Improved Richardson-Lucy image non-blind deblurring method
By introducing L0 regularization term and preprocessing technology into the Richardson-Lucy algorithm, combined with the dynamic termination iteration of image quality evaluation parameters, the problem of noise amplification leading to artifacts and ringing effects in the prior art is solved, and a more efficient image defuzzing effect is achieved.
Patent Information
- Application Number
- CN202510316895.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-18
- Publication Date
- 2025-06-17
AI Technical Summary
The existing Richardson-Lucy defuzzing method is prone to amplify the noise when image noise exists, resulting in artifact generation, and the high-frequency edge area is prone to ringing effects, making the number of iterations difficult to determine, which can easily lead to over-iteration or under-iteration.
The L0 regularization term was introduced into the Richardson-Lucy algorithm, the RL-L0 model was constructed, and the image was preprocessed through median filtering and Butterworth filtering, and dynamically terminated iterations with PSNR and SSIM.
Effectively suppress noise diffusion, reduce the noise standard deviation of the recovered image, reduce ringing effect, improve defuzzing effect, and reduce the number of iterations through dynamic termination strategy to avoid overfitting.
Smart Images
Figure CN120163735A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of image processing, and particularly to an improved Richardson-Lucy non-blind image deblurring method. Background Art
[0002] As an important medium for humans to perceive the outside world and transmit information, images play an important role in daily life and production activities. During the image acquisition process, there are situations such as motion blur, distortion, and defocus. In non-blind deblurring with a known blur kernel (direction and scale), the Richardson-Lucy deblurring method is one of the research hotspots. The Richardson-Lucy algorithm is based on maximum likelihood estimation and updates the image estimate through iteration. However, when there is noise in the image, the iteration process will gradually amplify the noise, resulting in artifact generation; moreover, the high-frequency edge region is prone to ringing effects during the iteration process, manifested as periodic oscillation artifacts around the edges; the number of iterations is also difficult to determine. A fixed number of iterations cannot dynamically adapt to changes in image quality, easily leading to over-iteration or under-iteration. Over-iteration may exacerbate noise and ringing, while under-iteration results in insufficient restoration. Therefore, we propose an improved Richardson-Lucy non-blind image deblurring method to solve the above problems. Summary of the Invention
[0003] (1) Technical Problems to be Solved
[0004] In view of the deficiencies of the prior art, the present invention provides an improved Richardson-Lucy non-blind image deblurring method, which solves the problems raised in the above background art.
[0005] (2) Technical Solutions
[0006] The present invention specifically adopts the following technical solutions to achieve the above objectives:
[0007] An improved Richardson-Lucy non-blind image deblurring method includes the following steps:
[0008] S1: Preprocess the blurred image to eliminate noise;
[0009] S2: Introduce the L0 regularization term into the Richardson-Lucy algorithm to construct the RL-L0 model;
[0010] S3: Start iterative operations on the preprocessed image based on the RL-L0 model;
[0011] S4: Calculate the PSNR and SSIM values of the image after each iteration, determine whether to terminate the iteration, and finally find the effective restored image that reaches the target range.
[0012] Further, the specific content of S1 is as follows: For the noisy and blurred image, first perform median filtering to remove salt-and-pepper noise. For each pixel point (i, j) in the image I, sort the pixel values within its neighborhood window and take the median value as the output:
[0013] I median (i, j) = median{I blur (i - k, j - l) | k, l ∈ [-n, n]} (1)
[0014] where n is the window radius;
[0015] Then, smooth the remaining high-frequency noise through Butterworth low-pass filtering to maintain the smooth result of the edges; the transfer function is:
[0016]
[0017] where D0 is the cut-off frequency, n is the filter order, and D(u, v) is the frequency domain distance.
