Total variation CT image denoising method based on local structure metric

Abstract

The present invention relates to a total variation CT image denoising method based on local structure measurement, and belongs to the field of image processing. The present invention is divided into two steps: distinguishing edges from flat areas, and denoising CT images. The edge detection function of the present invention is an adaptive one, which makes full use of the global information of the local structure measurement to obtain a more appropriate function, and a more appropriate norm can be obtained by using the function. This is more accurate for distinguishing the flat and edge areas of noisy CT images. In terms of image denoising, the traditional TV model cannot play a role in protecting the edge. The present invention adopts an adaptive norm method. The norm of the regularization term of the model for the flat area is close to 2, which can remove noise as much as possible; for the edge part, the norm of the regularization term of the model is close to 1, which will play a role in protecting the edge.

Description

Technical Field

[0001] The invention belongs to the field of image processing and relates to a total variation CT image denoising method based on local structure measurement. Background Art

[0002] Computed Tomography (CT) collects projection data by passing X-rays through the object to be measured and reconstructs the tomographic image of the object to be measured. However, in the process of scanning objects with CT, factors such as radiation dose, detector sensitivity, electronic circuit components and mechanical vibration will increase the noise of the image and reduce the quality of the CT image. Image denoising is the process of reducing the noise of digital images and retaining details such as edges and textures as much as possible. Therefore, it is of great practical significance to study the denoising of CT images with high noise levels.

[0003] In the prior art, Rudin, Osher and Fatemi first proposed the total variation (TV) model, which consists of a regularization term and a fidelity term. The purpose of the regularization term is to remove image noise, and the fidelity term is to avoid distortion caused by excessive smoothing of the image. The TV model is widely used, but since the regularization term of the TV model may bring about a step effect, a large number of scholars have studied and improved this model based on this problem. Stamatios et al. introduced the structure tensor into the total variation model and proposed the structure tensor total variation (STV) model. The structure tensor of the image can well reflect the structural information in the image, such as features such as target edges and target corners, but the STV model cannot clearly show the contour of the image edge after denoising. Bing Song et al. proposed a generalized total variation (GTV) model, which changed the 1 norm of the regularization term of the TV model to an adaptive P norm, where P is between 1 and 2, and an edge detector is used to adjust the value of P. The model can adaptively adjust the smoothing strength according to the image edge and flat area, use 2-norm smoothing for flat areas, and use a norm close to 1 for denoising the edge area, which can retain image details as much as possible. However, the edge detector of this model cannot well reflect the real details of the noisy image. When the noise is large, the noise points may be mistaken for edge points, resulting in poor denoising effect. In 2019, Congjin et al. proposed an adaptive total variation (Adaptive variational partial differential equation, VPDE) model based on structure tensor, which uses the structure tensor to construct an edge detector to distinguish between flat and edge areas. However, when the overall grayscale value difference of the image is small, the edge detector will mistake the noise for the image corner point, and the edge detection function is calculated using a fixed function when calculating the norm, which will result in an inappropriate norm.

[0004] Therefore, in order to more effectively remove the noise of CT images, the present invention proposes a new local structure measurement method and edge detection function based on the VPDE model to distinguish edges and flat areas, and uses the newly established edge detection function as the norm of the regularization term of the total variation model to control the smoothing strength of each local area of ​​the image, thereby achieving the purpose of CT image denoising. Compared with the VPDE denoising model, this method can further improve the edge detection ability of noisy CT images and the denoising effect of images. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a total variation CT image denoising method based on local structure measurement, and propose a new image local structure measurement method and edge detection function, which can more accurately distinguish the edge and flat area of ​​noisy CT images. For noisy CT images, it has a better denoising effect than the traditional total variation denoising algorithm.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A total variation CT image denoising method based on local structure measurement, which includes edge detection and image denoising;

[0008] The edge detection is as follows: firstly, a third-order Gaussian filter is performed on the image, then a structure tensor of the result image is obtained, and an eigenvalue corresponding to the structure tensor is obtained; a structure metric is obtained according to the eigenvalue, and an adaptive edge detection model is established to distinguish flat areas and edge areas for noisy images;

[0009] The edge detection comprises the following steps:

[0010] S1: Calculate the structure tensor:

[0011]

