An implementation method for image denoising based on improved hybrid-order total variation

Abstract

The present invention discloses an implementation method for image denoising based on improved hybrid-order total variation, including the following steps: S1, performing gray-scale conversion on the collected original image and adding noise thereto; S2, performing filtering using the combined Gauss-Laplace transform; S3, introducing an anisotropic diffusion tensor into the TV1 model and introducing an image feature extraction function based on differential curvature into the LLT model; S4, using an adaptive weight function to couple the TV1 model and the LLT model to obtain a coupled model; S5, post-processing the denoised image obtained through the coupled model using the fast non-local means filtering algorithm; S6, obtaining the discrete form of the coupled model using the discrete difference method, adopting an iterative method to update pixel values for denoising to obtain a denoised image, and verifying the effectiveness and feasibility of the coupled model using the peak signal-to-noise ratio and the structural similarity index. The present invention can ensure the integrity of image edge information and improve the denoising efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of image denoising, and particularly to an implementation method for improved hybrid-order total variation image denoising. Background Art

[0002] In today's digital age, images have become an important form of information dissemination and storage, deeply integrated into many fields such as scientific research, industry, medicine, and entertainment. With the rise of artificial intelligence and computer vision applications, people have higher and higher requirements for image quality. The quality of images directly affects the accuracy of information transmission and the quality of user experience, and has become an important support for the development of various fields. However, during the acquisition, transmission, and storage of images, they will inevitably be interfered by noise and degenerate, resulting in the inability of images to accurately present the original essential characteristics of things. In order to restore images to a state where they can truthfully reflect the true appearance of things, image denoising needs to be performed through image processing techniques. The total variation image denoising method is an important branch in the field of image denoising. Among them, the high-order variation LLT denoising model (LLT model) is prone to edge blurring due to excessive smoothing; the TV (Total Variation) denoising model (TV1 model) based on the norm is an anisotropic diffusion model, which can effectively preserve edges and smooth noise, but is prone to "staircase effects" in smooth areas. Summary of the Invention

[0003] Object of the Invention: The object of the present invention is to provide an implementation method for improved hybrid-order total variation image denoising to solve problems such as insufficient representation of image edge information, unsatisfactory denoising effect, and low iteration efficiency.

[0004] Technical Solution: An implementation method for improved hybrid-order total variation image denoising includes the following steps:

[0005] S1, performing grayscale conversion on the collected original image and adding noise to it;

[0006] S2, performing filtering using the combined Gaussian-Laplacian transform;

[0007] S3, introducing an anisotropic diffusion tensor into the TV1 model and introducing an image feature extraction function based on differential curvature into the LLT model;

[0008] S4, using an adaptive weight function to couple the TV1 model and the LLT model to obtain a coupled model;

[0009] S5, performing post-processing on the denoised image obtained through the coupled model using the fast non-local means filtering algorithm;

[0010] S6. The discrete form of the coupled model is obtained using the discrete difference method. The pixel values are updated by the iterative method for denoising to obtain the denoised image, and the effectiveness and feasibility of the coupled model are verified using the peak signal-to-noise ratio and the structural similarity index.

[0011] Furthermore, after introducing the anisotropic diffusion tensor, the expression of the TV1 model is:

[0012] ,

[0013] where is the minimized energy functional of the TV1 model, is the original grayscale image, is the noisy image function, is the gradient of the noisy image function, is the weight parameter;

[0014] represents the anisotropic diffusion tensor, and its expression is:

[0015] ,

[0016] ,

[0017] where the parameters and are used to adjust the intensity of the tensor, A is the direction of the image gradient, is the normal vector of the image gradient, T represents matrix transpose, and e represents the natural constant;

[0018] After introducing the image feature extraction function based on differential curvature, the expression of the LLT model is:

[0019] ,

[0020] where is the minimized energy functional of the LLT model;

[0021] is the image feature extraction function based on differential curvature, and its expression is:

[0022] ,

[0023] where represents the normalized differential curvature, represents a minimum value.