[0018] Further, the specific content of S2 is as follows: Under the condition of (f * h)(i), the blurred image g(i) should follow a Poisson distribution with (f * h)(i) as the parameter:
[0019]
[0020] where i is a pixel point;
[0021] Assuming that the noise is spatially independent, the probability of g occurring under the condition that the observed value is f is the likelihood function given by the following formula:
[0022]
[0023] where I is the set of all pixel points in the image;
[0024] The Richardson-Lucy algorithm solves for f by maximizing the likelihood function (5), and this problem can be solved by minimizing -lnP(g|f); minimizing -lnP(g|f) is equivalent to minimizing J1(f) given by the following formula:
[0025]
[0026] Since J1(f) is a convex function with respect to f, to solve for f, we only need to take the derivative of J1(f) with respect to f and set the derivative to 0, which is equivalent to:
[0027]
[0028] where f kDenote the estimate of \(f\) at the \(k\)-th iteration. The negative sign indicates flipping. So the recurrence relation of \(f\) can be given by the following formula:
[0029]
[0030]
[0031] Applying Total Variation (TV) to image denoising can preserve the prominent edges of the image while smoothing the noise. Incorporating the TV regularization term
[0032]
[0033] into the Richardson - Lucy model (6), we obtain the RL - TV model:
[0034]
[0035] where \(f\) is the original clear image to be solved, \(g\) is the observed blurred image, \(h\) is the blur kernel, \(\lambda\) TV is a parameter controlling the weight of the regularization term, taking values between 0 and 1. \(i\) is the pixel point. The goal is to find \(f\) that minimizes \(J_1(f)+J\) req (f);
[0036] Introduce three variables \(w\), \(s\), and \(v\) to replace \(f\) and \(f * h\) respectively. And for simplicity, the pixel point \(i\) is omitted in the formula, which actually sums over all pixel points \(i\) as in formula (10). Then finding the minimum point of (10) becomes solving such an optimization problem with constraints:
[0037]
[0038] Then add three squared penalty terms to transform the above optimization problem with constraints into an optimization problem without constraints:
[0039]
[0040]
[0041] where \(\mu_1\), \(\mu_2\), and \(\mu_3\) are parameters controlling the weights of the penalty terms, taking positive values;
[0042] Similarly, if the 0 - norm of the image gradient is used as the regularization term and added to the Richardson - Lucy algorithm model, the model becomes the RL - L0 model:
[0043]
[0044] where ∈ and are weights; similarly, the summation symbol represents the summation over all pixel points; due to the addition of the L0 regularization term, this optimization problem becomes an NP-hard problem;
[0045] To solve for f from the above equation, two variables w = (w h , w v ) T and v are introduced to replace and f * h respectively, and a quadratic penalty term is added to transform the constrained optimization problem into an unconstrained optimization problem. Thus, the objective function becomes:
[0046]
[0047] where μ and α are penalty term coefficients. When μ → ∞ and α → ∞, the solution of (14) approaches the solution of (13), and (14) can be solved by alternately minimizing v, f, and w.
[0048] Furthermore, the specific content of S3 is as follows: First, solve the v sub-problem:
[0049]
[0050] The above equation is differentiable as a function of v. Therefore, we only need to take the derivative of v and set it to 0 to obtain two solutions for v. We take the positive solution. Thus, in each iteration, v is solved as follows:
[0051]
[0052] In each iteration, the solution of u is obtained by solving the following equation:
[0053]
[0054] The closed-form solution of f is as follows:
[0055]
[0056] where and represent the horizontal and vertical gradient operators respectively;
[0057] After obtaining u, solving for w is transformed into solving the following equation:
[0058]
[0059] (19) is a point minimization problem, and the solution of w is as follows:
[0060]
[0061] Further, the specific content of S4 is as follows: When image noise cannot be ignored, as the number of iterations k increases, noise amplification causes a significant reduction in the convergence effect and even increases the image blur; in response to this situation, evaluation parameters of image quality such as PSNR and SSIM are used to calculate the image parameters after each iteration to find the image that meets the standard.
[0062] An image is composed of multiple pixel points, and there is an association between each pixel point (i, j). The required parameter values are used to judge the photo quality (N) and clarity (M) by calculating the correlation degree between pixel points.
[0063] Mean square error:
[0064]
[0065] Peak signal-to-noise ratio:
[0066]
[0067] Structural similarity:
[0068]
[0069] First, two parameter values are calculated for the image pixel points (i, j); through a large number of calculations on the picture by the algorithm, the appropriate parameter standards under different blur degrees are determined respectively. and After each iteration, the peak signal-to-noise ratio and structural similarity calculated for the image are compared with their parameter standards respectively. If both are greater than the parameter standards, the iterative operation is terminated, and the effective restored image within the target range is returned.
