Image processing method, device and medium based on fast inertial primal-dual

Abstract

The present invention provides an image processing method, device and medium based on fast inertial primal-dual, including: S100: acquiring an image to be repaired; S200: using a fast inertial primal-dual algorithm to perform denoising on the image to be repaired; S300: using a fast inertial primal-dual algorithm to perform deblurring on the blurred image. In order to solve the problems of low efficiency in repairing blurred images and poor convergence of algorithms, a fast inertial primal-dual algorithm is proposed to solve the minimization problem of the sum of smooth functions with Lipschitz gradients, non-smooth approximable functions and linear composite functions. The algorithm of the present invention can achieve the worst case o(1 / k 2 ) has the optimal convergence speed. This technical method has good effectiveness and effect in image denoising and image deblurring. The fast inertial primal-dual iterative algorithm is better than other existing primal-dual algorithms.

Description

Technical Field

[0001] The present invention relates to the field of image processing technology, and in particular to an image processing method, device and medium based on fast inertial primal-dual. Background Art

[0002] In the digital age, images have become an integral part of our lives. However, due to various factors, such as poor quality of the shooting equipment, environmental conditions, or improper post-processing, blurry images are common. These images fail to achieve the desired presentation quality and may even cause confusion to users. Therefore, blurry image restoration and sharpening technologies are becoming increasingly important.

[0003] In practical applications, blurred image restoration technology can be applied in many fields. For example, in the medical field, restoration of medical images can improve the accuracy and reliability of diagnoses; in the security field, it can be used to restore surveillance videos, improving their clarity and legibility; and in the field of digital art, restoration of old photographs or hand-painted works can be used to preserve and preserve cultural heritage. The principles of blurred image restoration are primarily based on image denoising and super-resolution reconstruction. Denoising aims to remove noise and interference from an image, resulting in a clearer image; super-resolution reconstruction uses algorithms and techniques to convert low-resolution images into high-resolution ones. Common methods include single-image super-resolution technology, deep learning-based denoising, and methods based on generative adversarial networks (GANs). Existing blurred image restoration algorithms suffer from poor convergence and low efficiency in restoring blurred images.

[0004] Therefore, it is necessary to propose an image processing method, device, equipment and medium based on fast inertial primal-dual to solve the above problems. Summary of the Invention

[0005] The purpose of the present invention is to provide an image processing method, device, equipment and medium based on fast inertial primal-dual to improve the problems of poor convergence and low efficiency of blur image restoration in existing blurred image restoration algorithms.

[0006] In a first aspect, the present invention provides an image processing method based on fast inertial primal-dual, the method comprising:

[0007] S100: Acquire the image to be repaired;

[0008] S200: performing denoising on the image to be restored using a fast inertial primal dual algorithm until a denoised image is output;

[0009] S300: Deblurring the denoised image using a fast inertial primal-dual algorithm until a clear image is output.

[0010] In a possible embodiment, the specific steps are as follows:

[0011]

[0012] Among them, p and q are regularization parameters and are both greater than 0; r is a parameter and r∈(0,4]; k is an iteration index and is greater than or equal to 0; t is a parameter updated during iteration; x is the original variable, x -1 ,x0∈X,X represents the domain or space of the original variable, x -1 =x0; y is the dual variable, y -1 ,y0∈Y,Y represents the domain or space of the dual variable, y -1 =y0;α k is the inertia parameter; ξ k and η k is an intermediate variable; is the value of the original variable updated by the proximity operator; is the value of the dual variable updated by the neighboring operator; prox is the neighboring operator; τ and σ are step size parameters and are both greater than 0; G is the regularization function; H* is the dual function of function H, which is a function of the dual variable y; ▽F is the gradient of function F, which is a differentiable function in the specific problem and represents the gradient of the data fidelity term; B is a linear operator; B * is the conjugate of operator B; ρ is the relaxation parameter.

[0013] In a possible embodiment, the solution includes the following optimization model:

[0014]

[0015] Wherein, u is the image to be restored; x is the denoised image; λ is the regularization parameter; C is the closed convex set of the prior information of the denoised image; || || TV is the total variation norm.