[0024] Furthermore, the expression of coupling the TV1 model and the LLT model using the adaptive weight function is:

[0025] ,

[0026] In the formula, represents the minimized energy functional of the coupling model; the first term is the regularization term and the second term is the fidelity term; is the noisy image function of the gradient magnitude; is the adaptive weight parameter that adjusts the weight of the fidelity term; is the adaptive weight function used to adjust the regularization terms of the TV1 model and the LLT model;

[0027] The said adaptive weight parameter has the expression:

[0028] ,

[0029] In the formula, ; has the expression:

[0030] ,

[0031] In the formula, is the minimum value of; is the maximum value of;

[0032] is the differential curvature, and its expression is:

[0033] ,

[0034] In the formula, is the second-order derivative of the image along the gradient direction, is the second-order derivative of the image along the edge direction; their expressions are respectively:

[0035] ,

[0036] ,

[0037] In the formula, is the first-order derivative of the noisy image function along the direction of, is the first-order derivative of the noisy image function along the direction of, is the second-order derivative of the noisy image function along the direction of, is the second-order derivative of the noisy image function along the direction of, is the noisy image function The second-order partial derivative of;

[0038] The adaptive weight function The expression is:

[0039] ,

[0040] In the formula, Is the arccosine function, which is a decreasing function; Is the noisy image function The gradient magnitude of, Is the adaptive gradient threshold; 、 Are respectively two thresholds with different values; Is the noise visibility function; The expression is:

[0041] ,

[0042] In the formula, Is the image Local variance, Is The gray value at the point;

[0043] Is the local mean, and its expression is:

[0044] ,

[0045] In the formula, h and q respectively represent the coordinate values on the x-axis and y-axis, both of which are variables; P and Q are constants, representing the half-widths of the image region block in the x-axis and y-axis directions respectively; (2P + 1) is the length of the image region block, (2Q + 1) is the width of the image region block, and (2P + 1)(2Q + 1) represents the area size of the image region block.

[0046] Furthermore, in step S5, in the fast non-local means filtering algorithm, for each pixel in the image, similar pixels are searched for within the search window centered on the pixel, and the similarity is measured by calculating the gray value difference between the neighborhoods around the two pixels.

[0047] Compared with the prior art, the remarkable effects of the present invention are as follows:

[0048] 1. The present invention uses the Gaussian-Laplace transform instead of Gaussian filtering, optimizes the image preprocessing process, solves the phenomenon of edge weakening after Gaussian filtering of the image, highlights the edge details, and makes the edges clearer and sharper;

[0049] 2. By introducing an anisotropic diffusion tensor into the TV1 model, the present invention precisely adjusts the edge diffusion direction, effectively solving key problems such as the balance between edge protection, noise removal, and detail preservation in image denoising, thereby maximizing the retention of image details while removing noise;

[0050] 3. By introducing an image feature extraction function based on differential curvature into the LLT model, the present invention effectively adjusts the diffusion strength in different regions of the image, enhances the smoothing strength at large noise points, and suppresses the "staircase effect" of the total variation model, making the LLT model more robust when dealing with large noise points, capable of reducing the generation of artifacts and improving the quality of the denoised image;

[0051] 4. By improving the adaptive weight function to couple the TV1 model and the LLT model, the present invention obtains a corresponding coupled model, which can effectively remove noise while protecting image details, thereby improving the robustness and generalization ability of image processing;

[0052] 5. The denoised image obtained by the coupled model is post-processed using the fast non-local means filtering algorithm, which can repair detail and texture information, further suppress residual noise, and then enhance the stability of the image quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flowchart of the present invention;

[0054] Figure 2 is the original image used in the experiments of the present invention: among them, (a) is the first water gauge diagram, (b) is the second water gauge diagram, (c) is Bird, (d) is the house, (e) is the tiger, and (f) is the arch;

