CN102567972B - Curvelet redundant dictionary based immune optimization image reconstruction - Google Patents
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Abstract
The invention discloses a curvelet redundant dictionary based immune optimization image reconstruction method, which solves the problem that the present 10-norm reconstruction technology acquires a reconstructed image with a poor visual effect, and is realized through the following steps: (1) clustering observation vectors; (2) initializing populations; (3) para-immunity optimizing; (4) reconstructing an initial image; (5) filtering and projecting onto convex sets; (6) judging whether or not the iteration number achieves the maximum value; (7) updating the sparsity; (8) updating the populations; (9) immune optimizing an image block; and (10) reconstructing the image. According to the invention, similar observation vectors are solved to obtain a common set of curvelet ground atoms by using the immune clone optimization technology, and then each observation vector is solved to obtain a set of curvelet ground atoms through combining the filtering and the projecting onto the convex sets. The curvelet redundant dictionary based immune optimization image reconstruction method eliminates the block effect in the reconstructed image, and obtains a reconstruction image with better visual effect.
Description
Technical Field
The invention belongs to the technical field of image processing, and further relates to an immune optimization image reconstruction method based on a Curvelet redundant dictionary in the fields of image reconstruction, image acquisition equipment development and the like. The method is used for obtaining high-quality clear images during image reconstruction, and can reduce hardware cost when being used in the field of image acquisition equipment development.
Background
In the field of compressed sensing image reconstruction, in order to solve sparse representation coefficients of image signals under a certain orthogonal basis dictionary or a certain transformation, a method of reconstructing the image signals from l is adopted0A method for solving a sparse representation coefficient approximation in a non-convex optimization problem in the norm sense. The currently common method is a greedy tracking algorithm, which approximates the original signal by selecting a locally optimal solution at each iteration.
Troppand et al in the document "J.Troppand, A.Gilbert' Signal recovery from random summary of the fact of being orthogonal in Matching the result of the search," IEEE trans. info. theory, vol.53, No.12, pp.4655-4666, Dec.2008 "propose to select from an overcomplete pool the atoms that best match the Signal structure and to achieve an approximation of the Signal by a series of stepwise increments. The method is based on the basic idea that atoms Gram-Schmidt are orthogonalized, then signals are projected on a space formed by the orthogonal atoms to obtain components and residual components of the signals on all selected atoms, and then sparse approximation of the signals is finally achieved through iterative processes of atom selection, residual updating and the like. The method has the defects that the characteristics of the signal, such as the characteristic of redundancy, and the blocking effect inherent in the block compression sensing are not considered, and a better reconstruction effect is difficult to obtain.
An image sparse decomposition algorithm based on one-dimensional fast Hartley transform and matching pursuit is disclosed in a patent application of southwest traffic university, namely an image sparse decomposition fast algorithm based on one-dimensional fast Hartley transform and matching pursuit (publication number: CN102148987A, application number: 201110088400.9, application date: 2011, 04, 11). The method comprises the steps of firstly constructing a core atom library, converting an original two-dimensional image into a one-dimensional real signal, sparsely decomposing atoms in the atom library into one-dimensional atoms, then realizing the cross-correlation operation of the image or the residual error of the image and the atoms by utilizing one-dimensional fast Hartley transform, searching the best atoms, and finally realizing the decomposition of the image. The patent uses one-dimensional fast Hartley transform, can carry out sparse decomposition on the image fast, and has better visual effect of the reconstructed image. The patent has the defects that the parameter lambda for controlling the balance between the reconstruction error and the signal sparsity has great influence on the whole solving process and the optimal solution, and the improper parameter can reduce the image decomposition speed and influence the image reconstruction effect.
In summary, although the method based on matching pursuit has a relatively fast running time, the intrinsic characteristics of the image signal are not considered, the prior art is not adaptive to the selection of the parameter λ, and to obtain the optimal solution, the appropriate parameter needs to be manually selected, which is troublesome for the whole solving process, and if the value of the parameter is not properly selected, the optimal solution is difficult to obtain.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides an immune optimization image reconstruction method based on a curvelet redundant dictionary, which avoids the problem of parameter lambda selection, considers the inherent structural characteristics of the image, and adds a filtering and convex projection method in the immune clone optimization learning technology, thereby finally improving the reconstruction quality of the image and obtaining a reconstructed image with better visual effect.
In order to achieve the purpose, the main idea of the invention is that the similarity between image sub-blocks is considered, firstly, a group of common Curvelet base atoms are solved for similar observation vectors by utilizing an immune clone optimization technology, and an initial image is reconstructed by using the common Curvelet base atoms; and then, according to the characteristics of the image, filtering and convex projection processing are carried out on the initial image, the processed image is used as priori knowledge, the sparsity of the image block is optimized and determined, then the follow-up solving of the optimal Curvelet base atom of the curve wave for a single observation vector is guided, and finally the better image reconstruction is realized.
