CN104166961B - The fuzzy core method of estimation that low-rank for blindly restoring image approaches - Google Patents
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Abstract
The invention discloses the fuzzy core method of estimation that a kind of low-rank for blindly restoring image approaches, and mainly solves the problems, such as how more accurately to realize fuzzy kernel estimates in method for blindly restoring image, and then restore preferable image.Implementation step is：The neighbor relationships of gradient image are considered, with autoregression (AR) policy improvement iteration threshold strategies so as to estimating a fuzzy core；On the other hand go to estimate another fuzzy core using heuristic wave filter enhancing image edge information；Then, strategy low-rank approached, which is incorporated into the estimation procedure of fuzzy core, to be gone to solve a relatively reliable fuzzy core.Finally restore clearly image using a kind of advanced image recovery method.It is of the invention that there is higher PSNR, SSIM and FSIM value compared with existing certain methods, visually also there is more preferable effect not only effectively to remove fuzzy, maintain more details, and the fuzzy core estimated is also more accurate.
Description
Technical Field
The invention belongs to the technical field of image processing, relates to the application of the field of image blind restoration, and particularly relates to a low-rank approximation fuzzy kernel estimation method for image blind restoration, which can be used for carrying out image restoration on various degraded images which are unknown and affected by slight noise.
Background
The blind restoration of an image refers to removing or reducing image blurring caused by various unknown factors in an acquired digital image, and meanwhile, the acquired image is also influenced by some inevitable noise. Blind restoration of images is therefore an important and challenging research context in image processing. It has important applications in many areas, such as medical image processing, material science image processing, public security, history, human photograph image restoration, surveillance video restoration, and scanned document processing. To address this problem, researchers have proposed a number of approaches.
Classical methods such as the maximum a posteriori probability based Method (MAP), fergus R, singh B, hertzmann A, et al, removing camera shade from a single photopraph [ C ]// ACM Transactions On Graphics (TOG). ACM,2006,25 (3): 787-794. This method first uses the variational Bayes strategy to obtain the blur kernel, and then uses a non-blind image restoration method to solve the sharp image. However, the mathematical principle of this method is too complex, and even the estimation of the image blur kernel containing slight noise is greatly affected. The cause of image blur can be described mathematically as a blur matrix, called a blur kernel.
Another type of method is to recover an image by using the edge information of the image, which is considered to play a role in the blind recovery of the image larger than other image information such as a homogeneous region. Comparing representative features such as s.cho and s.lee.fast motion deblocking. Acm trans. Graph, pages 145. This method also has the disadvantage that the estimation of the blur kernel is not accurate enough, since it relies too much on these heuristic filters.
Disclosure of Invention
The invention aims to provide a fuzzy core estimation method of low rank approximation for blind restoration of an image aiming at the defects of the prior art, so as to improve the accuracy of fuzzy core estimation and further ensure that the blind restoration effect of the image is better.
In order to achieve the above object, the present invention comprises the steps of:
(1) Setting a bilateral filter f with the side length of 3, the standard deviation of a spatial domain of 0.6 and the standard deviation of a value domain of 0.7 for preprocessing, and then carrying out bilateral filtering on the degraded image y to be processed to obtain an image y with sharpened edge and restrained noise influence (1) ；
(2) Initializing relevant conditions and parameters, and generating a gradient image matrix;
(3) For gradient image matrixIn the pyramid model (i.e. the image is down-sampled into n layers by using a bicubic difference method, and the ratio between two adjacent layers is in the invention) The ith (i =1,n) layer of (b) uses an impulse response filter to enhance sharp image edges as follows:
(4) From a gradient image matrixTraining Autoregressive (AR) coefficients for a current layer (i-th layer)(in the horizontal direction) with(vertical direction);
(5) Initializing and updating threshold adjusting parameter Cost before ＝LS cost +Re cost +AR cost ：
i =1,2.. N, wherein x (i) For the gradient map generated by updating in the ith iteration of the pyramid, the 1 st iteration is initialized toi＝1,2...n，k (i) The fuzzy kernel generated in the ith pyramid iteration process is updated. In addition, AR in iteration 1 cost =0, the values calculated in step (11 a) for other iterations are updated and calculated, | | · | | survival 2 Live with | · | 1 Respectively representing the 2-norm operation and the 1-norm operation of the matrix,denotes the F norm, λ is the likelihood termN, taken as 90 in the method;
(6) Optimizing using an iterative threshold algorithm (ISTA) optimization algorithm:
(7) Parameter Cost for calculating and updating iterative threshold algorithm (ISTA) threshold afer And judges Cost afer Whether greater than 1.12 by cost before Then processing is carried out;
(8) Least Squares (IRLS) de-optimization using re-weighted valuesAnd k is more than or equal to 0, sigma j k j And =1. Where k is j Refers to the pixel value of the blur kernel k at point j.