[0055] Figure 3 is the noisy image used in the experiments of the present invention with σ = 35, where (a) is the first water gauge diagram, (b) is the second water gauge diagram, (c) is Bird, (d) is the house, (e) is the tiger, and (f) is the arch;

[0056] Figure 4 is a comparison diagram of the denoising effects of the first water gauge using 6 models, where (a) is the NLM algorithm, (b) is the LLT model, (c) is the TV2 model, (d) is the TV1 model, (e) is the ZTV model, and (f) is the model of the present invention;

[0057] Figure 5 is a comparison diagram of the denoising effects of the second water gauge using 6 models, where (a) is the NLM algorithm, (b) is the LLT model, (c) is the TV2 model, (d) is the TV1 model, (e) is the ZTV model, and (f) is the model of the present invention;

[0058] Figure 6 It is a comparison chart of the denoising effects of a house using 6 models. Among them, (a) is the NLM algorithm, (b) is the LLT model, (c) is the TV2 model, (d) is the TV1 model, (e) is the ZTV model, and (f) is the model of the present invention;

[0059] Figure 7 It is a comparison chart of the denoising effects of a tiger using 6 models. Among them, (a) is the NLM algorithm, (b) is the LLT model, (c) is the TV2 model, (d) is the TV1 model, (e) is the ZTV model, and (f) is the model of the present invention;

[0060] Figure 8 It is a comparison chart of the denoising effects of an arch using 6 models. Among them, (a) is the NLM algorithm, (b) is the LLT model, (c) is the TV2 model, (d) is the TV1 model, (e) is the ZTV model, and (f) is the model of the present invention;

[0061] Figure 9 It is a comparison chart of the denoising effects of a Bird using 6 models. Among them, (a) is the NLM algorithm, (b) is the LLT model, (c) is the TV2 model, (d) is the TV1 model, (e) is the ZTV model, and (f) is the model of the present invention. Detailed implementation manner

[0062] The present invention will be further described in detail below in conjunction with the accompanying drawings of the specification and the specific implementation manner.

[0063] The present invention couples the TV1 model and the LLT model, and proposes an improved hybrid-order total variation image denoising method. This method has better denoising effects, better edge preservation effects, and more effectively suppresses the "staircase effect" of the TV1 model.

[0064] As Figure 1 shown, it is a flowchart for implementing the improved hybrid-order total variation image denoising method, including the following steps:

[0065] Step 1, perform gray-scale conversion on the collected original image and perform noise addition processing. The expression is:

[0066] ,

[0067] In formulas (1) and (2), is the original gray-scale image, is the noise-added image function, is the Gaussian kernel function, is the random noise variance; is the two-dimensional spatial coordinates in the image domain.

[0068] Preferably, the gray conversion uses the rgb2gray function in MATLAB to convert the acquired RGB image into a grayscale image; the image noise addition process uses the imnoise function in MATLAB to add Gaussian noise to verify the effectiveness of the improved model, and its calling format is , where represents the original grayscale image, gaussian represents Gaussian noise in MATLAB, m is the mean of the Gaussian noise, and s is the variance of the Gaussian noise. The original image as shown in Figure 2 is subjected to gray conversion, and the noisy image after gray conversion is as shown in Figure 3 .

[0069] Step 2, use the combined Gaussian-Laplacian transform to replace Gaussian filtering and optimize the filtering process of image preprocessing.

[0070] Preferably, the expression for filtering using the combined Gaussian-Laplacian transform is:

[0071] ,

[0072] Let be the noisy image function. From the commutativity of convolution and differentiation in the linear system, its expression is:

[0073] ,

[0074] where is the Laplacian operator, represents the noisy image function after the product of the noisy image function and the Gaussian kernel function and then the Laplace transform, represents the product of the Gaussian kernel function after the Laplace transform and the noisy image function

[0075] Step 3, introduce the anisotropic diffusion tensor in the TV1 model and introduce the image feature extraction function based on differential curvature in the LLT model;

[0076] Preferably, after introducing the anisotropic diffusion tensor, the expression of the TV1 model is:

[0077] ,

[0078] In the formula, is the minimized energy functional of the TV1 model, is the noisy image function, is the gradient of the noisy image function , is the weight parameter.