The method comprises the following specific steps:
(1) clustering observation vectors
Similar observation vectors are gathered together by adopting an affine propagation clustering AP algorithm to the observation vectors of all image blocks sent by an image sender to obtain a plurality of categories of observation vectors;
(2) initializing a population
2a) Setting the sparsity values of all image blocks to be 32, and numbering all base atoms in the Curvelet redundant dictionary by positive integers;
2b) for each type of clustered observation vectors, randomly selecting the numbers of 32 Curvelet base atoms as antibody elements to obtain an antibody, and obtaining a plurality of antibodies as initial populations of image blocks corresponding to the type of observation vectors according to the method;
2c) obtaining initial populations of image blocks corresponding to all the types of observation vectors according to the step 2b) for all the types of observation vectors after clustering;
(3) immune-like optimization
3a) Multiplying each type of observation vector by a generalized inverse matrix of a Gaussian observation matrix to obtain a sparse representation coefficient vector of the image block corresponding to each type of observation vector;
3b) calculating the affinities of all antibodies in the initial population of the image block corresponding to each type of observation vector according to the following affinity function A:
wherein f isAIs the affinity value, i is the index of the observed vector, j is the total number of observed vectors in each class after clustering, yiIs the ith observation vector in the class, phi is a Gaussian observation matrix, psi is a Curvelet redundant dictionary, alphaiThe coefficient vectors are sparsely represented for image blocks corresponding to the ith observation vector in the class,
is the square of the vector two norm;
3c) sequencing the affinity values of all antibodies in the population from large to small, and sequentially performing cloning, mutation and selection operations on all the antibodies;
3d) taking the antibody with the highest affinity obtained by the selection operation as an optimal antibody, storing the optimal antibody, and storing the optimized population;
3e) processing the initial population of the image blocks corresponding to all the class observation vectors according to the steps 3a), 3b), 3c) and 3d) in sequence to obtain the optimal antibodies and the optimized population of the image blocks corresponding to all the class observation vectors;
(4) reconstructing an initial image
4a) Multiplying the sparse representation coefficient vector of the image block corresponding to each type of observation vector by the Curvelet base corresponding to the optimal antibody to obtain the image block corresponding to each type of observation vector;
4b) processing all the class observation vectors according to the step 4a) to obtain image blocks corresponding to all the class observation vectors;
4c) all the image blocks are spliced together to obtain a whole image;
(5) carrying out filtering and convex projection operation on the whole image to obtain the whole image subjected to filtering convex projection;
(6) judging whether the iteration times reach the maximum value, and if so, outputting the reconstructed whole image; otherwise, executing the step (7);
(7) updating sparsity
7a) Partitioning the whole image subjected to convex filtering projection to obtain a plurality of image blocks;
7b) adding the step length to the sparsity value of each image block to obtain an increased sparsity value;
7c) obtaining a group of Curvelet-based atoms of the curve waves and sparse representation coefficient vectors of the image blocks by using an Orthogonal Matching Pursuit (OMP) algorithm for the image blocks, and obtaining antibodies corresponding to the image blocks by using the numbers of the Curvelet-based atoms of the curve waves as antibody elements;
7d) calculating the affinity of the antibody corresponding to the image block by using an affinity function B;
7e) judging whether the affinity values of all antibodies in the population obtained in the step 3e) are smaller than the affinity values of the antibodies corresponding to the image blocks, if so, adding the step length to the original sparsity value to serve as a new sparsity value, and repeatedly executing the step 7c) and the step 7d) until the affinity value of at least one antibody in the population obtained in the step 3e) is larger than the affinity value of the antibody corresponding to the image block, and taking the sparsity value at the moment as the updated sparsity value of the image block; if not, subtracting the step length from the original sparsity value to serve as a new sparsity value, and repeatedly executing the step 7c) and the step 7d) until the affinity value of at least one antibody in the population obtained in the step 3e) is larger than that of the antibody corresponding to the image block, and taking the sparsity value at the moment as the updated sparsity value of the image block;
7f) processing all image blocks according to the step 7b), the step 7c), the step 7d) and the step 7e) to obtain updated sparsity values of all image blocks;
(8) updating populations
8a) Judging the magnitude relation between the updated sparsity value and the original sparsity value of each image block, if the updated sparsity value is larger than the original sparsity value, setting the lengths of all antibodies in the population as the updated sparsity value on the basis of the population obtained in the step 3e), randomly selecting the number of Curvelet base atoms as elements of an antibody addition part, and storing all new antibodies as the updated population; if the updated sparsity value of the image block is smaller than the original sparsity value, setting the lengths of all antibodies in the population as the updated sparsity value on the basis of the population obtained in the step 3e), and storing all new antibodies as the updated population; if the updated sparsity value of the image block is equal to the original sparsity value, keeping the population obtained in the step 3e) unchanged;
8b) processing all image blocks according to the step 8a) to obtain the updated population of all image blocks;
(9) image block immune optimization
9a) Calculating the affinity of all antibodies in the population after each image block is updated by using an affinity function B;
9b) sequencing affinity values of all antibodies in the population from large to small, sequentially performing cloning, mutation and selection operations on all the antibodies, and storing the mutated population;
9c) taking the antibody with the highest affinity obtained by the selection operation as an optimal antibody, and storing the optimal antibody;
9d) processing all image blocks according to the step 9a), the step 9b) and the step 9c) to obtain the optimized population of all the image blocks and the corresponding optimal antibody;
(10) reconstructing an image
10a) Multiplying the Curvelet base of the curve wave corresponding to the optimal antibody of each image block by the sparse representation coefficient vector obtained in the step 7c) to obtain a reconstructed image block;
10b) processing all image blocks according to the step 10a) to obtain all reconstructed image blocks;
10c) all the reconstructed image blocks are spliced together to obtain a reconstructed whole image;
10d) and (5) turning to the step.
