CN102567972A - Curvelet redundant dictionary based immune optimization image reconstruction - Google Patents
Curvelet redundant dictionary based immune optimization image reconstruction Download PDFInfo
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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 technical field of image processing, further relate to the immune optimization image reconstructing method in the fields such as image reconstruction, image capture device exploitation based on curve ripple Curvelet redundant dictionary.The present invention is used for when image reconstruction, obtaining high-quality distinct image, is used for the image capture device development field and can reduces hardware cost.
Background technology
In compressed sensing image reconstruction field, in order to find the solution the rarefaction representation coefficient of picture signal under certain orthogonal basis dictionary or certain conversion, and adopt from l
0Find the solution the method for rarefaction representation coefficient approximate value in the non-protruding optimization problem under the norm meaning.Method commonly used at present has greedy tracing algorithm, selects a locally optimal solution to approach original signal during through each iteration.
People such as J.Troppand are at document " J.Troppand; A.Gilbert ' Signal recovery from random measurements via orthogonal Matching pursuit; ' IEEE Trans.Info.Theory, vol.53, no.12; pp.4655-4666, Dec.2008 " in propose from over-complete dictionary of atoms, to select atom that can the matched signal structure and realize approaching of signal through a series of progressively increasing progressively.Its basic thought is with atom Gram-Schmidt orthogonalization process; Again with signal projection on the space of these quadrature atomic buildings; Obtain signal and selected component and remaining component on the atom at each; Through iterative process such as atom selection and remaining renewals, realize that finally the sparse of signal approaches then.The deficiency that this method exists is, do not consider the characteristics that signal itself has, and like this characteristic of redundancy, the intrinsic blocking effect of piece compressed sensing itself also is difficult to obtain reconstruct effect preferably in addition.
The patented claim of Southwest Jiaotong University " image sparse based on quick hartley transform of one dimension and match tracing decomposes fast algorithm " (publication number: CN102148987A; Application number: 201110088400.9, applying date: on 04 11st, 2011) a kind of image sparse decomposition algorithm based on quick hartley transform of one dimension and match tracing is disclosed in.This method has at first been constructed the former word bank of core; With the original two dimensional image transitions is the one dimension real signal; Atom in the former word bank of Sparse Decomposition converts one dimensional atom into; Utilize the quick hartley transform of one dimension to realize image or the residual error of image and the computing cross-correlation of atom then, seek best atom, finally realize the decomposition of image.This patent can carry out Sparse Decomposition to image apace, and the reconstructed image visual effect is better because used the quick hartley transform of one dimension.The deficiency that this patent exists is, the parameter lambda of balance is very big to the influence of whole solution procedure and optimum solution between control reconstructed error and the signal degree of rarefication, and unsuitable parameter can reduce picture breakdown speed, influences the image reconstruction effect.
In sum, though very fast based on method ratio working time of match tracing, do not consider the characteristic that picture signal itself is intrinsic; Prior art is not adaptive to choosing of parameter lambda; Obtain optimum solution, need manually choose parameter compatibly, this is pretty troublesome to whole solution procedure; If the value of parameter is chosen words irrelevantly, be difficult to obtain optimum solution.
Summary of the invention
The present invention is directed to the problem of above-mentioned prior art; A kind of immune optimization image reconstructing method based on curve ripple redundant dictionary has been proposed; Avoided selecting the problem of parameter lambda, considered the intrinsic design feature of image itself, optimized the method that adds filtering and protruding projection in the learning art at immune clone; Finally improve the reconstruction quality of image, obtained visual effect reconstructed image preferably.
For realizing above-mentioned purpose; Main thought of the present invention is; Consider the similarity between the image subblock, at first utilize the immune clone optimisation technique that similar observation vector is found the solution one group of common curve ripple Curvelet base atom, reconstruct initial pictures with common curve ripple Curvelet base atom; Then according to the characteristics of image self; This initial pictures is carried out filtering, protruding projection process; With the image after handling as priori; Optimize to confirm the degree of rarefication of image block, and then instruct and follow-up single observation vector is found the solution optimum curve ripple Curvelet base atom, finally realize reconstructed image better.