[0016] In a possible embodiment, step S200 includes:

[0017] S210: Assign parameters, set p = 0.05, q = 0.7,

[0018] S220: Calculation x k+1 ,y k+1 ;

[0019] S230: Determine whether ||x is satisfied k+1 -x k ||<ε, if yes, then output the denoised image; if no, then let x k-1 =xk ,y k-1 =y k , t k-1 =t k , k=k+1, return to step S220;

[0020] Among them, p and q are regularization parameters; τ is the step size parameter; β is a parameter; r is a parameter; k is the iteration index; t is the parameter updated in the iteration; x is the original variable, x k+1 is the value of the original variable x after k+1 iterations of the algorithm; y is the dual variable, y k+1 is the value of the dual variable y after k+1 iterations of the algorithm; ε is the denoising convergence threshold.

[0021] In a possible embodiment, the solution also includes the following optimization model:

[0022]

[0023] Wherein, A is the blur operator; b is the denoised image; x is the clear image; λ is the regularization parameter; C' is the closed convex set of the clear image prior information; || || TV is the total variation norm.

[0024] In a possible embodiment, step S300 includes performing the following steps on the denoised image:

[0025] S310: Assign parameters, set p = 0.05, q = 0.7,

[0026] S320: Calculation x k+1 ,y k+1 ;

[0027] S330: Determine whether ||x is satisfied k+1 -x k ||<ε', if yes, then output a clear image; if not, let x k-1 =x k ,y k-1 =y k , t k-1 =t k , k=k+1, return to step S320;

[0028] Among them, p and q are regularization parameters; τ is the step size parameter; β is a parameter; r is a parameter; k is the iteration index; t is the parameter updated in the iteration; x is the original variable, x k+1 is the value of the original variable x after k+1 iterations of the algorithm; y is the dual variable, y k+1is the value of the dual variable y after k+1 iterations of the algorithm; ε' is the defuzzification convergence threshold.

[0029] In a possible embodiment, before step S200, the method further includes:

[0030] The image to be repaired is converted into a double-precision floating-point format, and a sequence number of the image to be repaired is determined.

[0031] In a second aspect, embodiments of the present invention further provide a fast inertial primal-dual image processing device, comprising modules / units for executing any one of the possible design methods of the first aspect. These modules / units may be implemented in hardware, or hardware may execute corresponding software implementations.

[0032] In a third aspect, an embodiment of the present invention further provides an electronic device comprising a processor and a memory. The memory is configured to store one or more computer programs; when the processor executes the one or more computer programs stored in the memory, the electronic device is capable of implementing any of the possible design methods of the first aspect.

[0033] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium, which includes a computer program. When the computer program runs on an electronic device, the electronic device executes any possible design method of the first aspect above.

[0034] In a fifth aspect, an embodiment of the present invention further provides a method comprising a computer program product, which, when the computer program product is run on an electronic device, enables the electronic device to execute any possible design of any of the above aspects.

[0035] The beneficial effects of the present invention are: to address the problems of low efficiency of blurred image restoration and poor algorithm convergence, a fast inertial primal dual algorithm is proposed to solve the minimization problem of the sum of smooth functions with Lipschitz gradients, non-smooth approximable functions and linear composite functions. The algorithm of the present invention can achieve the worst case o(1 / k 2 ) optimal convergence speed, this technical method has good effectiveness and effect in image denoising and image deblurring, and the fast inertial primal-dual iterative algorithm has better effect than the existing primal-dual algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of the flow of the image processing method based on fast inertial primal-dual of the present invention.

[0037] Figure 2This is a schematic diagram of converting the format of an image to be repaired and determining the sequence number in the image processing method based on fast inertial primal-dual of the present invention.

[0038] Figure 3 1 is a flow chart of an image processing method based on fast inertial primal-dual in one embodiment of the present invention.

[0039] Figure 4 Schematic diagram of an image processing device based on fast inertial primal-dual according to the present invention.

[0040] Figure 5 Schematic diagram of the structure of the electronic device of the present invention. DETAILED DESCRIPTION

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0042] In order to solve the problems existing in the above technologies, an embodiment of the present invention provides an image processing method based on fast inertial primal-dual. Figure 1 , the method comprising:

[0043] S100: Acquire an image to be repaired.

[0044] S200: performing denoising calculation on the noisy image using a fast inertial primal-dual algorithm until a denoising convergence condition is met, and outputting a denoised image.

[0045] S300: Deblurring the denoised image using a fast inertial primal-dual algorithm until the deblurring convergence condition is met, and a clear image is output.