(9) Repeating the steps (5) - (8) iter times to obtain the estimated fuzzy kernel k (i) N, iter is a user parameter in the method, 21 is taken in the experiment, and the user can be left to 21Right value is taken, and then a bilinear interpolation method is used for estimating the fuzzy kernel k (i) And x (i) Up-sampling and taking the up-sampled data as an initial value of a next layer of the pyramid;
(10) Repeating the steps (3) - (10) n times, wherein n is the image pyramid layer number set according to the size of the fuzzy core, and the calculation method is to multiply the minimum fuzzy core (3 in the method) by the image pyramid layer number in sequenceRounding, counting from 1 until the fuzzy kernel size reaches the set fuzzy kernel size, and estimating the fuzzy kernel k from the last pyramid layer to suppress noise 1 The value less than 0 in the pixel values is assigned as 0, and the estimated fuzzy kernel k is output at the last layer of the pyramid 1 ；
(11) And (3) performing no processing on the degraded image y to be processed, calculating the layer number n of the pyramid model in the same way as the step (2), and zooming y to the coarsest layer (layer 1) y by using a bilinear interpolation method i i =1 while using y i i =1 updatei =1, and sets the progressive multiple between the gradient image sizes of each layer toUpdating the blur kernel that initializes the coarsest layeri＝1；
(12) Repeating the steps (2), (4) and (11), and outputting the 2 nd estimated fuzzy core k 2 ；
(13) Using the estimated blur kernel k 1 And k 2 Solving a final fuzzy kernel k;
(14) Clear images are estimated by optimizing the formula (2) by using the estimated blur kernel k (the iteration number for solving the formula (2) is set to be 200)
Where x is the sharp image to be estimated, y is the observed degraded image, T f Is a toeplitz matrix.
(15) And outputting the processed sharp image x and the estimated blur kernel k.
The technical scheme of the invention considers the neighbor relation of the gradient image, and an Autoregressive (AR) strategy is used for improving an iteration threshold strategy so as to estimate a fuzzy core; using a heuristic filter to enhance the image edge information to estimate another fuzzy core; a low-rank approximation strategy is introduced into the fuzzy kernel estimation process to solve a more reliable fuzzy kernel. Finally, an advanced image restoration method is used to restore a clear image. Compared with the prior art, the invention has the following advantages:
1. the method reduces the inaccuracy of fuzzy kernel estimation caused by factors such as noise or other singular values existing in the degraded observed image;
2. the invention does not depend on a heuristic filter to utilize the edge information of the image;
3. according to the method, the neighbor relation of the gradient image is considered, so that a better fuzzy kernel can be searched in a self-adaptive manner in the iterative optimization process;
4. the method realizes the process of solving a fuzzy core with relatively more accurate and stable fuzzy by using two different fuzzy cores which are estimated, and experimental results show that the strategy generates a better blind restoration result of the image.