Concrete steps of the present invention are following:
(1) observation vector is carried out cluster
The observation vector of all images piece that the transmit leg of image is sent adopts affine propagation clustering AP algorithm that similar observation vector is got together, and obtains the observation vector of a plurality of classifications;
(2) initialization population
2a) the degree of rarefication value with all images piece is set at 32, and all the basic atoms in the curve ripple Curvelet redundant dictionary are numbered with positive integer;
2b) to each type observation vector after the cluster, the numbering of 32 curve ripples of picked at random Curvelet base atom obtains an antibody as the antibody element, according to said method obtains the initial population of a plurality of antibody as the corresponding image block of such observation vector;
2c) to all types observation vector after the cluster, according to step 2b) obtain the initial population of the corresponding image block of all types observation vector;
(3) para-immunity optimization
3a) each type of usefulness observation vector multiply by the generalized inverse matrix of Gauss's observing matrix, obtains the rarefaction representation coefficient vector of the corresponding image block of each type observation vector;
3b) calculate the affinity of all antibody in the initial population of the corresponding image block of each type observation vector according to following affinity function A:
Wherein, f
ABe the affinity value, i is the label of observation vector, and j is the sum of observation vector in each type after the cluster, y
iBe i observation vector in the class, Φ is Gauss's observing matrix, and Ψ is a curve ripple Curvelet redundant dictionary, α
iBe the rarefaction representation coefficient vector of the image block of i observation vector correspondence in the class,
Be vectorial two norms square;
3c) value to the affinity of all antibody in the population sorts from big to small, successively all antibody is carried out the clone, variation, selection operation;
The highest antibody of the affinity that 3d) selection operation is obtained is preserved optimum antibody as optimum antibody, preserves the population after optimizing;
3e) to the initial population of the corresponding image block of all types observation vector successively according to step 3a), step 3b), step 3c), step 3d) handle, the optimum antibody that obtains the corresponding image block of all types observation vector with optimize after population;
(4) reconstruct initial pictures
4a) the rarefaction representation coefficient vector curve ripple Curvelet base corresponding with optimum antibody of the image block that each type observation vector is corresponding multiplies each other, and obtains the corresponding image block of each type observation vector;
4b) with all types observation vector according to step 4a) handle, obtain the corresponding image block of all types observation vector;
4c) all images piece is stitched together obtains entire image;
(5) entire image is carried out filtering, protruding projection operation, obtain the entire image after the protruding projection of filtering;
(6) judge whether iterations reaches maximal value,, then export the entire image after the reconstruct if satisfy; Otherwise execution in step (7);
(7) upgrade degree of rarefication
7a) entire image after the protruding projection of filtering is carried out piecemeal, obtain a plurality of image blocks;
7b) the degree of rarefication value with each image block adds the degree of rarefication value after step-length obtains increasing;
7c) image block is obtained the rarefaction representation coefficient vector of sets of curves ripple Curvelet base atom and image block with orthogonal matching pursuit OMP algorithm, the numbering of curve ripple Curvelet base atom as the antibody element, is obtained the antibody of image block correspondence;
7d) with the affinity of the corresponding antibody of affinity function B computed image piece;
7e) determining step 3e) in the gained population affinity value of all antibody whether less than the affinity value of the corresponding antibody of image block; If; Then former degree of rarefication value is added that step-length is as new degree of rarefication value, repeated execution of steps 7c), step 7d); Up to step 3e) have the affinity value of the affinity value of an antibody in the gained population at least, the degree of rarefication value after the degree of rarefication value of this moment is upgraded as image block greater than the corresponding antibody of image block; If not; Then former degree of rarefication value is deducted step-length as new degree of rarefication value; Repeated execution of steps 7c); Step 7d), up to step 3e) have the affinity value of the affinity value of an antibody at least, the degree of rarefication value after the degree of rarefication value of this moment is upgraded as image block in the gained population greater than the corresponding antibody of image block;
7f) with all images piece according to step 7b), step 7c), step 7d), step 7e) handle the degree of rarefication value after obtaining all images piece and upgrading;
(8) new population more
8a) judge degree of rarefication value and the magnitude relationship of former degree of rarefication value after each image block upgrades; If the degree of rarefication value after upgrading is greater than former degree of rarefication value; Then at step 3e) degree of rarefication value after the length of all antibody is set to upgrade in the population on the basis of gained population; The numbering of choosing curve ripple Curvelet base atom randomly increases element partly as antibody, preserves all new antibodies as the population after upgrading; If the degree of rarefication value after image block upgrades is less than former degree of rarefication value, then at step 3e) degree of rarefication value after the length of all antibody is set to upgrade in the population on the basis of gained population, preserve all new antibodies as the population after upgrading; If the degree of rarefication value after image block upgrades equals former degree of rarefication value, then keeping step 3e) the gained population is constant;
8b) to all images piece according to step 8a) handle the population after obtaining all images piece and upgrading;
(9) image block immune optimization
9a) calculate the affinity of all antibody in the population after each image block upgrades with affinity function B;
9b) value to the affinity of all antibody in the population sorts from big to small, successively all antibody is carried out the clone, variation, and selection operation is preserved the population after the variation;
The highest antibody of the affinity that 9c) selection operation is obtained is preserved optimum antibody as optimum antibody;
9d) to all image blocks according to step 9a), step 9b), step 9c) handle population and corresponding optimum antibody after obtaining all images piece and optimizing;
(10) reconstructed image
10a) curve ripple Curvelet base and step 7c that the optimum antibody of each image block is corresponding) the rarefaction representation coefficient vector that obtains multiplies each other, and obtains the image block after the reconstruct;
10b) with all images piece according to step 10a) handle, obtain the image block after all reconstruct;
10c) image block after all reconstruct is stitched together obtains the entire image after the reconstruct;
10d) go to step (5).