Compared with the prior art, the invention has the following advantages:
1. the method considers the similarity among image subblocks, combines a filtering method and a convex projection method, solves a group of common Curvelet base atoms for similar observation vectors by utilizing an immune clone optimization technology, and reconstructs an initial image by using the common Curvelet base atoms, thereby overcoming the inherent blocking effect problem of the existing block compression sensing technology, eliminating the blocking effect in the reconstructed image and obtaining the reconstructed image with better visual effect.
2. The method converts the optimization problem under the zero norm meaning in the compressed sensing into the unconstrained problem, and separately processes the reconstruction error and the determined signal sparsity in the unconstrained problem, thereby avoiding the problem of selecting the parameter lambda for controlling the balance between the two parts, overcoming the problem that the parameter lambda influences the reconstruction quality in the prior reconstruction technology, improving the reconstruction quality of the image, and obtaining the reconstructed image with higher peak value signal-to-noise ratio.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of a Lena graph reconstructed by the orthogonal matching pursuit OMP method and the iterative hard threshold IHT method according to the present invention at a sampling rate of 25% respectively;
FIG. 3 is a graph comparing the trend of PSNR of the reconstructed peak signal-to-noise ratio (PSNR) of a Lena graph, a Barbara graph and an Elaine graph with the change of the sampling rate according to the orthogonal matching pursuit OMP method and the iterative hard threshold IHT method in the prior art;
fig. 4 is an analysis diagram of the influence of the parameter β for estimating the noise variance in the parameter maximum iteration number pmx and the BM3D filtering operation on the experimental result in the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1, the specific implementation steps of the present invention are as follows:
And clustering similar observation vectors of all image blocks sent by the image sender by adopting an affine propagation clustering AP algorithm to obtain a plurality of categories of observation vectors.
In the embodiment of the invention, a 512 × 512 image is divided into 16 × 16 image blocks to obtain 1024 image blocks; and storing all image blocks into column vectors by using matlab software in a computer, and multiplying the column vectors corresponding to all the image blocks by a Gaussian observation matrix to obtain 1024 observation vectors.
The affine propagation clustering AP algorithm comprises the following specific steps:
the method comprises the following steps of firstly, calculating Euclidean distances among observation vectors, storing negative values of the Euclidean distances in a similar matrix, and taking a column vector formed by median values of the similar matrix as a message matrix. The Euclidean distance formula is dij＝||xi-xj||2Wherein d isijIs the Euclidean distance value, x, of the ith observation vector and the jth observation vectoriFor the ith observation vector, xjFor the jth observation vector, | | | | | non-conducting phosphor2The two-norm vector is a two-norm vector, negative values of Euclidean distances are stored in a similar matrix, and a column vector formed by the median values of the similar matrix is used as a message matrix.
And step two, setting the moment when the iteration times reach the maximum value as an iteration termination condition. The maximum value of the iteration times in the embodiment of the invention is 100.
And thirdly, calculating the attraction degree and the attribution degree between the observation vectors by using the similarity matrix, and updating the message matrix. The calculation formulas of the attraction degree and the attribution degree are as follows:
where i, j, k, t is the index of the observation vector, R (i, j) is the attraction value of observation vector j to observation vector i, a (i, k) is the attribution value of observation vector i to observation vector k with an initial value of 0, S (i, k) is the similarity value of observation vector i and observation vector k, a (i, j) is the attribution value of observation vector i to observation vector j, R (t, j) is the attraction value of observation vector j to observation vector t.
And step four, judging whether iteration termination conditions are met, if so, executing the step five, otherwise, turning to the step three.
And fifthly, adding the attraction degree and the attribution degree of the observation vector, and taking the observation vector with the maximum sum as a clustering center.
Firstly, setting the sparsity values of all image blocks as 32, and numbering all base atoms in the Curvelet redundant dictionary by positive integers. In the embodiment of the invention, the Curvelet redundant dictionary has 3989 basic atoms, and 3989 basic atoms are numbered as 1, 2, 3 … … and 3989 respectively.
And secondly, randomly selecting the numbers of 32 Curvelet base atoms of each type of clustered observation vectors as antibody elements to obtain an antibody, and obtaining a plurality of antibodies as initial populations of image blocks corresponding to the type of observation vectors according to the method. In the present example, 10 antibodies were used as a population.
And thirdly, processing all the clustered observation vectors according to the second step to obtain the initial population of the image blocks corresponding to all the observation vectors.
And step one, multiplying each type of observation vector by a generalized inverse matrix of a Gaussian observation matrix to obtain a sparse representation coefficient vector of the image block corresponding to each type of observation vector. The embodiment of the invention obtains the generalized inverse matrix of the Gaussian observation matrix by matlab software in a computer.