[0079] Represents the anisotropic diffusion tensor, which can precisely adjust the edge diffusion direction and is beneficial to maintaining the integrity of edge information. Its expression is:

[0080] ,

[0081] ,

[0082] In the formula, the parameters and are used to adjust the intensity of the tensor. A is the direction of the image gradient, is the normal vector of the image gradient, T represents matrix transpose, and e represents the natural constant.

[0083] Preferably, after introducing the image feature extraction function based on differential curvature, the expression of the LLT model is:

[0084] ,

[0085] In the formula, is the minimized energy functional of the LLT model;

[0086] is the image feature extraction function based on differential curvature, which can adjust the diffusion strength in different regions of the image and simultaneously increase the smoothing strength at large noise points. Its expression is:

[0087] ,

[0088] In the formula, represents the normalized differential curvature, represents a minimum value to avoid the denominator being zero.

[0089] Step 4, use the adaptive weight function to couple the TV1 model and the LLT model to obtain the coupled model;

[0090] Preferably, using the adaptive weight function to couple the TV1 model and the LLT model, the expression of the coupled model is:

[0091] ,

[0092] In the formula, is the minimized energy functional of the coupled model; the first term is the regularization term, and the second term is the fidelity term; is the noisy image function of the gradient modulus; is the adaptive weight parameter, which can adaptively adjust the weight of the fidelity term; is the adaptive weight function, which is used to adjust the regularization terms of the TV1 model and the LLT model;

[0093] Preferably, the adaptive weight parameter has the following expression:

[0094] ,

[0095] wherein, to ensure that the adaptive weight parameter is always a positive number; is the normalized difference curvature, and its functional expression is:

[0096] ,

[0097] wherein, is the minimum value of; is the maximum value of; represents the difference curvature, and its expression is:

[0098] ,

[0099] wherein, is the second-order derivative of the image along the gradient direction, is the second-order derivative of the image along the edge direction; their expressions are respectively:

[0100] ,

[0101] ,

[0102] wherein, is the first-order derivative of the noisy image function along the x direction, is the first-order derivative of the noisy image function along the y direction, is the second-order derivative of the noisy image function along the x direction, is the second-order derivative of the noisy image function along the y direction, is the second-order partial derivative of the noisy image function .

[0103] Preferably, the adaptive weight function has the following expression:

[0104] ,

[0105] wherein, is the arccosine function, which is a decreasing function; is the gradient modulus value of the noisy image function , is the adaptive gradient threshold; is the noise visibility function, which is used to represent the intensity of noise. The greater the noise intensity, the greater the value of the visibility function; and are respectively two thresholds with different values, which are used to solve the optimal threshold. In this embodiment, and are taken; is the regularization term used to couple the TV1 model and the LLT model, which can effectively remove noise while protecting image details and achieve the balance between the two.

[0106] The expression is:

[0107] ,

[0108] In the formula, is the local variance of the image, is the gray value at point ; is the local mean, and its expression is:

[0109] ,

[0110] In the formula, h and q respectively represent the coordinate values on the x-axis and y-axis, both of which are variables; P and Q are constants, representing the half-widths of the image region block in the x-axis and y-axis directions respectively, (2P + 1) is the length of the image region block, (2Q + 1) is the width of the image region block, and (2P + 1)(2Q + 1) represents the area size of the image block.