[0012] Among them I x represents the first-order partial derivative of image I with respect to x, I xy It means that the image is derived with respect to y after taking the first-order partial derivative of x. y represents the first-order partial derivative of the image with respect to y, * represents the convolution symbol, G σ represents a third-order Gaussian filter with a standard deviation of σ;

[0013] S2: Calculate the eigenvalue corresponding to the structure tensor

[0014] When G σ When it is a third-order Gaussian filter, ST is a second-order matrix with at most two different eigenvalues. Let the eigenvalue λ1≥λ2, and record

[0015]

[0016] Among them, a 11 , a 12 , a 21 and a 22 are the elements of the matrix ST;

[0017]

[0018] Where λ1 is the larger eigenvalue of ST(x,y), and λ2 is the smaller eigenvalue of ST(x,y). The eigenvalue and eigenvector of ST(x,y) are used to extract the structural information of the image, including edges and corners.

[0019] S3: Constructing new local structure measures

[0020] The new local structure measure is:

[0021]

[0022] "An adaptive VPDE image denoising model based on structure tensor" points out that for a noisy CT image, when it is at the edge of the image, λ1≈λ2>>0, at this time m>>0; for the corner points in the image, λ1>>λ2>>0, at this time m>>0; when the image is a flat area, λ1≈λ2≈0, at this time m≈0; the size of the m value is used to distinguish the edge area and the flat area. When m>>0, it is judged as a flat area; when m≈0, it is judged as an edge area;

[0023] S4: Determine the norm using the new edge detection function

[0024] The calculation method of the norm p(m) is:

[0025]

[0026] Where m min represents the minimum value of all m, m max represents the maximum value of all m, represents the average value of all m, ε→0 + , a, b and c are unknown parameters, and the norm p(m) ranges from 1 to 2;

[0027] The image denoising comprises the following steps:

[0028] S5: Solving the total variation denoising model using the finite difference method

[0029] The total variation denoising model is

[0030]

[0031] Where I is the noisy image, is the gradient operator, Ω is the integrated area, f is the denoised image, λ is the penalty term coefficient, and J is the energy functional.

[0032] Optionally, the ε is 0.1.

[0033] Optionally, the total variation denoising model is solved by a finite difference method, and the specific solution process is as follows:

[0034] S51: Using the Lagrange multiplier method

[0035]

[0036] where u x It means to find the partial derivative of the noisy image with respect to x, is the symbol of partial derivative;

[0037] The corresponding partial differential equation is obtained as:

[0038]

[0039] S52: Use the steepest descent method to find the corresponding diffusion function

[0040]

[0041] S53: Discretization using finite difference methods

[0042]

[0043] Where n is the number of iterations, (i, j) represents the coordinates of the point, Δt is a parameter, and Λ0 represents the positions of neighboring points in four different directions of the target pixel, and the denoised CT image is obtained.

[0044] The beneficial effect of the present invention is that the present invention is divided into two steps: distinguishing edges from flat areas, and denoising CT images.

[0045] The present invention establishes a new local structure metric based on structure tensor. The local structure metric of the existing VPDE method will misjudge noise as image corner points for images with small overall grayscale value differences; the edge detection function of the existing VPDE method uses a fixed function to solve when calculating the norm, and does not make good use of the global information of the local structure metric data, which will lead to an inappropriate norm of the solution, and then lead to unsatisfactory denoising effect in some areas of the image.

[0046] The edge detection function of the present invention can avoid the above problems very well. The edge detection function of the present invention is adaptive. It makes full use of the global information of the local structure measurement in the previous step to obtain a more appropriate function. The function can be used to find a more appropriate norm. This is more accurate for distinguishing the flat and edge areas of noisy CT images. In terms of image denoising, the traditional TV model cannot play a role in protecting the edge. The present invention adopts an adaptive norm method. The norm of the regularization term of the model for the flat area is close to 2, which can remove noise as much as possible; for the edge part, the norm of the regularization term of the model is close to 1, which will play a role in protecting the edge.

[0047] 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

[0048] 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:

[0049] Figure 1 It is the edge detection function graph of VPDE;

[0050] Figure 2 is an edge detection function diagram of the present invention;

[0051] Figure 3 The figure is a flow chart of the image denoising method of the present invention. DETAILED DESCRIPTION

[0052] 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.

[0053] 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.

[0054] 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.