The present invention compared with prior art has the following advantages:
1. the present invention has considered the similarity between the image subblock; Method in conjunction with filtering and protruding projection; Utilize the immune clone optimisation technique that similar observation vector is found the solution one group of common curve ripple Curvelet base atom, reconstruct initial pictures, overcome the intrinsic blocking effect problem of existing piece compressed sensing technology with common curve ripple Curvelet base atom; Make the present invention eliminate the blocking effect in the reconstructed image, can obtain visual effect reconstructed image preferably.
2. the present invention is converted into unconstrained problem with the optimization problem under the zero norm meaning in the compressed sensing; And the reconstructed error in the unconstrained problem and definite signal degree of rarefication two parts separately handled; Avoided selecting the problem of the parameter lambda of balance between control two parts; Having overcome existing reconfiguration technique parameter lambda influences the problem of reconstruction quality, makes the present invention improve the reconstruction quality of image, can obtain the higher reconstructed image of Y-PSNR.
Description of drawings
Fig. 1 is a process flow diagram of the present invention;
Fig. 2 is that orthogonal matching pursuit OMP method, the iteration hard-threshold IHT method of the present invention and prior art schemed the restructuring graph under 25% sampling rate to Lena respectively;
Fig. 3 is the orthogonal matching pursuit OMP method of the present invention and prior art, the trend comparison diagram that iteration hard-threshold IHT method changes with sampling rate the reconstruct Y-PSNR PSNR that Lena schemes, Barbara schemes, Elaine schemes respectively;
Fig. 4 be among the present invention in parameter maximum iteration time pmx and the BM3D filtering operation parameter beta of estimating noise variance to the analysis chart of experimental result influence.
Embodiment
Below in conjunction with accompanying drawing the present invention is done and to further describe.
With reference to Fig. 1, practical implementation step of the present invention is following:
The observation vector of all images piece that the transmit leg of image is sent adopts affine propagation clustering AP algorithm that similar observation vector is got together, and obtains the observation vector of a plurality of classifications.
In the embodiment of the invention, the image with 512 * 512 is divided into 16 * 16 image block, obtains 1024 image blocks; In computing machine, with matlab software all images piece is preserved into column vector, the column vector that all images piece is corresponding multiply by Gauss's observing matrix, obtains 1024 observation vectors.
The concrete steps of affine propagation clustering AP algorithm are:
The first step is calculated the Euclidean distance between each observation vector, and its negative value is existed in the similar matrix, and the column vector that the intermediate value of similar matrix is formed is as message matrix.The Euclidean distance formula is d
Ij=|| x
i-x
j||
2, d wherein
IjBe the Euclidean distance value of i observation vector and j observation vector, x
iBe i observation vector, x
jBe j observation vector, || ||
2Be two norms of vector, the negative value of Euclidean distance existed in the similar matrix that the column vector that the intermediate value of similar matrix is formed is as message matrix.
In second step, iterations reaches the peaked moment and is set to stopping criterion for iteration.The maximal value of iterations gets 100 in the embodiment of the invention.
In the 3rd step, utilize Attraction Degree and degree of membership between the similarity matrix calculating observation vector, the updating message matrix.The computing formula of Attraction Degree and degree of membership is as follows:
Wherein, i, j, k; T is the label of observation vector, and (i j) is the Attraction Degree value of observation vector j to observation vector i, A (i to R; K) be the degree of membership value of observation vector i to observation vector k, its initial value is 0, and (i k) is the similarity value of observation vector i and observation vector k to S; (i j) is the degree of membership value of observation vector i to observation vector j to A, and (t, j) observation vector j is to the Attraction Degree value of observation vector t for R.
The 4th step judged whether to satisfy stopping criterion for iteration, if satisfy, then carried out the 5th step of this step, otherwise forwarded the 3rd step of this step to.
The 5th the step, with Attraction Degree and the degree of membership addition of observation vector, get its with the maximum observation vector as cluster centre.
The first step is set at 32 with the degree of rarefication value of all images piece, and all the basic atoms in the curve ripple Curvelet redundant dictionary are numbered with positive integer.In the embodiment of the invention, in the curve ripple Curvelet redundant dictionary 3989 basic atoms are arranged, 3989 basic atoms are numbered 1,2,3 respectively ..., 3989.
In second step, to each type observation vector after the cluster, the numbering of 32 curve ripples of picked at random Curvelet base atom obtains an antibody as the antibody element, according to said method obtains the initial population of a plurality of antibody as the corresponding image block of such observation vector.Among this clearly demarcated embodiment with 10 antibody as a population.
The 3rd step, to all types observation vector after the cluster, handle according to this step second step, obtain the initial population of the corresponding image block of all types observation vector.
The first step, each type of usefulness observation vector multiply by the generalized inverse matrix of Gauss's observing matrix, obtains the rarefaction representation coefficient vector of the corresponding image block of each type observation vector.The embodiment of the invention is the generalized inverse matrix that in computing machine, obtains Gauss's observing matrix with matlab software.
In second step, calculate the affinity of all antibody in the initial population of the corresponding image block of each type observation vector according to following affinity function A:
Wherein, f
ABe the affinity value, i is the label of observation vector, and j is the sum of observation vector in each type after the cluster, y
iBe i observation vector in the class, Φ is Gauss's observing matrix, and Ψ is a curve ripple Curvelet redundant dictionary, α
iBe the rarefaction representation coefficient vector of the image block of i observation vector correspondence in the class,
Be vectorial two norms square.