Secondly, calculating the affinities of all antibodies in the initial population of the image block corresponding to each type of observation vector according to the following affinity function A:
wherein f isAIs the affinity value, i is the index of the observed vector, j is the total number of observed vectors in each class after clustering, yiIs the ith observation vector in the class, phi is a Gaussian observation matrix, psi is a Curvelet redundant dictionary, alphaiThe coefficient vectors are sparsely represented for image blocks corresponding to the ith observation vector in the class,
is the square of the vector two norm.
And thirdly, sequencing the affinity values of all antibodies in the population from large to small, and sequentially performing cloning, mutation and selection operations on all the antibodies.
The size of each antibody clone in the population was calculated according to the following formula:
wherein m isiIs the cloning scale of the ith antibody, C is a set value relating to the cloning scale, and is in the range of [20, ∞ ]]，f(ai) Is an antibody aiThe value of (a) is determined,is the sum of the affinity values of all antibodies in the population, and in the present example C is taken to be 15;
replicate m for each antibody in the populationiObtaining corresponding antibody groups;
first, clone size m was calculated for all antibodies in the populationiThen replicating the antibody miObtaining all antibodiesAntibody population after somatic cloning.
The specific steps of the mutation operation are as follows:
firstly, taking the value of the variation probability of each antibody group after antibody cloning as 0.2; secondly, taking a random number from 0 to 1 for each antibody element in the antibody group, if the random number is less than or equal to 0.2, replacing the antibody element with the random number, otherwise, keeping the antibody element unchanged; treating all antibody elements in the antibody group according to the method to obtain a mutated antibody group; and thirdly, performing mutation operation on the antibody groups obtained after all the antibody clones to obtain the antibody groups obtained after all the antibodies are mutated.
The specific steps of the selection operation are as follows:
the affinities of all antibodies in each antibody and its variant antibody population were calculated as follows:
wherein f isBIs the affinity value, yiIs the ith observation vector, phi is a Gaussian observation matrix, psi is a Curvelet redundant dictionary, alphaiThe coefficient vectors are sparsely represented for image blocks corresponding to the ith observation vector,
is the square of the vector two norm;
selecting the antibody with the highest affinity as the optimal antibody, and storing the optimal antibody;
and (3) calculating the affinity of all antibodies in the population and the variant antibody population, selecting the optimal antibody, and storing all the optimal antibodies to obtain a new population.
And fourthly, processing the initial population of the image blocks corresponding to all the observation vectors in the first step, the second step and the third step in sequence to obtain the optimal antibodies and the optimized population of the image blocks corresponding to all the observation vectors.
The method comprises the following steps of firstly, multiplying sparse representation coefficient vectors of image blocks corresponding to each type of observation vectors by curve wave Curvelet bases corresponding to optimal antibodies to obtain the image blocks corresponding to each type of observation vectors.
And secondly, processing all the class observation vectors according to the first step to obtain image blocks corresponding to all the class observation vectors.
And thirdly, all the image blocks are spliced together to obtain the whole image.
And 5, carrying out filtering and convex projection operation on the whole image to obtain the whole image subjected to filtering convex projection.
And step one, processing the whole image obtained in the step 4 by using a three-dimensional block matching BM3D filter to obtain a filtered image.
And secondly, blocking the filtered image to obtain a series of image blocks. In the embodiment of the invention, the whole image is divided into 16 × 16 image blocks to obtain 1024 image blocks.
Thirdly, performing convex projection operation on each image block according to the following formula:
wherein,for the k-th image block after convex projection, thetakIs the k-th image block, phiTIs the transpose of the Gaussian observation matrix, phi is the Gaussian observation matrix, ykAnd the observation vector corresponding to the k-th image block.
And fourthly, processing all the image blocks according to the third step to obtain all the image blocks after the convex projection.
And fifthly, splicing all the image blocks subjected to convex projection together to obtain the whole image subjected to convex projection.
Step 6, judging whether the iteration times reach the maximum value, and if so, outputting the reconstructed whole image; otherwise step 7 is performed. In the embodiment of the invention, the maximum value of the iteration times is 5.
Step 7, updating the sparsity
Firstly, the whole image after the convex filtering projection is divided into blocks to obtain a plurality of image blocks. In the embodiment of the invention, the whole image after convex filtering projection is divided into 16 × 16 image blocks to obtain 1024 image blocks.
And secondly, adding the step length to the sparsity value of each image block to obtain an increased sparsity value. In the embodiment of the present invention, the value of the step size is 4.
And thirdly, obtaining a group of Curvelet base atoms of the curve wave and sparse representation coefficient vectors of the image block by using an Orthogonal Matching Pursuit (OMP) algorithm for the image block, and obtaining an antibody corresponding to the image block by using the number of the Curvelet base atoms of the curve wave as an antibody element.
