CN108564544B - Image blind deblurring combined sparse optimization method based on edge perception - Google Patents
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Abstract
The invention discloses an image blind deblurring combined sparse optimization method based on edge perception, which introduces a relative total variation regularization term on the basis of image L0 sparse prior to carry out blind deblurring on a natural image, and comprises the following steps: input blurred image yThe fuzzy kernel is k, and the clear image to be solved is x; initializing an image x to be solved as a blurred image y, and initializing parameters lambda, sigma and the like; solving a fuzzy kernel k from thick to thin by using a fuzzy kernel and image cross estimation method; non-blind deblurring of the blurred image y is carried out according to the blur kernel k calculated finally in the step 3), and a clear image x is obtained (L) The method comprises the steps of carrying out a first treatment on the surface of the And finally processing the clear image to obtain a final clear image.
Description
Technical field:
the invention relates to an image blind deblurring combined sparse optimization method based on edge perception, and belongs to the technical field of image processing.
The background technology is as follows:
the development of modern social science and technology, particularly computer and multimedia technology, is rapid, and the importance of information processing technology is recognized. As video cameras and cameras are widely used in ordinary households, images can be easily obtained, and therefore, it is becoming more and more important to ensure the high definition of the obtained images simply and efficiently. However, during daily photographing, we find that the obtained image is often blurred due to imaging devices, weather factors, processing and transmission modes and the like during the process of acquisition, recording, processing and transmission. The clear image can be estimated directly by using the degraded image information, but since many parameters are unknown at the time of imaging, we need to estimate the blur kernel of the image and the clear digital image at the same time. This estimation of a sharp image without knowledge of blur kernel information is the blind restoration of the image. In many cases, the blur kernel is often unknown, and efficient restoration of degraded blurred images is a challenging problem.
The theoretical basis of the image deblurring technology is as follows: modeling the image according to the reason of image degradation, and recovering or reconstructing the degraded image into an original image, which can be expressed as follows: y=k x+n, where y denotes the observed blurred image (degraded image), k denotes the blur kernel (which may also be called a blur function, a point spread function, a degradation factor, etc.), x denotes the convolution operation, x is the sharp image (original image) that needs to be restored, and n is additive noise (usually assumed to be gaussian noise), so the image deblurring problem mathematically is how to obtain the sharp image x from the blurred image y, which requires deconvolution. Blind deconvolution is a more challenging problem of pathological inversion. Because the blur kernel is unknown in the blind deblurring problem, its algorithm generally employs the step of separate alternating estimation of the blur kernel and the sharp image: 1) Firstly, estimating an image blur kernel k, namely estimating a blur kernel of an image by utilizing an initially recovered clear image; 2) And estimating the clear image x, and performing non-blind estimation by using the fuzzy check image obtained by the previous estimation to obtain a deblurred image. The two processes are sequentially alternated, and finally a clear image is obtained.
Throughout the earlier deblurring work, the success of blind deblurring of images is to utilize the prior knowledge of the images and the edge detection for kernel estimation as efficiently as possible, put forward regularization term constraint solution space and iteratively solve clear images. The conventional method generally realizes blind deblurring by taking the L0 norm of the gradient of the image as a priori knowledge, and is good for most natural images. Recently, pan et al achieved blind deblurring of a text image by combining the L0 norm priors of image brightness and image gradient, the image priors resulted from observing different properties of the text image, based on which a reliable intermediate result of the kernel estimation was generated. There is no need to detect protruding edges. In the final image restoration step, artifacts are removed and deblurred, further optimizing the natural image deblurring effect. The method basically achieves the best known results on the basis of the problem of blind recovery of the text image, and in fact, the method can obtain a good deblurring effect on images of natural images and low-illumination scenes. According to the statistical result of the text image, the text image is mainly bicolor (two gradient values) and does not accord with the gradient statistics of the heavy tail distribution of the natural image, if the image is blurred, other gradient values can appear, and the Pan method is to conduct regularization constraint by using the priori knowledge of the text image so as to obtain a clear image result. However, this statistical characteristic does not exist in the natural image, and since the brightness values of the natural image are rich and varied, the statistical characteristic (only two values) of the text image cannot be used as a constraint condition. There are, of course, many other ways of image blind deblurring, but with relatively higher computational complexity. Another recent work by Pan has attracted considerable attention: the blind deblurring effect with stronger robustness and higher accuracy is realized by combining the image gradient L0 norm and the image dark channel L0 norm, and the work brings a new thinking direction for researching the blind deblurring problem: whether the problem of image deblurring can be referred to as a method for processing other image problems or not and whether a better image prior representation method exists or not are solved.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person of ordinary skill in the art.