The 3rd step, the value of the affinity of all antibody in the population is sorted from big to small, successively all antibody are carried out the clone, variation, selection operation.
Calculate the scale of each antibody cloning in the population according to formula:
Wherein, m
iBe clone's scale value of i antibody, C is the setting value relevant with clone's scale, and span is [20, ∞], f (a
i) be antibody a
iThe affinity value,
Be all antibody in the population the affinity value with, C gets 15 in embodiments of the present invention;
Each antibody in the population duplicates m
iIndividual, obtain the corresponding antibody crowd;
All antibody in the population are all calculated clone's scale m earlier
i, again antibody is duplicated m
iIndividual, obtain the antibody population behind all antibody clonings.
The concrete steps of mutation operation are following:
At first, to the antibody population behind each antibody cloning, the value of getting its variation probability is 0.2; Secondly, each antibody element among the antagonist crowd is got a random number from 0 to 1, if random number smaller or equal to 0.2, then replaces the antibody element with random number, otherwise keeps the antibody element constant; All antibody elements are handled according to the method among the antagonist crowd, the antibody population after obtaining making a variation; Once more, the antibody population behind all antibody clonings is carried out mutation operation, obtain the antibody population behind all antibody variations.
The concrete steps of selection operation are following:
Affinity according to all antibody in the antibody population after following affinity function B each antibody of calculating and the variation thereof:
Wherein, f
BBe affinity value, y
iBe i observation vector, Φ is Gauss's observing matrix, and Ψ is a curve ripple Curvelet redundant dictionary, α
iBe the rarefaction representation coefficient vector of the corresponding image block of i observation vector,
Be vectorial two norms square;
Select the highest antibody of affinity as optimum antibody, preserve optimum antibody;
Antibody population to after all antibody in the population and the variation thereof all calculates affinity earlier, selects optimum antibody again, preserves all optimum antibody and obtains new population.
In the 4th step, successively according to this step first step, in second step, the 3rd step handled to the initial population of the corresponding image block of all types observation vector, the optimum antibody that obtains the corresponding image block of all types observation vector with optimize after population.
The first step, the rarefaction representation coefficient vector curve ripple Curvelet base corresponding with optimum antibody of the image block that each type observation vector is corresponding multiplies each other, and obtains the corresponding image block of each type observation vector.
Second step, all types observation vector is handled according to this step first step, obtain the corresponding image block of all types observation vector.
The 3rd goes on foot, and all images piece is stitched together obtains entire image.
The first step is mated the BM3D filter process to the entire image that step 4 obtains with three-dimensional bits, obtains filtered image.
Second step, filtered image is carried out piecemeal, obtain a series of image block.In the embodiment of the invention entire image is divided into 16 * 16 image block, obtains 1024 image blocks.
In the 3rd step, each image block is carried out protruding projection operation according to formula:
Wherein,
Be k image block after the protruding projection, θ
kBe k image block, Φ
TBe the transposed matrix of Gauss's observing matrix, Φ is Gauss's observing matrix, y
kIt is the corresponding observation vector of k image block.
The 4th step, all image blocks were handled according to this step the 3rd step, obtain the image block after all protruding projections.
In the 5th step, the image block after all protruding projections is pieced together the entire image that obtains together after the protruding projection.
Step 6 judges whether iterations reaches maximal value, if satisfy, then exports the entire image after the reconstruct; Otherwise execution in step 7.The iterations maximal value gets 5 in the embodiment of the invention.
Step 7 is upgraded degree of rarefication
The first step is carried out piecemeal to the entire image after the protruding projection of filtering, obtains a plurality of image blocks.In the embodiment of the invention, be divided into 16 * 16 image block to the entire image after the protruding projection of filtering, obtain 1024 image blocks.
In second step, the degree of rarefication value of each image block is added the degree of rarefication value after step-length obtains increasing.The value of step-length gets 4 in the embodiment of the invention.
The 3rd step obtained the rarefaction representation coefficient vector of sets of curves ripple Curvelet base atom and image block to image block with orthogonal matching pursuit OMP algorithm, and the numbering of the basic atom of curve ripple Curvelet as the antibody element, is obtained the antibody of image block correspondence.
Wherein, the concrete steps of orthogonal matching pursuit OMP algorithm are following:
Image block is set to initial residual signals, and the maximum atom number that the residue signal Sparse Decomposition need be chosen is set to the value of image block degree of rarefication;
Each atom and residual signals in the curve ripple Curvelet redundant dictionary are multiplied each other, obtain the inner product of each atom and residual signals;
All atoms in the curve ripple Curvelet redundant dictionary are multiplied each other with residual signals respectively, obtain the inner product of all atoms and residual signals;
Select the maximum atom of inner product as best atom, adopt the Gram-Schmidt orthogonalization method that best atom is handled, the best atom after the preservation orthogonalization is preserved the maximum inner product value;
Deduct best atom and the product of maximum inner product value after the orthogonalization with residual signals, obtain new residual signals;
Judge the maximum atom number whether iterations need be chosen greater than the signal Sparse Decomposition,, then stop iteration, all maximum inner product values as vector element, are obtained the rarefaction representation coefficient vector of image block if satisfy; Otherwise the inner product of each atom and residual signals in the continuation calculated curve ripple Curvelet redundant dictionary.