[0046] The Fast Inertial Primitive-Dual Algorithm is a highly efficient optimization algorithm that combines the primal-dual method with the inertia method. The primal-dual method transforms the problem into a dual form and exploits the properties of the dual problem to solve the primal problem. This method offers the advantages of fast convergence and high computational efficiency. The introduction of the inertia term further accelerates the algorithm's convergence, increasing the convergence speed and thus improving the efficiency of blurry image restoration.

[0047] During the iterative denoising process, the fast inertia primal-dual algorithm efficiently removes image noise while preserving edge and texture details. During the deblurring process, the fast inertia primal-dual algorithm effectively removes blurring effects, restoring a sharper image while preserving edge and texture details. The introduction of the inertia term significantly improves the algorithm's convergence speed. The inertia term leverages information from the previous iteration to guide the direction of the current iteration, accelerating the algorithm's convergence. The iterations are performed according to preset convergence criteria to ensure that the denoising effect meets predetermined standards, thereby improving convergence speed. The fast inertia primal-dual algorithm converges quickly during both denoising and deblurring, significantly improving the efficiency of image restoration.

[0048] In one embodiment, see Figure 2 , before step S200, further comprising:

[0049] Convert the image to be repaired into double-precision floating-point format (double type) and determine the sequence number of the image to be repaired.

[0050] Specifically, MatLab (Matrix Laboratory) is a high-performance numerical computing environment, mainly used for algorithm development, data analysis, visualization and engineering calculations. MatLab is used to convert the image to be repaired into a double-precision floating-point format. This process retains the original information of the image to be repaired, but scales the pixel value range from 0-255 to 0-1. The double-precision floating-point format provides higher numerical precision, improves calculation accuracy, better handles detailed information in the image, avoids problems such as loss of precision or numerical overflow in subsequent calculations, and helps reduce rounding errors in the calculation process, thereby providing a more accurate data basis for subsequent denoising and deblurring calculations. The length function in MatLab is used to determine the sequence number of the image to be repaired. The sequence number includes the size information of the image to be repaired, such as height, width, number of pixel values, and number of color channels.

[0051] In one embodiment, the fast inertial primal-dual algorithm includes the following formula:

[0052]

[0053] Among them, p and q are regularization parameters and are both greater than 0; r is a parameter and r∈(0,4]; k is an iteration index and is greater than or equal to 0; t is a parameter updated during iteration; x is the original variable, x -1 ,x0∈X,X represents the domain or space of the original variable, x -1 =x0; y is the dual variable, y -1 ,y0∈Y,Y represents the domain or space of the dual variable, y -1=y0;α k is the inertia parameter; ξ k and η k is an intermediate variable; is the value of the original variable updated by the proximity operator; is the value of the dual variable updated by the neighbor operator; prox is the neighbor operator; τ and σ are step size parameters and are both greater than 0; G is the regularization function; H * is the dual function of function H, H is a function of the dual variable y; ▽F is the gradient of function F, function F is a differentiable function in a specific problem, and represents the gradient of the data fidelity term; B is a linear operator; B * is the conjugate of operator B; ρ is the relaxation parameter.

[0054] t k The value of parameter t for the kth iteration is the parameter for updating the dynamics of the control algorithm. In the kth iteration, the parameter value t of the previous iteration is used. k-1 After scaling r and squaring it, add it to q and take the square root. This can be seen as the parameter value t from the previous iteration. k-1 A weighted adjustment of , where r controls the magnitude of the adjustment. Then p is combined with Add and divide by 2 to get t k The averaging operation helps to smooth the parameter changes, stabilize the iteration process, and avoid drastic fluctuations in parameter values. By introducing the square root and parameter r, the algorithm can calculate the value of the parameter t based on the previous iteration. k-1 Dynamically adjust the parameter value t of the current iteration k , in order to converge to the optimal solution faster. Through the averaging operation, the algorithm is more stable during the iteration process, reducing the risk of instability caused by too fast or too large parameter updates.

[0055] α k The value of the inertia parameter α at the kth iteration is a weight parameter related to the iteration step, which is used to balance the update of the previous iteration and the current iteration. k The information of the previous iteration is introduced, so that the solution of the current iteration depends not only on the current gradient or objective function value, but also on the solution of the previous iteration. k It can help the algorithm converge to the optimal solution faster, especially when the objective function has multiple local minima, it helps the algorithm jump out of the local minimum and accelerates convergence. k The calculation depends on t k and t k-1 The value of t k By t k-1 Updated, so α k The time helps to reduce fluctuations in the iteration process and make the algorithm more stable.