[0055] Figure 1 This is the edge detection function diagram of VPDE. The horizontal axis of the diagram is the local structure metric of the VPDE algorithm. The edge detection function is a function with fixed parameters. When the overall difference of the measured local structure metric is small, using this function will amplify the difference, making the smoothing force too large or too small, which will lead to poor image denoising effect.

[0056] Figure 2 The edge detection function of the present invention is a graph, the horizontal axis of which is the local structure metric of the present invention, and the vertical axis is the norm. The edge detection function of the present invention is an adaptive function, which uses the local structure metric to adjust the parameters of the edge detection function. When the difference between the measured local structure metric at both ends is small, such as Figure 2 As shown in the figure, the two ends of the function will become gentle and the middle will become steep, which makes the smoothing strength of parts with similar gray values ​​similar, and the smoothing strength of places with large gray values ​​has obvious differences, which can better distinguish edges and flat areas.

[0057] The present invention discloses a CT image denoising method based on a local structure metric of a structure tensor and used in a total variation model. The present invention is divided into two steps: edge detection and image denoising. For edge detection: first, a third-order Gaussian filter is performed on the image, and then the structure tensor of the result image is obtained to obtain the eigenvalue corresponding to the structure tensor. The structure metric is obtained according to the eigenvalue, and an adaptive edge detection model is established. The edge detection model can well distinguish between flat areas and edge areas for noisy images. For image denoising: the image denoising model of the present invention includes a regularization term and a fidelity term. A P norm is added on the basis of the regularization term of the classic TV model. The new local structure is processed using an adaptive edge detection function and used as the P norm. The regularization term is used to remove noise from the CT image. After being processed by the method, the CT image is protected at the edge while reducing a large amount of noise, and the denoising effect is more obvious for some flat areas.

[0058] Figure 3The image denoising method of the present invention comprises the following steps:

[0059] S1. Calculate the structure tensor;

[0060]

[0061] Among them I x represents the first-order partial derivative of image I with respect to x, I xy It means that the image is derived with respect to y after taking the first-order partial derivative of x. y represents the first-order partial derivative of the image with respect to y, * represents the convolution symbol, G σ Represents a third-order Gaussian filter with standard deviation σ.

[0062] This calculation method was first proposed by W. Forstner and E. Gulch in 1987 to extract structural information of images, such as corner points, continuous points, etc. The expression method of the structure tensor can effectively prevent the influence of positive and negative offset during gradient calculation, and the matrix has semi-positive definiteness, which can reduce the influence of noise after Gaussian filtering.

[0063] S2. Calculate the eigenvalue corresponding to the structure tensor;

[0064] When G σ When it is a third-order Gaussian filter, ST is a second-order matrix with at most two different eigenvalues. Let the eigenvalue λ1≥λ2, and record

[0065]

[0066] Among them, a 11 , a 12 , a 21 and a 22 are the elements of the matrix ST.

[0067]

[0068] Where λ1 is the larger eigenvalue of ST(x,y), and λ2 is the smaller eigenvalue of ST(x,y). The structural information of the image, such as edges and corners, can be quickly extracted using the eigenvalue and eigenvector of ST(x,y).

[0069] S3. Construct new local structure metrics;

[0070] The new local structure metric designed by the present invention is:

[0071]

[0072] For a noisy CT image, when it is at the edge of the image, λ1 and λ2 are both large and close, and the m value is large at this time; for the corner points in the image, λ1 is much larger than λ2 and greater than 0, and the m value is large at this time; when the image is a flat area, λ1 and λ2 are close and small, and the m value is small at this time. Therefore, for a noisy CT image, the size of the m value can be used to distinguish its edge area and flat area. When m is large, it is judged as a flat area; when m is small, it is judged as an edge area.

[0073] S4. Determine the norm using the new edge detection function;

[0074] The present invention designs an adaptive edge detection function for calculating the norm. The calculation method of the norm p(m) is:

[0075]

[0076] Where m min represents the minimum value of all m, m max represents the maximum value of all m, represents the average value of all m, ε is a small positive number, a, b and c are unknown parameters, and the norm p(m) ranges from 1 to 2. This function uses the maximum, minimum and average values ​​of the local structure metric obtained in the previous step in order to use global information to derive a more appropriate edge detection function, and does not require normalization in the VPDE method.