The 4th step is with the affinity of the corresponding antibody of affinity function B computed image piece.
The 5th step; Whether the affinity value of all antibody is less than the affinity value of the corresponding antibody of image block, if then former degree of rarefication value is added 4 as new degree of rarefication value in the determining step 3 gained populations; Repeat the 3rd step of this step; The 4th step had the affinity value of the affinity value of an antibody greater than the corresponding antibody of image block at least in step 3 gained population, the degree of rarefication value after the degree of rarefication value of this moment is upgraded as image block; If not; Then former degree of rarefication value is deducted 4 as new degree of rarefication value; Repeat the 3rd step of this step; The 4th step had the affinity value of the affinity value of an antibody greater than the corresponding antibody of image block at least in step 3 gained population, the degree of rarefication value after the degree of rarefication value of this moment is upgraded as image block.
In the 6th step, according to second step of this step, in the 3rd step, in the 4th step, the 5th step handled, and obtained the degree of rarefication value after all images piece upgrades with all images piece.
Step 8, more new population
The first step; Judge degree of rarefication value and the magnitude relationship of former degree of rarefication value after each image block upgrades; If the degree of rarefication value after upgrading is greater than former degree of rarefication value; Degree of rarefication value after then the length of all antibody is set to upgrade in the population on the basis of step 3 gained population, the numbering of choosing curve ripple Curvelet base atom randomly increases element partly as antibody, preserves all new antibodies as the population after upgrading; If the degree of rarefication value after image block upgrades is less than former degree of rarefication value, the degree of rarefication value after then the length of all antibody is set to upgrade in the population on the basis of step 3 gained population is preserved all new antibodies as the population after upgrading; If the degree of rarefication value after image block upgrades equals former degree of rarefication value, then keep step 3 gained population constant.
Second step, all images piece is handled according to this step first step, obtain the population after all images piece upgrades.
Step 9, the image block immune optimization
The first step is with the affinity of all antibody in the population after each image block renewal of affinity function B calculating.
Second step, the value of the affinity of all antibody in the population is sorted from big to small, successively all antibody are carried out the clone, variation, selection operation is preserved the population after the variation.
In the 3rd step, the highest antibody of the affinity that selection operation is obtained is preserved optimum antibody as optimum antibody.
In the 4th step, according to this step first step, in second step, the 3rd step handled to all image blocks, obtained population and corresponding optimum antibody after all images piece is optimized.
Step 10, reconstructed image
The first step, the curve ripple Curvelet base that the optimum antibody of each image block is corresponding multiplies each other with the rarefaction representation coefficient vector that step 7 obtains, and obtains the image block after the reconstruct.
Second step, all images piece is handled according to this step first step, obtain the image block after all reconstruct.
In the 3rd step, the image block after all reconstruct is stitched together obtains the entire image after the reconstruct.
In the 4th step, go to step 5.
Effect of the present invention can further specify through following emulation experiment.
Experiment one, checking the present invention orthogonal matching pursuit OMP method and iteration hard-threshold IHT method than prior art on visual effect has better reconstruct effect.Experimental result is as shown in Figure 2; Wherein Fig. 2 (a) is the Lena test primitive figure of standard; Fig. 2 (b) is among the present invention in sampling rate being 25% o'clock restructuring graph; Fig. 2 (c) is 25% o'clock restructuring graph for orthogonal matching pursuit OMP method in sampling rate, and Fig. 2 (d) is 25% o'clock restructuring graph in sampling rate for iteration hard-threshold IHT method.
The image that this experiment is used is 512 * 512 standard testing image Lena figure.The size of image block is decided to be 16 * 16 in the experiment, and population size n is set at 10, and the variation probability is set at 0.2, and the scale of curve ripple Curvelet redundant dictionary is 3989, maximum iteration time pmx=5.
As can be seen from Figure 2, Fig. 2 (b) does not have noise, does not have blocking effect, and is more clear, and Fig. 2 (c) has obvious noise, and Fig. 2 (d) has tangible blocking effect.Therefore, under identical sampling rate, the visual effect of the image of reconstruct of the present invention is better than orthogonal matching pursuit OMP method and iteration hard-threshold IHT method.
Experiment two, checking the present invention orthogonal matching pursuit OMP method, iteration hard-threshold IHT method than prior art on Y-PSNR PSNR has better reconstruct effect.Experimental result is as shown in Figure 3; Wherein Fig. 3 (a) for Lena figure respectively with the Y-PSNR PSNR of the present invention, orthogonal matching pursuit OMP method and iteration hard-threshold IHT method reconstructed image trend comparison diagram with the sampling rate variation; The trend comparison diagram that Fig. 3 (b) changes with sampling rate with the Y-PSNR PSNR of the present invention, orthogonal matching pursuit OMP method and iteration hard-threshold IHT method reconstructed image respectively for Barbara figure, Fig. 3 (c) schemes respectively the trend comparison diagram with the sampling rate variation with the Y-PSNR PSNR of the present invention, orthogonal matching pursuit OMP method and iteration hard-threshold IHT method reconstructed image for Elaine.