[0056] xk represents the value of the original variable x at the kth iteration, x -1 ,x0∈X,X represents the domain or space of the original variable, x -1 =x0.ξ k is the intermediate variable in the kth iteration, α k (x k -x k-1 ) This part introduces the variable changes of the previous iteration. k Represents the value of the dual variable y at the kth iteration, y -1 ,y0∈Y,Y represents the domain or space of the dual variable, y -1 =y0.η k is the intermediate variable in the kth iteration, α k (y k -y k-1 ) This part introduces the variable changes of the previous iteration. Inertia parameter α k This inertia effect helps the algorithm maintain momentum during the iteration, thereby accelerating convergence and possibly avoiding falling into a local minimum. k Through the current iteration variable x k and the previous iteration variable x k-1 The obtained η k Through the current iteration variable y k and the previous iteration variable y k-1 As a result, this update strategy helps smooth out changes in variables and reduce fluctuations during iterations. By incorporating information from previous iterations, the algorithm can converge to the optimal solution more quickly, especially when the objective function has multiple local minima. The inertia effect helps reduce fluctuations during iterations, making the algorithm more stable.

[0057] is the value of the original variable updated by the neighboring operator, that is, the original variable value of the next iteration. τ and σ are step size parameters used to control the step size of each iterative update. k ) is the function F in ξ k The gradient at ξ represents the gradient of the data fidelity term. k -τ▽F(ξ k ) This part is the standard gradient descent step, which is used to reduce the value of the function F. B is a linear operator used to map the original variables to the dual space. * η k is the dual variable η k By conjugation of the linear operator B. is the value of the dual variable updated by the neighboring operator, that is, the value of the dual variable in the next iteration. This part is the update step of the dual variable, which combines the current dual variable η k and updates to the original variables mapped by the linear operator B. By introducing the proximal operator, the algorithm can introduce regularization into the optimization process, adjusting the results of the gradient descent step to satisfy certain regularization or constraints. This helps prevent overfitting and improve the model's generalization ability. By appropriately selecting the step size τ and σ, as well as the proximal operator, the algorithm's convergence can be guaranteed.

[0058] ρ k The relaxation parameter ρ is used to control the mixing ratio of new estimated values ​​and old values. The relaxation parameter ρ allows the algorithm to rely not only on the new estimated values ​​but also retain some old variable values ​​in each iteration. This strategy helps stabilize the convergence of the algorithm, especially when dealing with non-convex optimization problems. The variable values ​​updated by the neighboring operator With the old value (ξ k ,η k ) is combined with the algorithm to preserve the information obtained in the previous iteration while exploring new possible solutions. This combination helps to avoid drastic fluctuations in the algorithm during the iteration process. In addition, the relaxation parameter ρ helps to reduce fluctuations during the iteration process and make the algorithm more stable. By properly choosing ρ k , the algorithm can converge to the optimal solution faster, especially when the objective function has multiple local minima.

[0059] In one embodiment, the denoising model includes the following formula: Where u is the image to be restored; x is the denoised image; λ is the regularization parameter used to balance the influence of the data fidelity term and the regularization term; C is the closed convex set of the denoised image prior information; || || TV is the total variation norm.

[0060] Is the data fidelity term, which is used to measure the difference between the denoised image x and the image to be repaired u, ensuring that the denoised image x and the image to be repaired u remain close. λ||x|| TV is the total variation regularization term, representing the L1 norm of the image gradient. This term minimizes image gradient variation, thereby maintaining image smoothness while preserving edge information. Total variation regularization helps effectively remove noise from images while also preserving image edges and details during the denoising process, avoiding oversmoothing. The overall optimization goal is to find a denoised image x that maintains a close relationship with the image to be restored u while exhibiting a small total variation. The introduction of the regularization parameter λ makes the algorithm more stable and capable of handling images with varying noise levels. By adjusting the regularization parameter λ and selecting an appropriate optimization algorithm, the algorithm can be adapted to different denoising requirements and image characteristics.