[0111] Step 5, post-process the denoised image obtained by the coupled model using the fast non-local mean filtering algorithm;

[0112] Preferably, the fast non-local mean filtering algorithm is an improvement of the non-local mean filtering algorithm. For each pixel in the image, similar pixels are searched for within the search window centered on the pixel, and the similarity is measured by calculating the gray value difference between the neighborhoods around the two pixels. Post-processing by the fast non-local mean filtering algorithm can effectively repair the detail and texture information, further suppress the residual noise, and improve the stability of the image quality.

[0113] Step 6, obtain the discrete form of the coupled model by the discrete difference method, and update the pixel values by the iterative method to achieve denoising and obtain the denoised image. Specifically, first calculate , and respectively from equations (6), (9) and (11), then calculate and from equation (22), and finally set and the number of iterations N, substitute , , , and N into Equation (28), and iterate in sequence according to Equation (28). Take the best denoised image of the new model within the range of the number of iterations N, and use the peak signal-to-noise ratio PSNR and structural similarity SSIM to verify the effectiveness and feasibility of the coupled model.

[0114] The expression of the peak signal-to-noise ratio PSNR is:

[0115] ,

[0116] wherein, represents the image size, is the original grayscale image; usually, the higher the PSNR value, the better the image quality.

[0117] The expression of the structural similarity SSIM is:

[0118] ,

[0119] wherein, is the average value of, is the average value of, is the variance of, is the variance of, is and the covariance of; c1 and c2 are parameters to make the denominator non-zero, and are usually taken as small non-negative constants.

[0120] The value range of SSIM is usually between 0 and 1. When the two images are exactly the same visually, the value of SSIM is 1. The lower the similarity between the two images, the closer the value of SSIM is to 0.

[0121] Preferably, the expression of the discrete form of the coupled model is:

[0122] ,

[0123] wherein, The expression is:

[0124] ;

[0125] Preferably, first introduce a difference equation to define the variables in the model , The discrete form of is :

[0126] ,

[0127] In the formula, h is the step size of the difference equation, and the boundary conditions are:

[0128] ,

[0129] ,

[0130] where J and I are the upper limits of the indices of the discretized grid in two different directions, used to define the range of the computational domain in the corresponding dimensions.

[0131] Now assume , ; then the boundary conditions are:

[0132] ,

[0133] ,

[0134] Let p be the descent direction of the gradient descent method. Therefore, the formula (21) is discretized using the finite difference method, and its discrete form is expressed as:

[0135] ,

[0136] where is the time step, is the anisotropic diffusion tensor after n iterations, is the adaptive weight parameter after n iterations, is the discretized original grayscale image at the pixel value at the position, is the descent direction of the gradient descent method.

[0137] Explanation of formula (10):

[0138] Point 1, in the TV1 model, the anisotropic diffusion tensor , and its properties are:

[0139] A1) can adaptively adjust the diffusion direction and intensity according to the local features of the image, such as gradient information, etc. At the image edge, the diffusion tensor will make the diffusion process proceed along the direction tangent to the edge, while suppressing the diffusion perpendicular to the edge direction, which can effectively avoid blurring the image edge during the denoising process, thus better retaining the details and edge information of the image, making the denoised image able to maintain a clear contour, improving the visual quality of the image and the accuracy of subsequent processing.

[0140] A2) It can process noises in different directions differently. It can identify the directional characteristics of noises and, based on the relationship between the noises and the image structure, perform appropriate diffusion denoising in areas with severe noises, while reducing diffusion in the smooth areas of the image to avoid loss of image information caused by over-smoothing. Compared with traditional isotropic diffusion methods, it can remove noises more accurately while preserving the original structure and texture of the image, improving the denoising effect and efficiency.

[0141] Therefore, an anisotropic diffusion tensor can be introduced into the TV1 model , which can adjust the edge diffusion direction and maintain the integrity of edge information.