The orthogonal matching pursuit OMP algorithm comprises the following specific steps:
setting an image block as an initial residual signal, and setting the maximum number of atoms required to be selected in residual signal sparse decomposition as a value of image block sparsity;
multiplying each atom in the Curvelet redundant dictionary by the residual signal to obtain an inner product of each atom and the residual signal;
multiplying all atoms in the Curvelet redundant dictionary by the residual error signal respectively to obtain the inner products of all the atoms and the residual error signal;
selecting an atom with the largest inner product as an optimal atom, processing the optimal atom by adopting a Gram-Schmidt orthogonalization method, storing the orthogonalized optimal atom, and storing the largest inner product value;
subtracting the product of the orthonormalized optimal atom and the maximum inner product value from the residual signal to obtain a new residual signal;
judging whether the iteration times are larger than the maximum number of atoms required to be selected in signal sparse decomposition, if so, stopping iteration, and taking all maximum inner product values as vector elements to obtain sparse representation coefficient vectors of the image blocks; and otherwise, continuously calculating the inner product of each atom in the Curvelet redundant dictionary and the residual signal.
And fourthly, calculating the affinity of the antibody corresponding to the image block by using the affinity function B.
Step five, judging whether the affinity values of all antibodies in the population obtained in the step 3 are smaller than the affinity values of the antibodies corresponding to the image block, if so, adding 4 to the original sparseness value to serve as a new sparseness value, repeatedly executing the step three and the step four until the affinity value of at least one antibody in the population obtained in the step 3 is larger than the affinity value of the antibody corresponding to the image block, and taking the sparseness value at the moment as the sparseness value after the image block is updated; if not, subtracting 4 from the original sparsity value to be used as a new sparsity value, repeatedly executing the third step and the fourth step until the affinity value of at least one antibody in the population obtained in the step 3 is larger than that of the antibody corresponding to the image block, and using the sparsity value at the moment as the updated sparsity value of the image block.
And sixthly, processing all the image blocks according to the second step, the third step, the fourth step and the fifth step of the step to obtain updated sparsity values of all the image blocks.
Step one, judging the magnitude relation between the updated sparsity value of each image block and the original sparsity value, if the updated sparsity value is larger than the original sparsity value, setting the lengths of all antibodies in the population as the updated sparsity value on the basis of the population obtained in the step 3, randomly selecting the number of Curvelet base atoms as elements of an antibody addition part, and storing all new antibodies as the updated population; if the updated sparsity value of the image block is smaller than the original sparsity value, setting the lengths of all antibodies in the population as the updated sparsity value on the basis of the population obtained in the step 3, and storing all new antibodies as the updated population; and if the updated sparsity value of the image block is equal to the original sparsity value, keeping the population obtained in the step 3 unchanged.
And secondly, processing all the image blocks according to the first step to obtain the updated population of all the image blocks.
Step 9, image block immune optimization
In the first step, the affinity function B is used to calculate the affinity of all antibodies in the population updated for each image block.
And secondly, sequencing the affinity values of all antibodies in the population from large to small, sequentially cloning, mutating and selecting all the antibodies, and storing the mutated population.
And thirdly, taking the antibody with the highest affinity obtained by the selection operation as an optimal antibody, and storing the optimal antibody.
And fourthly, processing all the image blocks according to the first step, the second step and the third step to obtain the optimized population of all the image blocks and the corresponding optimal antibody.
Step 10, reconstructing the image
Step one, multiplying the curve wave Curvelet base corresponding to the optimal antibody of each image block by the sparse representation coefficient vector obtained in the step 7 to obtain a reconstructed image block.
And secondly, processing all image blocks according to the first step to obtain all reconstructed image blocks.
Thirdly, all the reconstructed image blocks are spliced together to obtain a reconstructed whole image.
And fourthly, turning to the step 5.
The effects of the present invention can be further illustrated by the following simulation experiments.
First experiment proves that the method has better reconstruction effect in visual effect than the orthogonal matching pursuit OMP method and the iterative hard threshold IHT method in the prior art. The experimental results are shown in fig. 2, in which fig. 2(a) is a standard Lena test chart original, fig. 2(b) is a reconstruction chart at a sampling rate of 25% in the present invention, fig. 2(c) is a reconstruction chart at a sampling rate of 25% in the orthogonal matching pursuit OMP method, and fig. 2(d) is a reconstruction chart at a sampling rate of 25% in the iterative hard threshold IHT method.
The image used in this experiment is a 512 x 512 standard test image Lena map. In the experiment, the size of an image block is 16 × 16, the population size n is 10, the variation probability is 0.2, the scale of the Curvelet redundant dictionary is 3989, and the maximum iteration number pmx is 5.
As can be seen from fig. 2, fig. 2(b) has no noise and no blocking effect, and it is clear that fig. 2(c) has significant noise and fig. 2(d) has significant blocking effect. Therefore, under the same sampling rate, the visual effect of the reconstructed image is better than that of the orthogonal matching pursuit OMP method and the iterative hard threshold IHT method.