[0061] In one embodiment, see Figure 3 Step S200 includes:

[0062] S210: Assign parameters, set p = 0.05, q = 0.7,

[0063] S220: Calculation x k+1 ,y k+1 ;

[0064] S230: Determine whether ||x is satisfied k+1 -x k ||<ε, if yes, then output the denoised image; if no, then let x k-1 =x k ,y k-1 =y k , t k-1 =t k , k=k+1, return to step S220;

[0065] Among them, p and q are regularization parameters; τ is the step size parameter; β is a parameter; r is a parameter; k is the iteration index; t is the parameter updated in the iteration; x is the original variable, x k+1 is the value of the original variable x after k+1 iterations of the algorithm; y is the dual variable, x k+1 is the value of the original variable x after k+1 iterations of the algorithm; ε is the denoising convergence threshold.

[0066] By reasonably setting p and q to control the influence of the regularization term in the optimization process, the step size parameter τ is adjusted by β to control the amplitude of each iterative update. k Introducing the information of the previous iteration during the iteration process helps to reduce the fluctuations in the iteration process, making the algorithm more stable and helping to accelerate convergence. k and step size parameter τ, the algorithm can converge to the optimal solution faster. k+1 is the original variable of the k+1th iteration, y k+1 is the dual variable of the k+1th iteration. According to the denoising convergence threshold ε, the original variable of the k+1th iteration and the original variable of the kth iteration are calculated to determine whether they meet the convergence condition, that is, whether they are close enough. If they are close enough, the iteration is considered to have converged and the iteration is terminated. If the convergence condition is not met, the iteration is returned to continue the iterative convergence calculation. Through continuous iteration, the original variable x that meets the condition can be found. k+1 and the dual variable y k+1 By setting a reasonable denoising convergence threshold ε, we can ensure that the final solution has a high accuracy.

[0067] In one embodiment, the deblurring model includes the following formula:

[0068] Where A is the blur operator; b is the denoised image; x is the clear image; λ is the regularization parameter, which is used to balance the influence of the data fidelity term and the regularization term; C' is the closed convex set of the clear image prior information, || || TV is the total variation norm.

[0069] Is the data fidelity term, which is used to measure the difference between the clear image x and the denoised image b, ensuring that the clear image x and the denoised image b remain close. λ||x|| TV is the total variation regularization term, representing the L1 norm of the image gradient. This term minimizes image gradient variation, thereby maintaining image smoothness while preserving edge information. Total variation regularization helps effectively remove noise from images while preserving edges and details during the denoising process, avoiding oversmoothing. The overall optimization goal is to find a clear image x that maintains a close resemblance to the denoised image b while exhibiting a small total variation. The introduction of the regularization parameter λ makes the algorithm more stable and capable of handling images with varying noise levels. By adjusting the regularization parameter λ and selecting an appropriate optimization algorithm, the algorithm can be adapted to varying denoising requirements and image characteristics.

[0070] In one embodiment, see Figure 3 Step S300 includes performing the following steps on the denoised image:

[0071] S310: Assign parameters, set p = 0.05, q = 0.7,

[0072] S320: Calculation x k+1 ,y k+1 ;t k α k

[0073] S330: Determine whether ||x is satisfied k+1 -x k ||<ε', if yes, then output a clear image; if not, let x k-1 =x k ,y k-1 =y k , t k-1 =t k , k=k+1, return to step S320;

[0074] Among them, p and q are regularization parameters; τ is the step size parameter; β is a parameter; r is a parameter; k is the iteration index; t is the parameter updated in the iteration; x is the original variable, xk+1 is the value of the original variable x after k+1 iterations of the algorithm; y is the dual variable, y k+1 is the value of the dual variable y after k+1 iterations of the algorithm; ε' is the defuzzification convergence threshold.

[0075] By reasonably setting p and q to control the influence of the regularization term in the optimization process, the step size parameter τ is adjusted by β to control the amplitude of each iterative update. k Introducing the information of the previous iteration during the iteration process helps to reduce the fluctuations in the iteration process, making the algorithm more stable and helping to accelerate convergence. k and step size parameter τ, the algorithm can converge to the optimal solution faster. k+1 is the original variable of the k+1th iteration, y k+1 is the dual variable of the k+1th iteration. According to the defuzzification convergence threshold ε', the original variable of the k+1th iteration and the original variable of the kth iteration are calculated to determine whether they meet the convergence condition, that is, whether they are close enough. If they are close enough, the iteration is considered to have converged and the iteration is terminated. If the convergence condition is not met, the iteration is returned to continue the iterative convergence calculation. Through continuous iteration, the original variable x that meets the condition can be found. k+1 and the dual variable y k+1 By setting a reasonable defuzzification convergence threshold ε', the final solution can be guaranteed to have high accuracy.