This experiment is used is 512 * 512 standard testing image Lena figure, Barbara figure, Elaine figure.In this experiment the setting of parameter with test one identically, the degree of rarefication in three kinds of methods all is taken as 32 under different sampling rates.Respectively Lena figure, Barbara figure, Elaine figure are carried out reconstruct with the present invention, orthogonal matching pursuit OMP method and iteration hard-threshold IHT method, the Y-PSNR PSNR of the image of reconstruct is as shown in the table:
From table, can find out that under identical sampling rate, the Y-PSNR PSNR of the image of reconstruct of the present invention is higher than orthogonal matching pursuit OMP method iteration hard-threshold IHT method.From Fig. 3 (a), can find out among Fig. 3 (b) and Fig. 3 (c) that for same image, the Y-PSNR PSNR of the image of reconstruct of the present invention exceeds much with other two curves of curve ratio that sampling rate changes.Therefore, no matter under which kind of sampling rate, the present invention's orthogonal matching pursuit OMP method, iteration hard-threshold IHT method than prior art on Y-PSNR PSNR has better reconstruct effect.
Experiment three is analyzed among the present invention in the three-dimensional bits coupling BM3D filtering operation parameter beta of Noise Variance Estimation and maximum iteration time pmx to the influence of reconstruction result.Experimental result is as shown in Figure 4; Wherein Fig. 4 (a) be when sampling rate be 50%, β=1120 o'clock, the Y-PSNR PSNR of the Lena figure of reconstruct of the present invention is with the variation tendency of iterations; Fig. 4 (b) be when sampling rate be 50%; During maximum iteration time pmx=5, the Y-PSNR PSNR of the Barbara of reconstruct of the present invention figure, Lena figure is with the variation tendency of parameter beta, and Fig. 4 (c) is respectively 50%, 25% when sampling rate; During maximum iteration time pmx=5, the Y-PSNR PSNR of the Lena of reconstruct of the present invention figure is with the variation tendency of parameter beta.
The present invention when carrying out filtering with three-dimensional bits coupling BM3D wave filter, estimating noise variance η
t=α
-t-βIn parameter beta be very important parameters, wherein a η
tBe the noise variance of estimating, α is a constant, and the present invention is taken as
β is the parameter relevant with the image own characteristic.Maximum iteration time pmx influences the speed of image reconstruction.This experiment is chosen 512 * 512 standard testing image Lena figure and is schemed maximum iteration time pmx and parameter beta are analyzed with Barbara.
From Fig. 4 (a), can find out, under the situation that the parameter beta of estimating noise variance is fixed in three-dimensional bits coupling BM3D filtering operation, along with the increase of iterations; The Y-PSNR PSNR of the method restructuring graph among the present invention can be increasingly high; When iteration just began, the value of PSNR had tangible increase, was increased to after 5 but work as iterations; It is very slow that the value of PSNR promotes, and therefore in experiment, gets maximum iteration time pmx=5; Can find out that from Fig. 4 (b), 4 (c) under the situation that maximum iteration time pmx fixes, the parameter beta of estimating noise variance is very big to the influence of reconstruct experimental result in the three-dimensional bits coupling BM3D filtering operation; Under identical sampling rate; Image is different, makes the best β value of reconstruct effect different, and same width of cloth image is under the different sample rate; Make the best β value of reconstruct effect also can be different, value of this explanation parameter beta be not only relevant with the characteristics of image self and relevant with sampling rate.
In sum, the immune optimization image reconstructing method based on curve ripple redundant dictionary of the present invention, can be under the different sample rate the various natural images of reconstruct preferably, with existing data by MoM and MEI, reconstructed image good visual effect, reconstruction quality is higher.