Experiment II proves that the method has better reconstruction effect on peak signal-to-noise ratio (PSNR) than the Orthogonal Matching Pursuit (OMP) method and the iterative hard threshold IHT method in the prior art. The experimental result is shown in fig. 3, where fig. 3(a) is a trend comparison graph of peak signal-to-noise ratio PSNR of images reconstructed by Lena graph respectively using the method of the present invention, the orthogonal matching pursuit OMP method, and the iterative hard threshold IHT method as a function of the sampling rate, fig. 3(b) is a trend comparison graph of peak signal-to-noise ratio PSNR of images reconstructed by barbarbarbara graph respectively using the method of the present invention, the orthogonal matching pursuit OMP method, and the iterative hard threshold IHT method as a function of the sampling rate, and fig. 3(c) is a trend comparison graph of peak signal-to-noise ratio PSNR of images reconstructed by Elaine graph respectively using the method of the present invention, the orthogonal matching pursuit OMP method, and the iterative hard threshold ih.
The experiment used 512X 512 standard test images Lena, Barbara and Elaine. In the experiment, the parameter setting is the same as that in the experiment I, and the sparsity in the three methods is 32 under different sampling rates. The method, the orthogonal matching pursuit OMP method and the iterative hard threshold IHT method are used for respectively reconstructing a Lena image, a Barbara image and an Elaine image, and the peak signal-to-noise ratio PSNR of the reconstructed images is shown in the following table:
as can be seen from the table, under the same sampling rate, the peak signal-to-noise ratio (PSNR) of the reconstructed image is higher than that of the iterative hard threshold IHT method of the Orthogonal Matching Pursuit (OMP) method. As can be seen from fig. 3(a), 3(b) and 3(c), the peak signal-to-noise ratio PSNR of the reconstructed image according to the present invention varies with the sampling rate much higher than the other two curves for the same image. Therefore, no matter under what sampling rate, the method has better reconstruction effect on the peak signal-to-noise ratio (PSNR) than the Orthogonal Matching Pursuit (OMP) method and the iterative hard threshold IHT method in the prior art.
And thirdly, analyzing the influence of the parameter beta of the noise variance estimation and the maximum iteration number pmx on the reconstruction result in the three-dimensional block matching BM3D filtering operation. The experimental result is shown in fig. 4, where fig. 4(a) shows the variation trend of the peak signal-to-noise ratio PSNR of the Lena graph reconstructed by the present invention with the iteration number when the sampling rate is 50% and β is 1120, fig. 4(b) shows the variation trend of the peak signal-to-noise ratio PSNR of the Barbara graph and Lena graph reconstructed by the present invention with the parameter β when the sampling rate is 50% and the maximum iteration number pmx is 5, and fig. 4(c) shows the variation trend of the peak signal-to-noise ratio PSNR of the Lena graph reconstructed by the present invention with the parameter β when the sampling rate is 50% and 25% respectively and the maximum iteration number pmx is 5.
The invention estimates the noise variance eta when filtering with a three-dimensional block matching BM3D filtert＝α-t-βThe parameter β in (1) is a very important parameter, where ηtFor the estimated noise variance, α is a constant, which is taken as
β is a parameter related to the characteristics of the image itself. The maximum number of iterations pmx affects the speed of image reconstruction. The experiment was performed with a 512 x 512 standard test image Lena plot and Barbara plot for maximum iteration pmx and parameter β.
As can be seen from fig. 4(a), in the case that the parameter β for estimating the noise variance in the three-dimensional block matching BM3D filtering operation is fixed, as the number of iterations increases, the peak signal-to-noise ratio PSNR of the reconstructed image in the method of the present invention becomes higher and higher, when the iteration starts, the value of PSNR increases significantly, but when the number of iterations increases to 5, the value of PSNR increases very slowly, so that the maximum number of iterations pmx is taken as 5 in the experiment; as can be seen from fig. 4(b) and 4(c), under the condition that the maximum iteration number pmx is fixed, the parameter β for estimating the noise variance in the three-dimensional block matching BM3D filtering operation has a great influence on the reconstruction experimental result, the β value with the best reconstruction effect is different due to different images under the same sampling rate, and the β value with the best reconstruction effect is different due to different sampling rates of the same image, which means that the value of the parameter β is not only related to the characteristics of the image itself but also related to the sampling rate.
In conclusion, the immune optimization image reconstruction method based on the curvelet redundant dictionary can better reconstruct various natural images under different sampling rates, and compared with other existing methods, the reconstructed image has a good visual effect and high reconstruction quality.