[0142] Point 2, in the LLT model, the image feature extraction function based on differential curvature , its properties are as follows:

[0143] B1) Differential curvature can quantitatively describe the degree of curvature of curves or surfaces in an image. In an image, different object edges, textures, etc. often have unique curvature characteristics. By extracting these features based on differential curvature, local details of the image can be captured more precisely, such as the corners of objects in the image, the bending changes of lines, etc., enabling the LLT model to better distinguish different image structures when processing images.

[0144] B2) The edges of an image usually correspond to regions with large changes in differential curvature. The feature extraction function based on differential curvature can accurately locate the edge positions of the image by detecting these curvature changes. In the LLT model, this property can be used to perform special processing on the edge regions during the denoising process, adjusting the denoising intensity and method specifically to avoid over-smoothing or blurring the edges while removing noises, thereby better protecting the edge information of the image and making the contour of the denoised image clearer and more accurate.

[0145] Therefore, introducing the image feature extraction function based on differential curvature into the LLT model , can adjust the diffusion strength in different regions of the image and increase the smoothing strength at large noise points.

[0146] Point 3, using the adaptive weight function to couple the TV1 model and the LLT model, its properties are as follows:

[0147] In formula (16), when the noise points are small and the gradient modulus is large, and the product is less than at the edge regions or small noise points of the image, at this time , substituting into formula (10), at this time, the image is denoised by the TV1 model, which can effectively retain the edge texture details of the image. At the same time, an anisotropic diffusion tensor is introduced into the TV1 model, which can adaptively adjust the edge diffusion direction of the image and better retain the texture details; when the noise points are large and the gradient modulus is small, and the product is greater than , in the smooth area or large noise points of the image, at this time , substituting into formula (10), the image is denoised by the LLT model, which can effectively smooth the noise. And an image feature extraction function related to the differential curvature is introduced into the LLT model. The differential curvature value is small in the smooth area or large noise points of the image, so the feature extraction function is large, thus increasing the smoothing intensity at the large noise points. When the noise points and the gradient modulus are of moderate size, and the product is between , , in the transition area of the image, at this time , substituting into formula (10), the image realizes adaptive denoising by coupling the TV1 model and the LLT model through the function.

[0148] Therefore, in the edge area or small noise points, , the image is denoised by the TV1 model; in the smooth area or large noise points, , the image is denoised by the LLT model; in the transition area of the image, , the image realizes adaptive denoising by coupling the TV1 model and the LLT model through .

[0149] The following will be described in detail in combination with Figures 4 to 9 : Compared with the NLM algorithm, the LLT model, the TV2 model, the TV1 model, and the ZTV model, the beneficial effects of the improved model provided by this specific embodiment on image denoising.

[0150] Figures 4 to 9 is the comparison chart of the denoising effects of using the NLM algorithm, the LLT model, the TV2 model, the TV1 model, and the ZTV model respectively. Among them, Figure 4 in (a), Figure 5 in (a), Figure 6 in (a), Figure 7 in (a), Figure 8 in (a), Figure 9In (a), denoising is performed using the NLM algorithm; the NLM algorithm utilizes non-local similarity information in the image to denoise the image. It searches for pixels with similar neighborhood structures to the current pixel throughout the image and estimates the true value of the current pixel by weighted averaging of these similar pixels, being able to effectively remove various types of noise, especially Gaussian noise, and can well preserve the details and texture information of the image in the denoised image, making the image look more natural and clear.

[0151] Figure 4 In (b), Figure 5 In (b), Figure 6 In (b), Figure 7 In (b), Figure 8 In (b), Figure 9 In (b), denoising is performed using the LLT model, and the LLT model expression is:

[0152] ,

[0153] In the formula, The expression is

[0154] .

[0155] Figure 4 In (c), Figure 5 In (c), Figure 6 In (c), Figure 7 In (c), Figure 8 In (c), Figure 9 In (c), denoising is performed using the TV model based on the L2 norm (abbreviation: TV2 model), and the TV2 model expression is:

[0156] ,

[0157] In the formula, is the gradient operator; is the weight coefficient, and this model is an isotropic diffusion model.