Drawings
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a synthesized blurred slightly noisy degraded image used in simulation of the present invention, the lower right corner of the image being a blur kernel for synthesis;
FIG. 3 is a graph showing the results of recovery using the prior art maximum a posteriori probability based Method (MAP), fergus'06, fergus R, singh B, hertzmann A, et al, removing camera peak from a single photograph [ C ]// ACM Transactions On Graphics (TOG). ACM,2006,25 (3): 787-794;
fig. 4 is a result of recovery using the method of prior art edge-based method, cho'09, i.e., s.cho and s.lee.fast motion deblocking. Acm trans. Graph, pages 145;
fig. 5 is the result of blind deblurring performed on fig. 2 using the present invention.
Fig. 6 is a comparison of the local effect of the three methods of blind deblurring for fig. 2.
Detailed Description
Referring to fig. 1, the specific implementation steps of the present invention are as follows:
step 1, setting a bilateral filter f for preprocessing with the side length of 3, the standard deviation of a spatial domain of 0.6 and the standard deviation of a value domain of 0.7, and then carrying out bilateral filtering on a degraded image y to be processed to obtain an image y with sharpened edge and inhibited noise influence (1) ；
Step 2, initializing relevant conditions and parameters, and generating a gradient image matrix;
2a) Using a preset blur kernel size (i.e. the size of the blur kernel matrix) k size Calculating the number n of layers of the pyramid model according to the size and k of the fuzzy core of the coarsest layer (layer 1) size Using bilinear interpolation to scale y (1) To the coarsest layer (layer 1)i =1, and sets the progressive multiple between the gradient image sizes of each layer toSimultaneous initialization of the blur kernel of the coarsest layeri＝1；
2b) The horizontal gradient operator dx = [ -1,1;0,0]And perpendicular dy = [ -1,0;1,0]And pyramid and ith layer image respectivelyConvolution is carried out to obtain an image of a gradient domainAndn, and are connected and merged into a gradient image matrixi＝1,2...n；
Step 3, for the gradient image matrixThe following impulse response filter was used at the ith (i =1,n) level of the pyramid model to enhance the sharp image edges in the image:
3a) Replacing I in (1) with a gradient image matrixAnd and Δ I t Respectively, to a gradient image matrix using a Laplacian operator and a gradient operatorAndperforming operation;
3b) Setting dt as a medium attenuation factor of each iteration, taking 0.08 in the method, iterating for 5 times in the formula (1), merging and updating the processed gradient image matrix
Step 4, according to the gradient image matrixTraining the horizontal Autoregressive (AR) coefficients of the current layer (i-th layer)Coefficient of Autoregressive (AR) with vertical direction
4a) The window size required to train the Autoregressive (AR) coefficients as described above is taken to be 3 x 3, and the gradient image matrix is appliedAndthe mapping process is performed one pixel around the boundary. According to the size of 3X 3 windowAndis drawn into m i X 9 matrixAndi＝1,2；
4b) Extracting matricesAndline 5 of (1), denoted as Y 1 And Y 2 According to Respectively calculate(in the horizontal direction) with(vertical direction) i =1,2;
step 5, initializing and updating a threshold value adjusting parameter Cost before ＝LS cost +Re cost +AR cost ：
N, wherein x is (i) For the gradient map generated by updating in the ith iteration of the pyramid, the 1 st iteration is initialized toi＝1,2...n，k (i) And updating the generated fuzzy core in the ith pyramid layer iteration process. In addition, AR in iteration 1 cost =0, the values calculated in step (11 a) for other iterations are updated and calculated, | | · | | survival 2 Live with | · | 1 Respectively representing the 2-norm operation and the 1-norm operation of the matrix,representing F norm, λ being a likelihood termN, taken in the method as 90;
and 6, optimizing by using an iterative threshold algorithm (ISTA) optimization algorithm:
step 7, calculating a parameter Cost for updating an iterative threshold algorithm (ISTA) threshold afer And judges Cost afer Whether or not it is greater than 1.12 × cost before Then processing is carried out;
7a) X updated by iteration (i) Is decomposed intoAndaccording to 3X 3 window decomposition, pull it into m i X 9 matrixAndn, i =1,2.. N, extractionAndline 5 of (1), asAnd withi＝1,2...n；
7b) According toAndi =1,2, where γ is 10, the update is calculatedi＝1,2；
7c) After iterative update of computationAnd calculatingi =1,2.. N where λ is the likelihood term coefficient, taken as 90 in the method;
7d) Calculating and updating threshold adjusting parameter Cost after iteration afer ＝LS cost +Re cost +AR cost ；
7e) If Cost afer >1.12*Cost before Adjusting the threshold value of the next iteration of the ISTA to be 0.62 times of the current iteration;
7f) If Cost afer <1.12*Cost before If the threshold value of the next iteration of the ISTA is not changed, stopping the ISTA optimization and jumping into the step (8);
step 8, using least square method (IRLS) of re-weighting value to optimizeAnd k is more than or equal to 0, sigma j k j And =1. Where k is j Refers to the pixel value of the blur kernel k at point j.