Claims (8)
1. the immune optimization image reconstructing method based on curve ripple redundant dictionary comprises the steps:
(1) observation vector is carried out cluster
The observation vector of all images piece that the transmit leg of image is sent adopts affine propagation clustering AP algorithm that similar observation vector is got together, and obtains the observation vector of a plurality of classifications;
(2) initialization population
2a) the degree of rarefication value with all images piece is set at 32, and all the basic atoms in the curve ripple Curvelet redundant dictionary are numbered with positive integer;
2b) to each type observation vector after the cluster, the numbering of 32 curve ripples of picked at random Curvelet base atom obtains an antibody as the antibody element, according to said method obtains the initial population of a plurality of antibody as the corresponding image block of such observation vector;
2c) to all types observation vector after the cluster, according to step 2b) obtain the initial population of the corresponding image block of all types observation vector;
(3) para-immunity optimization
3a) each type of usefulness observation vector multiply by the generalized inverse matrix of Gauss's observing matrix, obtains the rarefaction representation coefficient vector of the corresponding image block of each type observation vector;
3b) calculate the affinity of all antibody in the initial population of the corresponding image block of each type observation vector according to following affinity function A:
Wherein, f
ABe the affinity value, i is the label of observation vector, and j is the sum of observation vector in each type after the cluster, y
iBe i observation vector in the class, Φ is Gauss's observing matrix, and Ψ is a curve ripple Curvelet redundant dictionary, α
iBe the rarefaction representation coefficient vector of the image block of i observation vector correspondence in the class,
Be vectorial two norms square;
3c) value to the affinity of all antibody in the population sorts from big to small, successively all antibody is carried out the clone, variation, selection operation;
The highest antibody of the affinity that 3d) selection operation is obtained is preserved optimum antibody as optimum antibody, preserves the population after optimizing;
3e) to the initial population of the corresponding image block of all types observation vector successively according to step 3a), step 3b), step 3c), step 3d) handle, the optimum antibody that obtains the corresponding image block of all types observation vector with optimize after population;
(4) reconstruct initial pictures
4a) the rarefaction representation coefficient vector curve ripple Curvelet base corresponding with optimum antibody of the image block that each type observation vector is corresponding multiplies each other, and obtains the corresponding image block of each type observation vector;
4b) with all types observation vector according to step 4a) handle, obtain the corresponding image block of all types observation vector;
4c) all images piece is stitched together obtains entire image;
(5) entire image is carried out filtering, protruding projection operation, obtain the entire image after the protruding projection of filtering;
(6) judge whether iterations reaches maximal value,, then export the entire image after the reconstruct if satisfy; Otherwise execution in step (7);
(7) upgrade degree of rarefication
7a) entire image after the protruding projection of filtering is carried out piecemeal, obtain a plurality of image blocks;
7b) the degree of rarefication value with each image block adds the degree of rarefication value after step-length obtains increasing;
7c) image block is obtained the rarefaction representation coefficient vector of sets of curves ripple Curvelet base atom and image block with orthogonal matching pursuit OMP algorithm, the numbering of curve ripple Curvelet base atom as the antibody element, is obtained the antibody of image block correspondence;
7d) with the affinity of the corresponding antibody of affinity function B computed image piece;
7e) determining step 3e) in the gained population affinity value of all antibody whether less than the affinity value of the corresponding antibody of image block; If; Then former degree of rarefication value is added that step-length is as new degree of rarefication value, repeated execution of steps 7c), step 7d); Up to step 3e) have the affinity value of the affinity value of an antibody in the gained population at least, the degree of rarefication value after the degree of rarefication value of this moment is upgraded as image block greater than the corresponding antibody of image block; If not; Then former degree of rarefication value is deducted step-length as new degree of rarefication value; Repeated execution of steps 7c); Step 7d), up to step 3e) have the affinity value of the affinity value of an antibody at least, the degree of rarefication value after the degree of rarefication value of this moment is upgraded as image block in the gained population greater than the corresponding antibody of image block;
7f) with all images piece according to step 7b), step 7c), step 7d), step 7e) handle the degree of rarefication value after obtaining all images piece and upgrading;
(8) new population more
8a) judge degree of rarefication value and the magnitude relationship of former degree of rarefication value after each image block upgrades; If the degree of rarefication value after upgrading is greater than former degree of rarefication value; Then at step 3e) degree of rarefication value after the length of all antibody is set to upgrade in the population on the basis of gained population; The numbering of choosing curve ripple Curvelet base atom randomly increases element partly as antibody, preserves all new antibodies as the population after upgrading; If the degree of rarefication value after image block upgrades is less than former degree of rarefication value, then at step 3e) degree of rarefication value after the length of all antibody is set to upgrade in the population on the basis of gained population, preserve all new antibodies as the population after upgrading; If the degree of rarefication value after image block upgrades equals former degree of rarefication value, then keeping step 3e) the gained population is constant;
8b) to all images piece according to step 8a) handle the population after obtaining all images piece and upgrading;
(9) image block immune optimization
9a) calculate the affinity of all antibody in the population after each image block upgrades with affinity function B;
9b) value to the affinity of all antibody in the population sorts from big to small, successively all antibody is carried out the clone, variation, and selection operation is preserved the population after the variation;
The highest antibody of the affinity that 9c) selection operation is obtained is preserved optimum antibody as optimum antibody;
9d) to all image blocks according to step 9a), step 9b), step 9c) handle population and corresponding optimum antibody after obtaining all images piece and optimizing;
(10) reconstructed image
10a) curve ripple Curvelet base and step 7c that the optimum antibody of each image block is corresponding) the rarefaction representation coefficient vector that obtains multiplies each other, and obtains the image block after the reconstruct;
10b) with all images piece according to step 10a) handle, obtain the image block after all reconstruct;
10c) image block after all reconstruct is stitched together obtains the entire image after the reconstruct;
10d) go to step (5).