[0070] (III) Beneficial effects
[0071] Compared with the prior art, the present invention provides an improved Richardson-Lucy image non-blind deblurring method, which has the following beneficial effects:
[0072] The present invention effectively suppresses salt-and-pepper noise and high-frequency noise and reduces the ringing effect through the preprocessing of combining median filtering and Butterworth filtering for the blurred image; introduces the L0 regularization term into the Richardson-Lucy algorithm to construct the RL-L0 model, restrains the gradient sparsity through the L0 norm, further suppresses the noise diffusion during the iteration process, and reduces the noise standard deviation of the restored image; based on the dynamic termination strategy of PSNR and SSIM, finds the effective restored image within the target range, reduces the number of iterations, and avoids overfitting of the iterative image. Description of the drawings
[0073] Figure 1 It is the flowchart of the image non-blind deblurring of the present invention;
[0074] Figure 2 is the Cameraman grayscale image;
[0075] Figure 3 is Figure 2 the blurred image;
[0076] Figure 4 is Figure 3 the image with added noise;
[0077] Figure 5 is Figure 4 the denoised image;
[0078] Figure 6 is Figure 5 the deblurred image. Specific implementation manner
[0079] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.
[0080] Embodiment
[0081] As Figure 1 shown, an improved Richardson-Lucy image non-blind deblurring method proposed in an embodiment of the present invention selects a Cameraman image with a size of 256×256 as Figure 2 shown, manually adds motion blur with a blur scale of 30 pixels and a blur angle of 15°, and forms a blurred image as Figure 3 shown. For the blurred image Figure 3 adds salt-and-pepper noise as Figure 4 shown. Figure 4 The non-blind deblurring specifically includes the following steps:
[0082] S1: Preprocesses the noisy blurred image Figure 4 by using median filtering and Butterworth filtering to obtain a denoised image as Figure 5 shown;
[0083] For Figure 4 first performs median filtering with a filtering window of 3x3. For each pixel point (i,j) of the image, the pixel values in its neighborhood window are sorted, and the median value is taken as the output:
[0084] I median (i,j) = mdeian{I blur(i - k, j - l)|k, l ∈ [-n, n]} (1)
[0085] where the window radius n is taken as 1;
[0086] Then, the residual high-frequency noise is smoothed by Butterworth low-pass filtering to maintain the smooth result of the edge. The transfer function is:
[0087]
[0088] where the cut-off frequency D0 is 50 and the filter order n is 2;
[0089] S2: Introduce the L0 regularization term into the Richardson-Lucy algorithm to construct the RL-L0 model;
[0090] Under the condition of (f * h)(i), the blurred image g(i) should be a Poisson distribution with (f * h)(i) as a parameter:
[0091]
[0092] where i is a pixel point.
[0093] Assume that the noise is spatially independent. Under the condition that the observed value is f, the probability of g occurring is the likelihood function given by the following formula:
[0094]
[0095] where I is the set of all pixel points in the image.
[0096] The Richardson-Lucy algorithm solves for f by maximizing the likelihood function (5), and this problem can be solved by minimizing -ln P(g|f). Minimizing -ln P(g|f) is equivalent to minimizing J1(f) given by the following formula:
[0097]
[0098] Since J1(f) is a convex function with respect to f, to solve for f, we only need to take the derivative of J1(f) with respect to f and set the derivative to 0, which is equivalent to:
[0099]
[0100] where f k represents the estimate of f at the k-th iteration, and the negative sign represents flipping. So the recurrence relation of f can be given by the following formula:
[0101]
[0102] Applying Total Variation (TV) to image denoising can preserve the prominent edges of the image while smoothing the noise. Incorporating the TV regularization term
[0103]
[0104] into the Richardson-Lucy model (6), we obtain the RL-TV model:
[0105]
[0106] where f is the original clear image to be solved, g is the observed blurred image, h is the blur kernel, λ TV is a parameter controlling the weight of the regularization term, taking values between 0 and 1, i is the pixel point, and the goal is to find f that minimizes J1(f) + J req (f).