The invention comprises the following steps:
the invention aims to provide an image blind deblurring combined sparse optimization method based on edge perception, which improves the result of an algorithm on fuzzy kernel and clear image estimation, thereby overcoming the defects in the prior art.
In order to achieve the above purpose, the present invention provides the following solutions: the method has the advantages that the relative total variation regularization term is introduced on the basis of the image L0 sparse prior, blind deblurring is carried out on the natural image, the edge information of the image is better reserved, and therefore good results are obtained. According to the definition of the relative total variation, the value of the relative total variation term in the blurred image is larger than that of the clear image, and the image is constrained by taking the value as the prior when blind deblurring, specifically, the method comprises the following steps:
s1, inputting a fuzzy image y, wherein a fuzzy kernel is k, and a clear image to be solved is x;
s2, initializing an image x to be solved into a blurred image y, and initializing parameters lambda, sigma and the like;
s3, solving a fuzzy kernel k from thick to thin by using a fuzzy kernel and image cross estimation method;
s4, performing non-blind deblurring on the blurred image y according to the blur kernel k calculated finally in the step 3), and obtaining a clear image x (L) ；
S5, performing final processing on the clear image to obtain a final clear image.
The technical scheme is further defined as follows:
preferably, in the above technical solution, step3 specifically includes:
(1) roughly estimating the fuzzy kernel as k (0) The method comprises the steps of carrying out a first treatment on the surface of the Initializing the number of times of non-blind deblurring to be l=0;
(2) from the above roughly estimated blur kernel k, the clear intermediate image is solved using the following equation 1:
wherein x(l) Representing a clear image to be solved obtained after the first lambda iteration solution,
representing the minimum values x, u and g of the objective function, u and g are manually introduced auxiliary variables, and correspond to the structural image S and the image gradient respectively
x (l-1) Represents the clear image to be solved after the first-1 iteration solution, k (l-1) Representing the blur kernel after the first-1 iteration solution, y representing the blurred image, x representing the convolution operation, +.>
Representing the square of the 2 norms +.>
Representing image x (l-1) Is used for the gradient of (a), I.I. | 0 Represents 0 norm, S (l-1) Represents x (l-1) λ, σ are regular term coefficients, μ, β are coefficients of the introduced variable, and β=2λσ, μ=2λ, +.>
Representing an image x (l-1) Is a relative total variation regularization term of (1), wherein D h (p)、D v (p) is the window total variation, L h (p)、L v (p) is the window inherent variation, p is a pixel point on the image, h and v represent the horizontal and vertical directions respectively, ε is a very small positive number, avoid denominator L h(p) and Lv (p) is 0; />
(3) The sharp image x estimated from (2) (l) The blur kernel can be solved directly with the following equation 2:
k (l) represented is the blur kernel obtained after the first solution,
representing the value of the minimum value k of the objective function, x (l) Clear image after first solving of representation, k (l-1) Represents the blur kernel after the first-1 solving, y represents the blurred image, x represents convolution operation,/and->
Representing the square of the 2 norms, gamma being the regularized term parameter;
(4) updating the value of lambda, judging whether L is smaller than the maximum cycle number L, updating l=l+1, repeating (2) and (3) to obtain the final fuzzy kernel k=k (L) 。
Preferably, in the above technical solution, the l0+rtv regularization model constructed in step 3;
the regularization model based on significant edge priors and relative total variation of the image gradient L0 norms is as follows:
the method of the formula 3 is that,
let u=s and,
when μ and β approach infinity, equation 3 changes to equation 4:
let the values of u, g approach zero, then calculate equation 5:
the sharp image x can be obtained by the following formula 6:
wherein: f (&) and F -1 (. Cndot.) represents the fourier transform and the inverse fourier transform,