Claims (8)
1. An immune optimization image reconstruction method based on a curvelet redundant dictionary comprises the following steps:
(1) clustering observation vectors
Similar observation vectors are gathered together by adopting an affine propagation clustering AP algorithm to the observation vectors of all image blocks sent by an image sender to obtain a plurality of categories of observation vectors;
(2) initializing a population
2a) Setting the sparsity values of all image blocks to be 32, and numbering all base atoms in the Curvelet redundant dictionary by positive integers;
2b) for each type of clustered observation vectors, randomly selecting the numbers of 32 Curvelet base atoms as antibody elements to obtain an antibody, and obtaining a plurality of antibodies as initial populations of image blocks corresponding to the type of observation vectors according to the method;
2c) obtaining initial populations of image blocks corresponding to all the types of observation vectors according to the step 2b) for all the types of observation vectors after clustering;
(3) immune-like optimization
3a) Multiplying each type of observation vector by a generalized inverse matrix of a Gaussian observation matrix to obtain a sparse representation coefficient vector of the image block corresponding to each type of observation vector;
3b) calculating the affinities of all antibodies in the initial population of the image block corresponding to each type of observation vector according to the following affinity function A:
wherein, fA is affinity value, i is label number of observation vector, j is total number of observation vector in each class after clustering, yiIs the ith observation vector in the class, phi is a Gaussian observation matrix, psi is a Curvelet redundant dictionary, alphaiAs the ith observation in the classThe sparse representation of the image block to which the vector corresponds is a coefficient vector,
is the square of the vector two norm;
3c) sequencing the affinity values of all antibodies in the population from large to small, and sequentially performing cloning, mutation and selection operations on all the antibodies;
3d) taking the antibody with the highest affinity obtained by the selection operation as an optimal antibody, storing the optimal antibody, and storing the optimized population;
3e) processing the initial population of the image blocks corresponding to all the class observation vectors according to the steps 3a), 3b), 3c) and 3d) in sequence to obtain the optimal antibodies and the optimized population of the image blocks corresponding to all the class observation vectors;
(4) reconstructing an initial image
4a) Multiplying the sparse representation coefficient vector of the image block corresponding to each type of observation vector by the Curvelet base corresponding to the optimal antibody to obtain the image block corresponding to each type of observation vector;
4b) processing all the class observation vectors according to the step 4a) to obtain image blocks corresponding to all the class observation vectors;
4c) all the image blocks are spliced together to obtain a whole image;
(5) carrying out filtering and convex projection operation on the whole image to obtain the whole image subjected to filtering convex projection;
(6) judging whether the iteration times reach the maximum value, and if so, outputting the reconstructed whole image; otherwise, executing the step (7);
(7) updating sparsity
7a) Partitioning the whole image subjected to convex filtering projection to obtain a plurality of image blocks;
7b) adding the step length to the sparsity value of each image block to obtain an increased sparsity value;
7c) obtaining a group of Curvelet-based atoms of the curve waves and sparse representation coefficient vectors of the image blocks by using an Orthogonal Matching Pursuit (OMP) algorithm for the image blocks, and obtaining antibodies corresponding to the image blocks by using the numbers of the Curvelet-based atoms of the curve waves as antibody elements;
7d) calculating the affinity of the antibody corresponding to the image block by using an affinity function B;
7e) judging whether the affinity values of all antibodies in the population obtained in the step 3e) are smaller than the affinity values of the antibodies corresponding to the image blocks, if so, adding the step length to the original sparsity value to serve as a new sparsity value, and repeatedly executing the step 7c) and the step 7d) until the affinity value of at least one antibody in the population obtained in the step 3e) is larger than the affinity value of the antibody corresponding to the image block, and taking the sparsity value at the moment as the updated sparsity value of the image block; if not, subtracting the step length from the original sparsity value to serve as a new sparsity value, and repeatedly executing the step 7c) and the step 7d) until the affinity value of at least one antibody in the population obtained in the step 3e) is larger than that of the antibody corresponding to the image block, and taking the sparsity value at the moment as the updated sparsity value of the image block;
7f) processing all image blocks according to the step 7b), the step 7c), the step 7d) and the step 7e) to obtain updated sparsity values of all image blocks;
(8) updating populations
8a) Judging the magnitude relation between the updated sparsity value and the original sparsity value of each image block, if the updated sparsity value is larger than the original sparsity value, setting the lengths of all antibodies in the population as the updated sparsity value on the basis of the population obtained in the step 3e), randomly selecting the number of Curvelet base atoms as elements of an antibody addition part, and storing all new antibodies as the updated population; if the updated sparsity value of the image block is smaller than the original sparsity value, setting the lengths of all antibodies in the population as the updated sparsity value on the basis of the population obtained in the step 3e), and storing all new antibodies as the updated population; if the updated sparsity value of the image block is equal to the original sparsity value, keeping the population obtained in the step 3e) unchanged;
8b) processing all image blocks according to the step 8a) to obtain the updated population of all image blocks;
(9) image block immune optimization
9a) Calculating the affinity of all antibodies in the population after each image block is updated by using an affinity function B;
9b) sequencing affinity values of all antibodies in the population from large to small, sequentially performing cloning, mutation and selection operations on all the antibodies, and storing the mutated population;
9c) taking the antibody with the highest affinity obtained by the selection operation as an optimal antibody, and storing the optimal antibody;
9d) processing all image blocks according to the step 9a), the step 9b) and the step 9c) to obtain the optimized population of all the image blocks and the corresponding optimal antibody;
(10) reconstructing an image
10a) Multiplying the Curvelet base of the curve wave corresponding to the optimal antibody of each image block by the sparse representation coefficient vector obtained in the step 7c) to obtain a reconstructed image block;
10b) processing all image blocks according to the step 10a) to obtain all reconstructed image blocks;
10c) all the reconstructed image blocks are spliced together to obtain a reconstructed whole image;
10d) and (5) turning to the step.