[0076] In a specific embodiment, after step S300, the method further includes:

[0077] The clear image is post-processed to obtain a processed image, where the post-processing includes at least one of color correction, sharpening, noise reduction, contrast enhancement, and image enhancement.

[0078] Color correction aims to adjust the image's color balance to ensure accurate and natural colors. Color correction involves adjusting image parameters such as color temperature, hue, saturation, and contrast. Sharpening enhances edge details in an image, making it appear clearer. Common sharpening methods include Unsharp Mask (USM) and Smart Sharpen. When performing sharpening, it's important to balance the degree of sharpening with the potential for noise. Noise reduction removes noise from an image, which can be caused by sensor noise, compression algorithms, and other factors. Common noise reduction methods include mean filtering, median filtering, and Gaussian filtering. Advanced noise reduction algorithms may also utilize machine learning or deep learning techniques to more accurately identify and remove noise. Contrast enhancement adjusts the contrast of an image to make it more vivid. Contrast enhancement involves adjusting the brightness and shadows of an image and using techniques such as histogram equalization to enhance contrast. Image enhancement aims to comprehensively improve image quality through a series of processing steps, making it more suitable for specific applications.

[0079] This paper proposes a fast inertial primal-dual image processing method based on a fast inertial primal-dual algorithm with a combined optimization model, which is generally related to deblurring or sharpening techniques in image processing. The goal of this method is to improve image clarity through mathematical models and optimization algorithms, especially to restore a clear image from a blurred image. The following are the general steps of this method:

[0080] 1. Build the model

[0081] First, we need to build a combinatorial optimization model to describe the image sharpening problem. This usually involves the mathematical expression of the image deblurring problem, which can be expressed in the following form: Where x is the clear image that we want to restore, A is the blur matrix, b is the blurred image, Φ(x) is the regularization term (such as total variation regularization), and λ is the regularization parameter.

[0082] 2. Fast Inertial Primal-Dual Algorithm

[0083] To solve the above optimization problem, the Fast Inertial Primal-dual Algorithm (FIPA) can be used. This is an accelerated optimization algorithm that combines the primal-dual method with inertia techniques to accelerate convergence. This algorithm alternately updates the primal and dual variables and incorporates an inertia term during iteration to improve the algorithm's dynamics.

[0084] 3. Image clarity processing

[0085] The above optimization problem is solved iteratively using the fast inertial primal-dual algorithm until convergence is satisfied. Each iteration produces a result that is closer to the original clear image. In this way, clear details can be gradually restored from the blurred image.

[0086] 4. Post-processing

[0087] After obtaining the output of the optimization algorithm, some post-processing steps may be required to further improve the image quality. This may include operations such as denoising and contrast enhancement.

[0088] 5. Results Evaluation

[0089] Finally, the effectiveness of image sharpening needs to be evaluated. This can be done through subjective visual inspection or objective image quality evaluation metrics such as PSNR, SSIM, etc.

[0090] Image sharpening methods based on a fast inertial primal-dual algorithm with a combinatorial optimization model are part of advanced image processing research. This approach requires a deep understanding of image processing, optimization theory, and algorithm design. While this method can achieve good results in image deblurring, its performance depends on the accuracy of the model and the effectiveness of the algorithm. In practical applications, it may be necessary to adjust the model and algorithm parameters based on the specific problem and data.

[0091] The present invention proposes an image processing method based on fast inertial primal-dual. The technical effects of the image processing method are explained in detail below.