is a complex conjugate form of fourier transform, +.>
Differential operators representing horizontal and vertical directions, respectively;
setting a clear image x, and calculating values of u and g through formulas 7, 8 and 9 respectively:
then:
the clear intermediate image x in the first iteration can be obtained by calculating u and g according to the above formula and combining with formula 6 (l) 。
Preferably, in the above technical solution, the added RTV regularization term calculates formula 10 of the structural image:
wherein ,
is the value of the minimum value S of the objective function, S is the structural image, I is the input image,
the pixel point difference values of the output image and the input image are summed to ensure the accuracy of the output structural image, eta is a regularization parameter, and a regularization term is +.>
Is the relative total variation, D x (p)、D y (p) is the window total variation, specifically
L x (p)、L y (p) is a window inherent variation which has no relation to the gradient direction, specifically +.>
g p,q Is a weight function defined according to the spatial correlation, wherein alpha controls the window scale, p is the central pixel point of the variation region R (p), q is any point epsilon, epsilon in the variation region R (p) S Is a very small positive number.
The specific calculation for the relative total variation term is as follows equation 11:
wherein equations 12 and 13 are respectively:
U xp representing that each pixel point combines gradient information in the field of the point, W xp The representation is related only to the gradient of the point; similarly, the expression in the y direction is as follows formulas 14 and 15:
by splitting the relative total variation term, equation 10 can be written as the following matrix form 16:
wherein ,Cx 、C y The toeplitz matrix obtained by approximating a discrete gradient operator by forward search is v S 、v I Vector representations of S and I, U x 、U y 、W x 、W y Is a diagonal matrix with a value of U on the diagonal x [i,i]＝u xi ，U y [i,i]＝u yi ，W x [i,i]＝w xi ，W y [i,i]＝w yi The method comprises the steps of carrying out a first treatment on the surface of the Equation 12 is calculated using the Euler-Lagrangian equation and the minimization problem is converted to linear problem equation 17:
where E is the identity matrix and where,
is based on the structural vector->
Calculated weight matrix, (E+ηL t ) Is a non-negatively symmetric Laplacian matrix;
the structural image S can be obtained by a plurality of iterative calculations 12, 13, 14, 15, 17.
Compared with the prior art, the invention has the following beneficial effects:
firstly, the invention combines L0 sparsity and relative total variation based on edge perception, better reserves edge detail information of the image, and more accurately estimates fuzzy kernels, thereby improving the estimated clear image effect.
Secondly, compared with the original method, the method has good deblurring effect on natural images, and the effect on the Levin data set is basically higher than that of the known blind deblurring method.
Description of the drawings:
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a blurred image to be processed;
FIG. 3a is the deblurring result of FIG. 2 using the deblur method disclosed in Li Xu, cewu Lu et al, article "mage Smoothing via L0 Gradient Minimization";
FIG. 3b is the deblurring result of FIG. 2 using the deblurring method disclosed by Jinhan Pany, zhe Hu et al in article "Deblurring Text Images via L0-Regularized Intensity and Gradient Prior";
FIG. 3c is a plot of the deblurring result of FIG. 2 using the method of the present invention;
FIG. 4a blurred text image;
FIG. 4b is the deblurring result of FIG. 4a using the method of Li Xu, cewu Lu et al;
FIG. 4c is a deblurring result of FIG. 4a using the method of Jinhan Pan, zhe Hu et al;
FIG. 4d is a deblurring result of FIG. 4a using the method of the present invention.
The specific embodiment is as follows:
the following detailed description of specific embodiments of the invention is, but it should be understood that the invention is not limited to specific embodiments.
Throughout the specification and claims, unless explicitly stated otherwise, the term "comprise" or variations thereof such as "comprises" or "comprising", etc. will be understood to include the stated element or component without excluding other elements or components.