2. The curvilinear wave redundant dictionary-based immune optimization image reconstruction method according to claim 1, wherein the affine propagation clustering AP algorithm in the step (1) comprises the following steps:
the method comprises the following steps of firstly, calculating Euclidean distances among observation vectors, storing negative values of the Euclidean distances in a similar matrix, and taking a column vector formed by median values of the similar matrix as a message matrix;
step two, setting the moment when the iteration times reach the maximum value as an iteration termination condition;
thirdly, calculating the attraction degree and the attribution degree between the observation vectors by using the similarity matrix, and updating the message matrix;
step four, judging whether iteration termination conditions are met, if so, executing the step five, otherwise, turning to the step three;
and fifthly, adding the attraction degree and the attribution degree of the observation vector, and taking the maximum observation vector of the sum as a clustering center.
3. The curvilinear wave redundant dictionary-based immune optimization image reconstruction method according to claim 1, wherein the cloning operation in step 3c) and step 9b) comprises the following specific steps:
in the first step, the size of each antibody clone in the population is calculated according to the following formula:
wherein m isiIs the cloning scale of the i-th antibody, C is a set value relating to the cloning scale, and is in the range of [20, + ∞ ], f (a)i) Is an antibody aiThe value of (a) is determined,
is the sum of the affinity values of all antibodies in the population;
second, replicate m for each antibody in the populationiObtaining corresponding antibody groups;
and step three, processing all antibodies in the population according to the step one and the step two to obtain the antibody population after all antibodies are cloned.
4. The method for reconstructing an immune optimized image based on a curvelet redundant dictionary as claimed in claim 1, wherein the mutation operations in step 3c) and step 9b) are as follows:
firstly, taking the value of the variation probability of each antibody group after antibody cloning as 0.2;
secondly, taking a random number from 0 to 1 for each antibody element in the antibody group, if the random number is less than or equal to 0.2, replacing the antibody element with the random number, otherwise, keeping the antibody element unchanged;
thirdly, processing all antibody elements in the antibody group according to the second step to obtain a mutated antibody group;
and step four, processing all antibody groups subjected to antibody cloning according to the steps of the first step, the second step and the third step to obtain all antibody groups subjected to antibody variation.
5. The curvilinear wave redundant dictionary-based immune optimization image reconstruction method according to claim 1, wherein the specific steps of the selection operation in step 3c) and step 9b) are as follows:
in the first step, the affinities of all antibodies in each antibody and its variant antibody population are calculated according to the following affinity function B:
wherein f isBIs the affinity value, yiFor the ith observation vector, phi is GaussMeasuring matrix, psi is Curvelet redundant dictionary, alphaiThe coefficient vectors are sparsely represented for image blocks corresponding to the ith observation vector,
is the square of the vector two norm;
secondly, selecting an antibody with the highest affinity as an optimal antibody, and storing the optimal antibody;
and thirdly, processing all antibodies in the population and the variant antibody population according to the first step and the second step, and storing all optimal antibodies to obtain a new population.
6. The method for reconstructing an immune optimized image based on a curvelet redundant dictionary as claimed in claim 1, wherein the step (5) of performing filtering and convex projection operation comprises the following specific steps:
step one, processing the image obtained in the step 4c) by using a three-dimensional block matching BM3D filter to obtain a filtered image;
secondly, blocking the filtered image to obtain a series of image blocks;
thirdly, performing convex projection operation on each image block according to the following formula:
wherein,
for the k-th image block after convex projection, thetakIs the kth image block, phiTIs the transpose of the Gaussian observation matrix, [ phi ] is the Gaussian observation matrix, ykAn observation vector corresponding to the kth image block;
fourthly, processing all the image blocks according to the third step to obtain all the image blocks after convex projection;
and fifthly, splicing all the image blocks subjected to convex projection together to obtain the whole image subjected to convex projection.
7. The curvilinear wave redundant dictionary-based immune optimization image reconstruction method according to claim 1, wherein the step length in step 7b) is a positive integer between 1 and 100.
8. The curvilinear wave redundant dictionary-based immune optimization image reconstruction method according to claim 1, wherein the orthogonal matching pursuit OMP algorithm of step 7c) comprises the following specific steps:
firstly, setting an image block as an initial residual signal, and setting the maximum number of atoms required to be selected in residual signal sparse decomposition as a value of image block sparsity;
step two, multiplying each atom in the Curvelet redundant dictionary by the residual signal to obtain an inner product of each atom and the residual signal;
thirdly, processing all atoms in the Curvelet redundant dictionary according to the second step to obtain inner products of all atoms and residual signals;
fourthly, selecting the atom with the largest inner product as the optimal atom, processing the optimal atom by adopting a Gram-Schmidt orthogonalization method, storing the orthogonalized optimal atom, and storing the largest inner product value;
fifthly, subtracting the product of the orthonormalized optimal atom and the maximum inner product value from the residual signal to obtain a new residual signal;
sixthly, judging whether the iteration times are larger than the maximum number of atoms required to be selected in signal sparse decomposition, if so, stopping iteration, and taking all maximum inner product values as vector elements to obtain sparse representation coefficient vectors of the image blocks; otherwise, go to the second step.
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