[0077] from Figure 2 Look, it is Figure 1 Compared with the function of VPDE shown in the figure, the area near the two ends of the function is smoother. In the edge area of ​​the image, the norm p(m) obtained by using the edge detection function will be smaller than the norm of VPDE and closer to 1, indicating that the invention has a better effect of protecting the edge at the edge of the image; in the flat area, the norm obtained by the invention is larger than the norm of VPDE and closer to 2, indicating that the invention has a stronger ability to remove noise in the flat area of ​​the image. In summary, the invention has a stronger ability to distinguish the edge and flat area of ​​the noisy CT image, and the denoising effect is also better.

[0078] S5. Solve the total variation model using the finite difference method;

[0079] The total variation denoising model of the present invention is

[0080]

[0081] Where I is the noisy image, ▽ is the gradient operator, Ω is the integrated area, f is the denoised image, λ is the penalty term coefficient, and J is the energy functional. The model is solved using the finite difference method, and the specific solution process is as follows:

[0082] S51. Using Lagrange multiplier method

[0083]

[0084] where u x It means to find the partial derivative of the noisy image with respect to x, is the symbol of partial derivative.

[0085] The corresponding partial differential equation is obtained as:

[0086]

[0087] S52. Use the steepest descent method to find the corresponding diffusion function

[0088]

[0089] S53. Discretization using the finite difference method

[0090]

[0091] Where n is the number of iterations, (i, j) represents the coordinates of the point, Δt is a parameter, and Λ0 represents the positions of neighboring points in four different directions of the target pixel. The denoised CT image can be obtained from the above formula.

[0092] 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 total variation CT image denoising method based on local structure measurement, characterized by: The method includes edge detection and image denoising; The edge detection is as follows: firstly, a third-order Gaussian filter is performed on the image, then a structure tensor of the result image is obtained, and an eigenvalue corresponding to the structure tensor is obtained; The structural metric is obtained based on the eigenvalues, and an adaptive edge detection model is established to distinguish the flat area and edge area for the noisy image. The edge detection comprises the following steps: S1: Calculate the structure tensor: Among them I x represents the first-order partial derivative of image I with respect to x, I xy It means that the image is derived with respect to y after taking the first-order partial derivative of x. y represents the first-order partial derivative of the image with respect to y, * represents the convolution symbol, G σ represents a third-order Gaussian filter with a standard deviation of σ; S2: Calculate the eigenvalue corresponding to the structure tensor When G σ When it is a third-order Gaussian filter, ST is a second-order matrix with at most two different eigenvalues. Let the eigenvalue λ1≥λ2, and record Among them, a 11 , a 12 , a 21 and a 22 are the elements of the matrix ST; Where λ1 is the larger eigenvalue of ST(x,y), and λ2 is the smaller eigenvalue of ST(x,y). The eigenvalue and eigenvector of ST(x,y) are used to extract the structural information of the image, including edges and corners. S3: Constructing new local structure measures The new local structure measure is: For a noisy CT image, when it is at the edge of the image, the size of the m value is used to distinguish the edge area and the flat area; S4: Determine the norm using the new edge detection function The calculation method of the norm p(m) adopts the adaptive norm method. For the flat area model, the regularization term norm is close to 2, which can remove noise as much as possible; for the edge part, the regularization term norm of the model is close to 1, which will play a role in protecting the edge. Specifically: Where m min represents the minimum value of all m, m max represents the maximum value of all m, represents the average value of all m, ε→0 + , a, b and c are unknown parameters, and the norm p(m) ranges from 1 to 2; The image denoising comprises the following steps: S5: Solving the total variation denoising model using the finite difference method The total variation denoising model is Where I is the noisy image, is the gradient operator, Ω is the integrated area, f is the denoised image, λ is the penalty term coefficient, and J is the energy functional.

2. The total variation CT image denoising method based on local structure metric according to claim 1, characterized in that: The ε is set to 0.

1.

3. The total variation CT image denoising method based on local structure metric according to claim 1, characterized in that: The total variation denoising model is solved by the finite difference method. The specific solution process is as follows: S51: Using the Lagrange multiplier method where u x It means to find the partial derivative of the noisy image with respect to x, is the symbol of partial derivative; The corresponding partial differential equation is obtained as: S52: Use the steepest descent method to find the corresponding diffusion function S53: Discretization using finite difference methods Where n is the number of iterations, (i, j) represents the coordinates of the point, Δt is a parameter, and Λ0 represents the positions of neighboring points in four different directions of the target pixel, and the denoised CT image is obtained.

Images