The experiments will be described in further detail with reference to the accompanying drawings.
Referring to fig. 1, the specific steps of the present invention are as follows:
step1: inputting a blurred image:
inputting a fuzzy image y, wherein the fuzzy kernel is k, and the clear image to be solved is x;
step2: initializing parameters:
initializing parameters such as lambda, sigma and the like by initializing an image x to be solved as an original blurred image y;
step3: calculating a fuzzy core:
the fuzzy kernel is solved from thick to thin by using a fuzzy kernel and image cross estimation method:
(1) initializing a fuzzy kernel, roughly estimating to be k (0) Initializing the number of non-blind deblurring to l=0;
(2) initializing β=2λσ, initializing μ max 、β max And calculating the value of the auxiliary variable u by using a formula (8) according to the fuzzy kernel k roughly estimated above.
Wherein the structural image S, the specific calculation can be implemented with the following code:
step1: inputting an image I, parameters eta and alpha;
step2: initializing t= 0,S 0 ＝I；
Step3: calculating the weight U using the formulas (12), (13), (14), (15) x 、U y 、W x 、W y ；
Step4: jie Xianxing equation (17);
step5: iterating step3 and step4 as many times as required;
step6: the structural image S is output.
(3) Calculating the value of the auxiliary variable g using equation (9)
(4) Calculating a sharp image using equation (6)
x (l) Representing clear images to be solved obtained after the first lambda cycle solution, u and g are auxiliary variables corresponding to S and S respectively
k (l-1) Representing the blur kernel after the first-1 loop solution, y representing the blurred images, F (&) and F -1 (. Cndot.) represents the Fourier transform and the inverse Fourier transform,>
is a complex conjugate form of the fourier transform,
representing differential operators in the horizontal and vertical directions, respectively.
(5) Based on the idea of cross estimation, the clear image x estimated by (3) is utilized (l) Solving a fuzzy kernel:
k (l) represented is the blur kernel obtained after the first solution,
representing the value of the minimum value k of the objective function, x (l) Clear image after first solving of representation, k (l-1) Represents the blur kernel after the first-1 solving, y represents the blurred image, x represents convolution operation,/and->
Representing the square of the 2 norms, gamma being the regularized term parameter;
(6) updating the value of lambda, judging whether L is greater than the maximum number of loops L, updating l=l+1, updating the structure S of the image, repeating the step of cross estimation above to obtain the final fuzzy kernel k=k (L) ；
Step4: calculating a sharp image
According to the fuzzy kernel k calculated in the last iteration in the step 3), carrying out non-blind deblurring on the original fuzzy image y, and calculating the definitionImage x of (2) (L) ；
Step5: and (3) obtaining a clear image, and performing necessary processing on the image obtained in the step (4), such as removing artificial artifacts and the like, so as to obtain a final clear image.
The deblurring effect of the present invention is further described below in connection with experimental conditions.
1. Experimental conditions
The experimental operation system of the invention is an Inter (R) Core (TM) i7CPU@3.4GHz and 64-bit Windows operating system, and the simulation software used is MATLAB (R2014 a). The source of blurred images used in the experiment was a database of blurred natural images in article "Understanding and evaluating blind deconvolution algorithms" published by A.Levin, Y.Weiss, F.Durand, W.T.Freeman et al, as shown in fig. 2.
2. Experimental details
The blind deblurring process of fig. 2 is performed using the present invention and the three prior deblurring methods, and the results are shown in fig. 3.
FIG. 3a is the deblurring result of FIG. 2 using the deblur method disclosed in Li Xu, cewu Lu et al, article "mage Smoothing via L0 Gradient Minimization";
FIG. 3b is the deblurring result of FIG. 2 using the deblurring method disclosed by Jinhan Pany, zhe Hu et al in article "Deblurring Text Images via L0-Regularized Intensity and Gradient Prior";
FIG. 3c is a plot of the deblurring result of FIG. 2 using the method of the present invention;
3. simulation result analysis
In the simulation experiment, the experimental result is evaluated by adopting a peak signal-to-noise ratio PSNR index, wherein PSNR is defined as:
wherein: x represents the original sharp image and Z represents the restored deblurred image. The higher peak signal-to-noise ratio indicates better deblurring performance.