Step 9, repeating the steps (5) to (8) iter times to obtain the estimated fuzzy kernel k (i) i =1,2.. N, iter is a user parameter in the method, and 21 is generally taken; then, the estimated fuzzy kernel k is processed by a bilinear interpolation method (i) And x (i) Up-sampling and taking the up-sampled data as an initial value of a next layer of the pyramid;
step 10, repeating the steps (3) to (10) n timesThe value of n is the same as that in step 2, the number of pyramid layers is defined, and in addition, in order to inhibit the noise influence, the last pyramid layer is used for estimating a fuzzy kernel k 1 The pixel value smaller than 0 is assigned as 0, and the estimated fuzzy kernel k is output at the last layer of the pyramid 1 ；
And 11, performing no treatment on the degraded image y to be treated, calculating the layer number n of the pyramid model in the same way as the step 2, and zooming y to the coarsest layer (layer 1) y by using a bilinear interpolation method i i =1 while using y i i =1 updatei =1, and sets the progressive multiple between the gradient image sizes of each layer toUpdating a blur kernel that initializes a coarsest layeri＝1；
Step 12, repeating steps (2), (4) to (11), outputting the 2 nd estimated blur kernel k 2 ；
Step 13, utilizing the estimated fuzzy kernel k 1 And k 2 Solving a final fuzzy kernel k;
13a) The estimated fuzzy kernel k 1 And k 2 Respectively pulled into a column and combined together to be marked as D k Then carrying out low-rank decomposition by using a Go-dec algorithm;
13b) Recording the decomposed low-rank part as ker, and restoring the ker into k according to the size of a preset fuzzy core size ×k size The blur kernel k of (1);
step 14, estimating a sharp image by using the estimated fuzzy kernel k through an optimization formula (2) (the iterative loop solving times is set to be 200 times)
Where x is the sharp image to be estimated, y is the observed degraded image, T f Is the Toeplitz (toeplitz) matrix.
And step 15, outputting the processed sharp image x and the estimated fuzzy kernel k.
The effect of the present invention can be further illustrated by the following experimental simulation:
1. experimental conditions and methods
The hardware platform is as follows: intel Core2 Duo CPU [email protected], 2GB RAM;
the software platform is as follows: MATLAB R2013a;
the experimental method comprises the following steps: the methods of the present invention and Fergus '06, (1) and Cho'09, (2), respectively, are representative methods in the art.
2. Simulation content and results
Blind restoration simulation is respectively carried out on the Sailing blurred image shown in the figure 2 by using the method of the invention and the prior Fergus '06 method and the Cho'09 method, wherein the lower right part of the figure is a real blurred kernel used for synthesis; wherein the Sailing blind restoration result obtained by the method is shown in figure 5, and the estimated fuzzy core is shown in the right lower part of the figure; the result of Sailing blind restoration obtained by the prior Fergus'06 method is shown in figure 3, and the estimated fuzzy core is shown in the lower right of the figure; the result of the Sailing blind restoration obtained by the existing edge-based method is shown in fig. 4, and the estimated blur kernel is shown in the lower right of the figure.