[0092] 1. The image processing method based on fast inertia primal-dual achieves the worst case o(1 / k 2 ) optimal convergence speed. As the number of iterations increases, the performance of the algorithm will improve at a quadratic rate, which significantly accelerates the convergence speed and greatly improves the convergence efficiency of the algorithm. Since the image processing method based on fast inertial primal-dual achieves o(1 / k 2) has an optimal convergence speed of o(1 / k). Compared with the traditional o(1 / k) convergence speed, the image processing method based on fast inertia primal-dual can approach the optimal solution faster with the same number of iterations. This means faster processing speed and higher computational efficiency in practical applications. In terms of image denoising and deblurring, the image processing method based on fast inertia primal-dual can restore higher quality images by effectively minimizing the objective function. This is due to the algorithm's ability to handle complex mathematical structures and its fast convergence. Because the algorithm adopts the primal-dual framework and inertia terms, it exhibits greater robustness and stability when processing different types of blurred images and noise, and is more reliable and practical in practical applications.

[0093] 2. The fast inertial primal-dual image processing method is capable of minimizing the sum of smooth functions, nonsmooth approximable functions, and linear composite functions with Lipschitz gradients. This method demonstrates excellent results in image denoising and deblurring. Its fast inertial primal-dual iterative algorithm outperforms existing primal algorithms. Specifically, the fast inertial primal-dual algorithm introduces an inertia term and leverages information from the previous iteration to accelerate the convergence of the current iteration, thereby improving algorithm efficiency. This method is particularly well-suited for denoising and deblurring problems in image processing, as it effectively handles the nonsmooth nature of image data while preserving image edges and detail. Convergence analysis of the algorithm demonstrates that it can reach a preset convergence threshold within a limited number of iterations, resulting in high-quality denoised and deblurred images. This proposed algorithm provides a new solution for image restoration, particularly for applications requiring high computational efficiency and algorithmic convergence. The algorithm employs a primal-dual framework, which helps accelerate the solution while preserving the problem structure and leveraging information in the dual space. Primal-dual methods often have advantages in dealing with complex constraints and optimization problems.

[0094] 3. Due to the complexity of the image and the huge amount of data, traditional optimization algorithms often face difficulties such as low computational efficiency and slow convergence when dealing with these problems. The image processing method based on fast inertial primal-dual of the present invention can be easily applied to large-scale applications and can handle image reconstruction problems involving large amounts of data. The image processing method based on fast inertial primal-dual supports parallel computing and can utilize multi-core processors or distributed computing resources to accelerate the calculation process, further improving processing efficiency. The image processing method based on fast inertial primal-dual is specifically used to solve convex optimization models related to image reconstruction problems. Convex optimization problems have the uniqueness of global optimal solutions, which enables the algorithm to stably find the optimal solution. By converting the image reconstruction problem into a convex optimization problem, the algorithm can more effectively deal with noise, blur and other interference factors in the image. The algorithm continuously optimizes the objective function through an iterative process, thereby achieving clear processing of blurred images. Due to the high efficiency of the algorithm, high-quality images can be restored in a relatively short time, which is very important for the real-time requirements in practical applications.

[0095] 4. In addition to sharpening, the Fast Inertial Primitive-Dual image processing method can also repair damaged images. By minimizing the objective function, the Fast Inertial Primitive-Dual image processing method can restore missing or damaged parts of the image, making it more complete and accurate.

[0096] In addition, the present invention also proposes an image restoration device, see Figure 4 The apparatus includes: an acquisition module 401 for acquiring an image to be restored; a denoising module 402 for performing denoising calculations on the image to be restored using a fast inertial primal-dual algorithm until the denoising convergence condition is met, and outputting a denoised image; and a deblurring module 403 for performing deblurring calculations on the denoised image using a fast inertial primal-dual algorithm until the deblurring convergence condition is met, and outputting a clear image. All relevant details of each step involved in the above method embodiment can be referenced in the functional description of the corresponding functional module and will not be repeated here.

[0097] In other embodiments of the present invention, an electronic device is disclosed. Figure 5 The electronic device may include: one or more processors 501; a memory 502; a display 503; one or more applications (not shown); and one or more computer programs 504. The above components may be connected via one or more communication buses 505. The one or more computer programs 504 are stored in the memory 502 and configured to be executed by the one or more processors 501. The one or more computer programs 504 include instructions, which may be used to execute the following instructions: Figure 1 and Figure 4and each step in the corresponding embodiment.

[0098] Through the description of the above embodiments, those skilled in the art will clearly understand that for the sake of convenience and brevity, only the division of the above functional modules is used as an example. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. The specific working processes of the above-described systems, devices, and units can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0099] Each functional unit in each embodiment of the present invention may be integrated into a processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit. The above-mentioned integrated units may be implemented in the form of hardware or software functional units.