[0158] Figure 4 In (d), Figure 5 In (d), Figure 6 In (d), Figure 7 In (d), Figure 8 In (d), Figure 9 In (d), denoising is performed using the TV model based on the L1 norm (abbreviation: TV1 model), and the TV1 model expression is:

[0159] ,

[0160] In the formula, is the gradient operator; is the weight coefficient, and the model is an anisotropic diffusion model; u is the noisy image function, and its expression is ; v is the original grayscale image, and its expression is .

[0161] Figure 4 in (e), Figure 5 in (e), Figure 6 in (e), Figure 7 in (e), Figure 8 in (e), Figure 9 in (e) uses the ZTV model for denoising, and the expression of the ZTV model is:

[0162] ,

[0163] The model has the characteristics of the TV1 model and the TV2 model, is the regularization term exponent, and its expression is:

[0164] .

[0165] Figure 4 in (f), Figure 5 in (f), Figure 6 in (f), Figure 7 in (f), Figure 8 in (f), Figure 9 in (f) uses the coupled model constructed by the present invention for denoising.

[0166] From Figures 4 to 9 it can be seen that the NLM algorithm is a denoising algorithm based on the similarity of pixel blocks in the image. Since this algorithm has multiple parameters that need to be set, such as the search window size, block size, similarity measurement method, etc. The selection of these parameters has a great impact on the denoising effect. And when the noise intensity in the image is large, it may seriously interfere with the matching process of similar blocks, making the found similar blocks not actually similar. Therefore, the NLM model has the worst denoising effect; LLT is a high-order variational denoising model that can suppress the "staircase effect" of the TV1 model, but due to the large smoothing strength, it blurs the texture of the image. Therefore, the denoising effect of the LLT model is poor; the TV2 model is an isotropic diffusion model that blurs the edge texture information of the image during the denoising process. Therefore, the denoising effect of the TV2 model is also poor; although the TV1 model retains the edge texture information of the image during the denoising process, it generates false edges in the smooth area of the image. Therefore, the denoising effect of the TV1 model is also poor; the ZTV model improves the regularization term exponent of the adaptive variational model and has a good denoising effect; the NEW model couples the TV1 model and the LLT model through the function to achieve adaptive denoising, and the IMOTV model has the best denoising effect.

[0167] To further specifically compare the denoising effects of the six models, Tables 1 to 3 show the PSNR, SSIM, and Time values after denoising six images using the NLM algorithm, LLT model, TV2 model, TV1 model, ZTV model, and the coupled model constructed by the present invention under the conditions where the standard deviation of added noise σ = 15, 20, 25, 30, 50.

[0168] From the PSNR and SSIM values in Tables 1 to 3, it can be seen that the PSNR and SSIM values of the model proposed in this example are significantly higher than those of the NLM model, LLT model, TV2 model, TV1 model, and ZTV model. From the calculation time Time, it can be known that the calculation time of the NEW model is only about 2.3 times that of the TV1 model with the shortest calculation time, and it is shorter than the calculation time of NLM. Therefore, while ensuring the basic denoising efficiency and combining the two indicators of PSNR and SSIM, the NEW model requires less calculation time.

[0169] Table 1 PSNR (dB) values of the images after denoising by the coupled model constructed by the present invention and other comparison models

[0170]

[0171] Table 2 SSIM values of the images after denoising by the coupled model constructed by the present invention and other comparison models

[0172]

[0173] Table 3 Time (s) values of the images after denoising by the coupled model constructed by the present invention and other comparison models

[0174]

[0175] From the above results, it can be intuitively and effectively seen that the improved hybrid-order total variation image denoising model of the present invention has a better visibility effect, effectively suppresses the "staircase effect" that appears in the smooth area, protects the edge texture information of the image, and at the same time improves the denoising efficiency, which is more conducive to practical applications.