In the simulation experiment, peak signal to noise ratio (PSNR), structural Similarity Index (SSIM), and structural similarity (FSIM) were used as evaluation indexes.
The evaluation results are shown in Table 1, wherein Alg1 is the method of the present invention, and Alg2 is the method of Fergus '06, that is, alg3 is Cho' 09.
TABLE 1 PSNR values (in dB) obtained in simulation experiments for the present invention and two comparative methods, and SSIM, FSIM
3. Analysis of Experimental results
Comparing the blind restoration result obtained by the invention with the blind restoration result of the method of fig. 5 fergus '06, fig. 3 and the restoration result obtained by the method of Cho'09, fig. 4 shows that the Sailing blind restoration result obtained by the invention shown in fig. 5 obtains better experimental results compared with other two methods, fig. 5 not only effectively removes blur, but also retains more image details, and the estimated blur kernel is closer to a real blur kernel; the method of Fergus'06 shown in figure 3 results in blind restoration that is not effective in removing blur while being affected by noise and produces serious artifacts; the method of Cho'09 shown in FIG. 4 is effective in removing blur, but does not work with the effect of noise and loses some of the image details.
As can be seen from Table 1, the method has higher PSNR, SSIM and FSIM values than other two comparison methods, has better effect in vision, not only effectively removes the blur and keeps more details, but also has more accurate estimated blur kernel.
Claims (5)
1. A fuzzy core estimation method of low rank approximation for blind restoration of images comprises the following steps:
step 1: setting a bilateral filter f for preprocessing with the side length of 3, the standard deviation of a spatial domain of 0.6 and the standard deviation of a value domain of 0.7, and then carrying out bilateral filtering on the degraded image y to be processed to obtain an image y with sharpened edge and inhibited noise influence (1) ；
Step 2: initializing relevant conditions and parameters, and generating a gradient image matrix;
and step 3: for gradient image matrixAt the ith layer of the pyramid model, an impulse response filter is used to enhance sharp image edges, where i =1, n,
and 4, step 4: from a gradient image matrixTraining the horizontal Autoregressive (AR) coefficients of the current layer, i.e. the ith layerCoefficient of Autoregressive (AR) with vertical direction
And 5: initializing and updating threshold adjusting parameter Cost before ＝LS cost +Re cost +AR cost ：
Wherein x (i) For the gradient map generated by updating in the ith iteration of the pyramid, the 1 st iteration is initialized tok (i) Updating a fuzzy kernel generated in the ith pyramid iteration process; in addition, AR in iteration 1 cost =0, the values calculated in step 7 b) for the other iterations are updated, | · survival 2 (ii) counting & lt | & gt | & lt | & gt 1 Respectively representing the 2-norm operation and the 1-norm operation of the matrix,denotes the F norm, λ is the likelihood term λThe coefficient of (a) in the present method is 90;
step 6: optimizing using an iterative threshold algorithm (ISTA) optimization algorithm:
and 7: parameter Cost for calculating and updating ISTA threshold of iterative threshold algorithm afer And judges Cost afer Whether greater than 1.12 by cost before Then, processing is carried out, which specifically comprises:
7a) X to be iteratively updated (i) Is decomposed intoAndaccording to 3X 3 window decomposition, pull it into m i X 9 matrixAnd withExtraction ofAndline 5 of (1), asAnd
7b) According toAndwhere gamma is 10, compute update
7c) After iterative update of computationAnd calculating Wherein, the lambda is the likelihood item coefficient, and the value is 90 in the method;
7d) Calculating and updating threshold adjusting parameter Cost after iteration afer ＝LS cost +Re cost +AR cost ；
7e) If Cost afer >1.12*Cost before Adjusting the threshold value of the next iteration of the ISTA to be 0.62 times of the current iteration;
7f) If Cost afer <1.12*Cost before If the threshold value of the next iteration of the ISTA is not changed, stopping the ISTA optimization and jumping to the step 8;