The PSNR value of fig. 3a is 32.13dB;
the PSNR value for fig. 3b is 31.66dB;
the PSNR value of fig. 3c is 33.08dB. The partial data are the results of experiments carried out on the figure 2 by three methods, the figure 2 is a specific blurred picture in the Levin data set, eight different blurred kernels are contained in the Levin data set, and the experimental results of the table are the results after blind deblurring of the blurred pictures corresponding to the eight blurred kernels of the original clear image.
To better compare the deblurring performance of these three methods, we performed experiments on a set of standard blurred pictures on the Levin dataset, the results of which are shown in table 1.
Table 1 shows the experimental results of blurred pictures:
| ker01 | ker02 | ker03 | ker04 | ker05 | ker06 | ker07 | ker08 | average PSNR | |
| Xu et al. | 32.13 | 30.09 | 33.89 | 27.83 | 34.06 | 29.33 | 33.83 | 33.09 | 31.78 |
| Pan et al. | 33.10 | 30.52 | 33.67 | 29.55 | 34.83 | 32.96 | 31.17 | 32.76 | 32.32 |
| Ours | 33.08 | 31.09 | 35.42 | 28.67 | 34.04 | 34.07 | 30.87 | 32.01 | 32.41 |
。
From the data obtained, it can be seen that the PSNR value of the deblurring result of the method of the present invention is higher than that of the deblurring result of other methods, i.e. the present invention has a better deblurring effect than the prior art.
During the experiment we found that the method of the invention also gave good results for deblurring text images, as shown in figure 4 d. The source of the blurred text image is the database in the article "Deblurring Text Images via L-Regularized Intensity and Gradient Prior" by jinhan Pan, zhe Hu et al.
FIG. 4a blurred text image;
FIG. 4b is the deblurring result of FIG. 4a using the method of Li Xu, cewu Lu et al;
FIG. 4c is a deblurring result of FIG. 4a using the method of Jinhan Pan, zhe Hu et al;
FIG. 4d is a deblurring result of FIG. 4a using the method of the present invention.
The foregoing descriptions of specific exemplary embodiments of the present invention are presented for purposes of illustration and description. It is not intended to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain the specific principles of the invention and its practical application to thereby enable one skilled in the art to make and utilize the invention in various exemplary embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims and their equivalents.
Claims (3)
1. The image blind deblurring combined sparse optimization method based on edge perception is characterized in that a relative total variation regularization term is introduced on the basis of image L0 sparse prior, and the blind deblurring is carried out on a natural image, and the method comprises the following steps:
s1, inputting a fuzzy image y, wherein a fuzzy kernel is k, and a clear image to be solved is x;
s2, initializing an image x to be solved into a blurred image y, and initializing parameters lambda and sigma;
s3, solving a fuzzy kernel k from thick to thin by using a fuzzy kernel and image cross estimation method;
S4.non-blind deblurring is carried out on the blurred image y according to the blur kernel k calculated finally in the step3, and a clear image x is obtained (L) ；
S5, performing final treatment on the clear image to obtain a final clear image;
the step S3 specifically comprises the following steps:
(1) roughly estimating the fuzzy kernel as k (0) The method comprises the steps of carrying out a first treatment on the surface of the Initializing the number of times of non-blind deblurring to be l=0;
(2) from the above roughly estimated blur kernel k, the clear intermediate image is solved using the following equation 1:
wherein x(l) Representing the first
Clear image to be solved obtained after iterative solution, < +.>
Representing the minimum values x, u and g of the objective function, u and g are manually introduced auxiliary variables, and correspond to the structural image S and the image gradient ∈>
x (l-1) Represents the clear image to be solved after the first-1 iteration solution, k (l-1) Representing the blur kernel after the first-1 iteration solution, y representing the blurred image, x representing the convolution operation, +.>
Representing the square of the 2 norms +.>
Representing image x (l-1) Is used for the gradient of (a), I.I. | 0 Represents 0 norm, S (l-1) Represents x (l-1) λ, σ are regular term coefficients, μ, β are coefficients of the introduced variable, and β=2λσ, μ=2λ, +.>