[0107] Introduce three variables w, s, and v to replace f and f*h respectively. And for simplicity, the pixel point i is omitted in the formula, and actually it is the same as in formula (10) to sum over all pixel points i. Then, finding the minimum point of (10) becomes solving such an optimization problem with constraints:
[0108]
[0109] Then add three squared penalty terms to transform the above optimization problem with constraints into an optimization problem without constraints:
[0110]
[0111] where μ1, μ2, and μ3 are parameters controlling the weights of the penalty terms, taking positive values.
[0112] Taking the 0-norm of the image gradient as the regularization term and adding it to the Richardson-Lucy algorithm model, the model becomes the RL-L0 model:
[0113]
[0114] where ∈ and are weights. Similarly, the summation symbol represents summing over all pixel points. Due to the addition of the L0 regularization term, this optimization problem becomes an NP-hard problem.
[0115] To solve for f from the above formula, introduce two variables w = (w h , w v ) T and v to replace And \(f*h\), and add a quadratic penalty term to transform the optimization problem with constraints into an optimization problem without constraints. Then the objective function becomes:
[0116]
[0117] where \(\mu\) and \(\alpha\) are penalty coefficients. When \(\mu\rightarrow\infty\) and \(\alpha\rightarrow\infty\), the solution of (14) approaches the solution of (13), and (14) can be solved by alternately minimizing \(v\), \(f\), and \(w\).
[0118] S3: Based on the RL-L0 model, Figure 5 Start iterative operations;
[0119] First, solve the \(v\) sub-problem:
[0120]
[0121] The above formula is differentiable as a function of \(v\). Therefore, we only need to take the derivative of \(v\) and set the derivative to 0. There are two solutions for \(v\), and we take the positive solution. So, in each iteration, \(v\) is solved as follows:
[0122]
[0123] In each iteration, the solution of \(u\) is obtained by solving the following formula:
[0124]
[0125] The closed-form solution of \(f\) is as follows:
[0126]
[0127] where and represent the horizontal and vertical gradient operators respectively.
[0128] After obtaining \(u\), solving \(w\) is transformed into solving the following formula:
[0129]
[0130] (19) is a point minimization problem, and the solution of \(w\) is as follows:
[0131]
[0132] S4: Calculate the PSNR and SSIM values of the image after each iteration of the RL-L0 model, and determine whether it meets the termination iteration condition. If it does not meet, update the penalty term \(\mu = 2\mu\), and the initial value of the penalty term is If it meets, output the effective restored image within the target range as Figure 5 shown;
[0133] Calculate the image parameters after each iteration using the evaluation parameters of image quality, PSNR and SSIM, and find the images that meet the standards.
[0134] An image is composed of multiple pixels, and there is a relationship between each pixel point (i, j). The required parameter values are used to judge the photo quality (N) and clarity (M) by calculating the correlation degree between pixel points.
[0135] Mean square error:
[0136]
[0137] Peak signal-to-noise ratio:
[0138]
[0139] Structural similarity:
[0140]
[0141] First, calculate two parameter values for the image pixel points (i, j). Through a large number of calculations on the picture by the algorithm, determine the appropriate parameter standards under different blur degrees respectively. and In this example, the selected parameter standards are After each iteration, the peak signal-to-noise ratio and structural similarity calculated for the image are compared with their parameter standards respectively. If both are greater than the parameter standards, terminate the iterative operation and return the effective restored image that reaches the target range. Otherwise, update the penalty term and continue the iterative operation. Finally, the restored image obtained after 23 iterations is as Figure 5 shown in Figure 6 as follows.
[0142] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions recorded in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.
Claims
1. An improved Richardson-Lucy image non-blind deblurring method, characterized in that: The steps include: S1: preprocess the blurred image to eliminate noise; S2: Introduce the L0 regularization term into the Richardson-Lucy algorithm to build the RL-L0 model; S3: Start iterative operation on the preprocessed image based on the RL-L0 model; S4: Calculate the PSNR and SSIM values after each iteration of the image, determine whether to terminate the iteration, and finally find the effective restored image that reaches the target range.
2. The improved Richardson-Lucy image non-blind deblurring method according to claim 1, characterized in that: The specific content of S1 is: first use median filtering to remove salt and pepper noise from the noisy fuzzy image, sort the pixel values in the neighborhood window of each pixel point (i, j) in the image I, and take the middle value as the output: I median (i,j)=median{I blur (i-k,j-l)|k,l∈[-n,n]} (1) Where n is the window radius; Then, the residual high-frequency noise is smoothed by Butterworth low-pass filtering to maintain the smooth result of the edge; the transfer function is: Where D0 is the cutoff frequency, n is the filter order, and D(u,v) is the frequency domain distance.
