the first term to obtain the intermediate image f (k+1 / 2) ; Subproblem 1 becomes the following problem (8): Get the analytical solution to the problem: S332: Sub-problems about u: Observed is the quadratic term and (D d u i ) 2 The objective (10) is reformulated as the following optimization problem (11): Where L d is the Toeplitz matrix in the d direction, used to calculate the forward difference of image u; Q d (d∈{x,y}) means that the i-th diagonal element is diagonal matrix; use the iterative method to solve the above problem (11); S333: Update Lagrange multiplier b: b←b-f+u(12).

8. The method for mobile C-arm CT image reconstruction based on anisotropic self-guided filtering according to claim 1, characterized in that: In S4, when the iterative algorithm in S3 stops iterating, the reconstructed image is output.

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