and 8: least Squares (IRLS) optimization using re-weighted valuesAnd k is greater than or equal to 0, sigma k j =1, where k j The pixel value of a fuzzy kernel k at a point j is referred to;
and step 9: repeating the step 5 to 8iter times to obtain the estimated fuzzy kernel k (i) i =1,2.. N, iter is a user parameter in the method, and 21 is generally taken; then, a bilinear interpolation method is used for estimating the fuzzy kernel k (i) And x (i) Sampling up, and taking the sampled data as an initial value of a next pyramid layer;
step 10, repeating the step 3-10 i times, wherein the value of i is the same as that of the step 3 and is goldThe number of layers of the pyramid, and the last layer of the pyramid is estimated to obtain a fuzzy kernel k for suppressing the influence of noise 1 The pixel value smaller than 0 is assigned as 0, and the estimated fuzzy kernel k is output at the last layer of the pyramid 1 ；
Step 11: and (4) not processing the degraded image y to be processed, calculating the layer number i of the pyramid model in the same way as the step (3), and zooming y to the coarsest layer, namely the layer 1 y by using a bilinear interpolation method i i =1 while using y i i =1 updateAnd setting the progressive multiple between the gradient image sizes of each layer to beUpdating a blur kernel that initializes a coarsest layer
Step 12: repeating the steps 2, 4-11 and outputting the 2 nd estimated fuzzy kernel k 2 ；
Step 13: using estimated blur kernel k 1 And k 2 Solving a final fuzzy kernel k;
step 14: estimating a sharp image by optimizing the formula (2) by using the estimated blur kernel k
Where x is the sharp image to be estimated, y is the observed degraded image, T f Is a Toeplitz (toeplitz) matrix;
step 15: and outputting the processed sharp image x and the estimated blur kernel k.
2. The method of claim 1, wherein initializing correlation conditions and parameters and generating a gradient image matrix comprises:
2a) Using a predetermined blur kernel size k size Calculating the number n of layers of the pyramid model according to the size and k of the fuzzy core of the coarsest layer (layer 1) size Using bilinear interpolation to scale y (1) To the coarsest layer (layer 1)And setting the progressive multiple between the gradient image sizes of each layer to beSimultaneous initialization of the blur kernel of the coarsest layer
2b) The horizontal gradient operator dx = [ -1,1;0,0]Dy = [ -1,0;1,0]And pyramid and ith layer image respectivelyConvolution is carried out to obtain an image of a gradient domainAndconnected and merged into a gradient image matrix
3. The method for fuzzy core estimation of low rank approximation for blind restoration of images as claimed in claim 1, wherein the formula (1) of step 3 comprises:
3a) Replacing I in formula (1) with a gradient image matrixAnd and Δ I t Respectively, to gradient image matrices using laplace operator and gradient operatorAndperforming operation;
3b) Setting dt as a medium attenuation factor of each iteration, taking 0.08 in the method, iterating for 5 times in the formula (1), merging and updating the processed gradient image matrix
4. The method of fuzzy core estimation for low rank approximation for blind restoration of images as claimed in claim 1, wherein step 4 comprises:
4a) Taking the window size required by training Autoregressive (AR) coefficients as 3 x 3, and matching the gradient image matrixAndthe mapping process is performed one pixel around the boundary, while the 3 x 3 window size will beAndto be pulled into m i Moment of x 9MatrixAnd with
4b) Extracting matricesAndline 5 of (1), denoted as Y 1 And Y 2 According to Respectively calculate(in the horizontal direction) with(vertical direction) i =1,2.
5. The method for fuzzy core estimation of low rank approximation for blind restoration of images as claimed in claim 1, wherein step 13 specifically comprises:
13a) The estimated fuzzy kernel k 1 And k 2 Respectively pulled into a column and combined together to be marked as D k Then carrying out low-rank decomposition by utilizing a Go-dec algorithm;
13b) Recording the decomposed low-rank part as ker, and restoring the ker into k according to the size of a preset fuzzy core size ×k size K is the blur kernel.
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