3. The improved Richardson-Lucy image non-blind deblurring method according to claim 2, characterized in that: The specific content of S2 is: under the condition of (f*h)(i), the blurred image g(i) should be a Poisson distribution with (f*h)(i) as a parameter: Where i is a pixel; Assuming that the noise is independent of space, the probability of g occurring under the condition that the observation value is f is given by the likelihood function: Where I is the set of all pixels in the image; The Richardson-Lucy algorithm solves f by maximizing the likelihood function (5), which can be solved by minimizing -lnP(g|f); minimizing -lnP(g|f) is equivalent to minimizing J1(f) given by: Since J1(f) is a convex function about f, to solve f, we only need to differentiate J1(f) with respect to f and set the derivative to 0, which is equivalent to: where f k represents the estimate of f at the kth iteration, and the negative sign indicates a flip; so the recursive relationship of f can be given by the following formula: Using Total Variation (TV) for image denoising can smooth the noise while maintaining the significant edges of the image. The TV regularization term Added to the Richardson-Lucy model (6), we get the RL-TV model: Where f is the original clear image to be solved, g is the observed blurred image, h is the blur kernel, λ TV is the parameter that controls the weight of the regularization term, and its value is between 0 and 1. i is a pixel point. The goal is to find the value that makes J1(f)+J req (f) the smallest f; Introduce three variables w, s and v to replace f and f*h, and for the sake of simplicity, the pixel point i is omitted in the formula. In fact, the sum of all pixel points i is the same as formula (10); therefore, solving the minimum point of (10) becomes solving such an optimization problem with constraints: Then add three square penalty terms to transform the above optimization problem with constraints into an optimization problem without constraints: Among them, μ1, μ2 and μ3 are parameters that control the weight of the penalty term and are positive; Similarly, if the 0-norm of the image gradient is When added as a regular term to the Richardson-Lucy algorithm model, the model becomes an RL-L0 model: where ∈ and is the weight; similarly, the sum sign represents the sum of all pixels; due to the addition of the L0 regularization term, this optimization problem becomes an NP-hard problem; In order to solve f from the above formula, we introduce two variables w = (w h ,w v ) T and v are used to replace and f*h, and adding a quadratic penalty term transforms the optimization problem with constraints into an optimization problem without constraints, so the objective function becomes: Where μ and α are penalty coefficients. When μ→∞, α→∞, the solution of (14) approaches the solution of (13), and (14) can be solved by alternately minimizing v, f and w.
4. The improved Richardson-Lucy image non-blind deblurring method according to claim 3, characterized in that: The specific content of S3 is: first solve the v sub-problem: The above formula is differentiable as a function of v, so we only need to take the derivative of v and set the derivative to 0. We can find that v has two solutions. We take the positive solution, so in each iteration, v is solved as follows: In each iteration, the solution of u is obtained by solving the following equation: The closed-form solution of f is as follows: in and denote the horizontal and vertical gradient operators respectively; After finding u, solving w is transformed into solving the following formula: (19) is a point minimization problem, so the solution of w is as follows:
5. The improved Richardson-Lucy image non-blind deblurring method according to claim 4, characterized in that: The specific content of S4 is: when the image noise cannot be ignored, as the number of iterations k increases, the noise amplification leads to a significant reduction in the convergence effect, and even increases the image blur; in view of this situation, the image quality evaluation parameters PSNR and SSIM are used to calculate the image parameters after each iteration to find the image that meets the standard; An image is composed of multiple pixels, and each pixel (i, j) is associated with each other. The required parameter values are used to determine the photo quality (N) and clarity (M) by calculating the association between the pixels. Mean Square Error: Peak signal-to-noise ratio: Structural similarity: First, two parameter values are calculated for the image pixel (i, j); a large number of calculations are performed on the image through the algorithm to determine the appropriate parameter standards under different blur levels. and After each iteration, the peak signal-to-noise ratio and structural similarity of the image are calculated and compared with their parameter standards. If both are greater than the parameter standards, the iteration operation is terminated and a valid restored image that reaches the target range is returned.