2. the immune optimization image reconstructing method based on curve ripple redundant dictionary according to claim 1 is characterized in that, the step of the described affine propagation clustering AP algorithm of step (1) is following:
The first step is calculated the Euclidean distance between each observation vector, and its negative value is existed in the similar matrix, and the column vector that the intermediate value of similar matrix is formed is as message matrix;
In second step, iterations reaches the peaked moment and is set to stopping criterion for iteration;
In the 3rd step, utilize Attraction Degree and degree of membership between the similarity matrix calculating observation vector, the updating message matrix;
The 4th step judged whether to satisfy stopping criterion for iteration, if satisfy, then carried out for the 5th step, otherwise forwarded for the 3rd step to;
The 5th the step, with the Attraction Degree and the degree of membership addition of observation vector, get itself and maximum observation vector as cluster centre.
3. the immune optimization image reconstructing method based on curve ripple redundant dictionary according to claim 1 is characterized in that step 3c) and step 9b) concrete steps of described clone operations are following:
The first step, calculate the scale of each antibody cloning in the population according to formula:
Wherein, m
iBe clone's scale value of i antibody, C is the setting value relevant with clone's scale, and span is [20, ∞], f (a
i) be antibody a
iThe affinity value,
Be all antibody in the population the affinity value with;
In second step, each antibody in the population is duplicated m
iIndividual, obtain the corresponding antibody crowd;
In the 3rd step, according to the first step, second step handled, and obtained the antibody population behind all antibody clonings to all antibody in the population.
4. the immune optimization image reconstructing method based on curve ripple redundant dictionary according to claim 1 is characterized in that step 3c) and step 9b) concrete steps of described mutation operation are following:
The first step, to the antibody population behind each antibody cloning, the value of getting its variation probability is 0.2;
In second step, each antibody element among the antagonist crowd is got a random number from 0 to 1, if random number smaller or equal to 0.2, then replaces the antibody element with random number, otherwise keeps the antibody element constant;
In the 3rd step, all antibody elements are handled the antibody population after obtaining making a variation according to second step among the antagonist crowd;
In the 4th step, according to the first step, in second step, the 3rd step handled, and obtained the antibody population behind all antibody variations to the antibody population behind all antibody clonings.
5. the immune optimization image reconstructing method based on curve ripple redundant dictionary according to claim 1 is characterized in that step 3c) and step 9b) concrete steps of described selection operation are following:
The first step, calculate the affinity of all antibody in the antibody population after each antibody and the variation thereof according to following affinity function B:
Wherein, f
BBe affinity value, y
iBe i observation vector, Φ is Gauss's observing matrix, and Ψ is a curve ripple Curvelet redundant dictionary, α
iBe the rarefaction representation coefficient vector of the corresponding image block of i observation vector,
Be vectorial two norms square;
Second step, select the highest antibody of affinity as optimum antibody, preserve optimum antibody;
In the 3rd step, according to the first step, second step handled, and preserved all optimum antibody and obtained new population to the antibody population after all antibody in the population and the variation thereof.
6. the immune optimization image reconstructing method based on curve ripple redundant dictionary according to claim 1 is characterized in that, the described execution filtering of step (5), and the concrete steps of protruding projection operation are following:
The first step is to step 4c) image that obtains is with three-dimensional bits coupling BM3D filter process, obtains filtered image;
Second step, filtered image is carried out piecemeal, obtain a series of image block;
In the 3rd step, each image block is carried out protruding projection operation according to formula:
Wherein,
Be k image block after the protruding projection, θ
kBe k image block, Φ
TBe the transposed matrix of Gauss's observing matrix, Φ is Gauss's observing matrix, y
kIt is the corresponding observation vector of k image block;
The 4th step, all image blocks were handled according to the 3rd step, obtain the image block after all protruding projections;
In the 5th step, the image block after all protruding projections is pieced together the entire image that obtains together after the protruding projection.
7. the immune optimization image reconstructing method based on curve ripple redundant dictionary according to claim 1 is characterized in that step 7b) value of described step-length is the positive integer between 1 to 100.
8. the immune optimization image reconstructing method based on curve ripple redundant dictionary according to claim 1 is characterized in that step 7c) concrete steps of described orthogonal matching pursuit OMP algorithm are following:
The first step, image block are set to initial residual signals, and the maximum atom number that the residue signal Sparse Decomposition need be chosen is set to the value of image block degree of rarefication;
Second step, each atom and residual signals in the curve ripple Curvelet redundant dictionary are multiplied each other, obtain the inner product of each atom and residual signals;
The 3rd step, all atoms in the curve ripple Curvelet redundant dictionary were handled according to second step, obtain the inner product of all atoms and residual signals;
The 4th step, select the maximum atom of inner product as best atom, adopt the Gram-Schmidt orthogonalization method that best atom is handled, the best atom after the preservation orthogonalization is preserved the maximum inner product value;
The 5th step deducted best atom and the product of maximum inner product value after the orthogonalization with residual signals, obtained new residual signals;
The 6th step, judge the maximum atom number whether iterations need be chosen greater than the signal Sparse Decomposition, if satisfied, then stop iteration, all maximum inner product values as vector element, are obtained the rarefaction representation coefficient vector of image block; Otherwise went to for second step.
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