[0176] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and refinements can still be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for image denoising based on improved mixed-order total variation, characterized in that: The steps include: S1, converting the collected original image into grayscale and performing noise processing; S2, filtering using Gaussian-Laplace joint transform; S3, anisotropic diffusion tensor is introduced into TV1 model, and image feature extraction function based on differential curvature is introduced into LLT model; S4, using the adaptive weight function to couple the TV1 model and the LLT model to obtain a coupled model; the expression of the coupled model is: In the formula, min u E2(u) represents the minimized energy functional of the coupled model; the first term is the regularization term, and the second term is the fidelity term; is the gradient modulus of the noisy image function u; λ2 is the adaptive weight parameter, which adjusts the weight of the fidelity term; w is the adaptive weight function, which is used to adjust the regularization term of the TV1 model and the LLT model; The adaptive weight parameter λ2 is expressed as: Where δ>0; the expression of d is: Where min(D(x,y)) is the minimum value of D(x,y); max(D(x,y)) is the maximum value of D(x,y); D(x,y) is the differential curvature, and its expression is: In the formula, |u ηη | is the second-order derivative of the image along the gradient direction, is the second-order derivative of the image along the edge direction; its expressions are: In the formula, u x is the first-order derivative of the noisy image function u along the x direction, u y is the first-order derivative of the noisy image function u along the y direction, u xx is the second-order derivative of the noisy image function u along the x direction, u yy is the second-order derivative of the noisy image function u along the y direction, u xy is the second-order partial derivative of the noisy image function u; The adaptive weight function w is expressed as: Where arccot(·) is the inverse cosine function, which is a decreasing function; is the gradient modulus of the noisy image function u, k is the adaptive gradient threshold; β1 and β2 are two thresholds with different values; M(x, y) is the noise visibility function; the expression of M(x, y) is: In the formula, is the local variance of the image u(x,y), u(h,q) is the gray value at the point (h,q); m u (x,y) is the local mean, and its expression is: Wherein, h and q represent the coordinate values ​​of the x-axis and y-axis respectively, both of which are variables; P and Q are constants, representing the half width of the image area block in the x-axis and y-axis directions respectively; (2P+1) is the length of the image area block, (2Q+1) is the width of the image area block, and (2P+1)(2Q+1) represents the area size of the image area block; S5, post-processing the denoised image obtained by the coupling model using a fast non-local mean filtering algorithm; S6, the discrete difference method is used to obtain the discrete form of the coupling model, and the pixel value is updated by the iterative method for denoising to obtain the denoised image. The peak signal-to-noise ratio and structural similarity indicators are used to verify the effectiveness and feasibility of the coupling model.

2. The method for implementing image denoising based on improved mixed-order total variation according to claim 1, characterized in that: After introducing the anisotropic diffusion tensor, the expression of the TV1 model is: In the formula, min u E2(u) TV1 is the minimized energy functional of the TV1 model, u0 is the original grayscale image, u is the noise image function, is the gradient of the noisy image function, and λ is the weight parameter; H 1 / 2 represents the anisotropic diffusion tensor, which is expressed as: In the formula, the parameters α and γ are used to adjust the strength of the tensor, A is the direction of the image gradient, and A ⊥ is the normal vector of the image gradient, T represents the matrix transpose, and e represents the natural constant; After introducing the image feature extraction function based on differential curvature, the expression of the LLT model is: In the formula, min u E2(u) LLT is the minimized energy functional of the LLT model; g is the image feature extraction function based on differential curvature, and its expression is: Where d represents the normalized differential curvature and ε represents a minimum value.

3. The method for implementing image denoising based on improved mixed-order total variation according to claim 1, characterized in that: In step S5, in the fast non-local means filtering algorithm, for each pixel in the image, a pixel similar to it is searched in a search window centered on the pixel, and the similarity is measured by calculating the difference in grayscale values ​​of the neighborhoods around the two pixels.

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