Representing an image x (l-1) Is a relative total variation regularization term of (1), wherein D h (p)、D v (p) is the window total variation, L h (p)、L v (p) is the window inherent variation, p is a pixel point on the image, h and v represent the horizontal and vertical directions respectively, ε is a very small positive number, avoid denominator L h(p) and Lv (p) is 0;
(3) the sharp image x estimated from (2) (l) The blur kernel is solved directly with the following equation 2:
k (l) represented is the blur kernel obtained after the first solution,
representing the value of the minimum value k of the objective function, x (l) Clear image after first solving of representation, k (l-1) Represents the blur kernel after the first-1 solving, y represents the blurred image, x represents convolution operation,/and->
Representing the square of the 2 norms, gamma being the regularized term parameter;
(4) updating the value of lambda, judging whether L is smaller than the maximum cycle number L, updating l=l+1, repeating (2) and (3) to obtain the final fuzzy kernel k=k (L) ,l＝0。
2. The image blind deblurring combined sparse optimization method based on edge perception according to claim 1, wherein the l0+rtv regularization model constructed in step S3;
the regularization model based on significant edge priors and relative total variation of the image gradient L0 norms is as follows:
the method of the formula 3 is that,
/>
let u=s and,
when μ and β approach infinity, equation 3 changes to equation 4:
let the values of u, g approach zero, then calculate equation 5:
the sharp image x is obtained by the following equation 6:
wherein: f (&) and F -1 (. Cndot.) represents the fourier transform and the inverse fourier transform,
is a complex conjugate form of fourier transform, +.>
Differential operators representing horizontal and vertical directions, respectively;
setting a clear image x, and calculating values of u and g through formulas 7, 8 and 9 respectively:
then:
from the above formulas, u and g are calculated, and the clear intermediate image x at the first iteration is obtained in combination with formula 6 (l) 。
3. The edge-aware-based image blind deblurring combined sparse optimization method of claim 1, wherein the added RTV regularization term computes equation 10 for the structural image:
wherein ,
is the value of the minimum value S of the objective function, S is the structural image, I is the input image,
the pixel point difference values of the output image and the input image are summed to ensure the accuracy of the output structural image, wherein eta is a regularization parameterRegular term->
Is the relative total variation, D x (p)、D y (p) is the window total variation, specifically +.>
L x (p)、L y (p) is a window inherent variation which has no relation to the gradient direction, specifically +.>
g p,q Is a weight function defined according to the spatial correlation, wherein alpha controls the window scale, p is the central pixel point of the variation region R (p), q is any point epsilon, epsilon in the variation region R (p) S Is a very small positive number;
the specific calculation for the relative total variation term is as follows equation 11:
wherein equations 12 and 13 are respectively:
U xp representing that each pixel point combines gradient information in the field of the point, W xp The representation is related only to the gradient of the point; the expression in the y-direction is expressed as follows in formulas 14 and 15:
by splitting the relative total variation term, (10) is written in the following matrix form 16:
wherein ,Cx 、C y The toeplitz matrix obtained by approximating a discrete gradient operator by forward search is v S 、v I Vector representations of S and I, U x 、U y 、W x 、W y Is a diagonal matrix with a value of U on the diagonal x [i,i]＝u xi ，U y [i,i]＝u yi ，W x [i,i]＝w xi ，W y [i,i]＝w yi The method comprises the steps of carrying out a first treatment on the surface of the Equation 12 is calculated using the Euler-Lagrangian equation and the minimization problem is converted to linear problem equation 17:
where E is the identity matrix and where,
is based on the structural vector->
Calculated weight matrix, (E+ηL t ) Is a non-negatively symmetric Laplacian matrix;
the structural image S is obtained by a number of iterative calculations 12, 13, 14, 15, 17.
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