[0100] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present invention, or the part that contributes to the existing technology, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) or a processor to perform all or part of the steps of the various embodiments of the present invention. The aforementioned storage medium includes: flash memory, mobile hard disk, read-only memory, random access memory, magnetic disk or optical disk, etc., various media that can store program code.

[0101] Although the embodiments of the present invention have been described in detail above, it is obvious to those skilled in the art that various modifications and variations can be made to these embodiments. However, it should be understood that such modifications and variations are within the scope and spirit of the invention in the claims. Moreover, the invention described herein may have other embodiments and may be implemented or realized in a variety of ways. Unless otherwise defined, the technical terms or scientific terms used herein should be understood by people with ordinary skills in the field to which the invention belongs. The words "including" and the like used herein mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

Claims

1. An image processing method based on fast inertial primal-dual, characterized in that: The method comprises: S100: Acquire the image to be repaired; S200: performing denoising on the image to be restored using a fast inertial primal-dual algorithm until a denoised image is output; S300: Deblurring the denoised image using a fast inertial primal-dual algorithm until a clear image is output; The specific steps are as follows: Among them, x -1 ,x0∈X,X represents the domain or space of the original variable, x -1 =x0;y -1 ,y0∈Y,Y represents the domain or space of the dual variable, y -1 =y0;α k is the inertia parameter; ξ k and η k is an intermediate variable; is the value of the original variable updated by the proximity operator; is the value of the dual variable updated by the neighbor operator; prox is the neighbor operator; τ and σ are step size parameters and are both greater than 0; G is the regularization function; H * is the dual function of function H, where H is a function of the dual variable y; is the gradient of function F, which is a differentiable function in a specific problem and represents the gradient of the data fidelity term; B is a linear operator; B * is the conjugate of operator B; ρ is the relaxation parameter; Step S200 includes: S210: Assign parameters, set p = 0.05, q = 0.7, S220: Calculation x k+1 ,y k+1 ; S230: Determine whether ||x is satisfied k+1 -x k ||<ε, if yes, then output the denoised image; if no, then let x k-1 =x k ,y k-1 =y k , t k-1 =t k , k=k+1, return to step S220; Among them, p and q are regularization parameters and are both greater than 0; τ is the step size parameter; β is a parameter; r is a parameter and r∈(0,4]; k is the iteration index and is greater than or equal to 0; t is the parameter updated in the iteration; x is the original variable, x k+1 is the value of the original variable x after k+1 iterations of the algorithm; y is the dual variable, y k+1 is the value of the dual variable y after k+1 iterations of the algorithm; ε is the denoising convergence threshold; Step S300 includes performing the following steps on the denoised image: S310: Assign parameters, set p = 0.05, q = 0.7, S320: Calculation x k+1 ,y k+1 ; S330: Determine whether ||x is satisfied k+1 -x k ||<ε', if yes, then output a clear image; if not, let x k-1 =x k ,y k-1 =y k , t k-1 =t k , k=k+1, return to step S320; Where ε' is the deblurring convergence threshold.

2. The method according to claim 1, characterized in that The solution includes the following optimization models: Wherein, u is the image to be restored; x is the denoised image; λ is the regularization parameter; C is the closed convex set of the prior information of the denoised image; || || TV is the total variation norm.

3. The method according to claim 1, characterized in that The solution also includes the following optimization model: Wherein, A is the blur operator; b is the denoised image; x is the clear image; λ is the regularization parameter; C' is the closed convex set of the clear image prior information; || || TV is the total variation norm.

4. The method according to claim 1, wherein Before step S200, the method further includes: The image to be repaired is converted into a double-precision floating-point format, and a sequence number of the image to be repaired is determined.

5. An image processing device based on fast inertial primal-dual, for executing the method according to any one of claims 1 to 4, characterized in that: The device comprises: An acquisition module, used to acquire the image to be repaired; a denoising module, configured to perform denoising on the image to be restored using a fast inertial primal-dual algorithm until a denoised image is output; The deblurring module is used to perform deblurring processing on the denoised image by using a fast inertial primal-dual algorithm until a clear image is output.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

7. An electronic device, characterized in that: include: A processor and a memory, wherein the memory is used to store computer programs; The processor is configured to execute the computer program stored in the memory, so as to enable the electronic device to perform the method according to any one of claims 1 to 4.

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