CN106780399A - Based on multiple dimensioned group of sparse compressed sensing image reconstructing method - Google Patents
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Abstract
The invention belongs to signal transacting and rarefaction representation technical field, and in particular to a kind of image reconstructing method for being applied to compressed sensing.Present invention introduces the Multi-scale model group sparse characteristic of image, it is proposed that a kind of based on the multiple dimensioned group of compressed sensing image reconstructing method of sparse model.The method make use of the openness and multi-scale self-similarity of natural image simultaneously, structural self similarity group is built from multiple dimensioned group of sparse domain of image, then to each group training self-adapting dictionary, and sparse coefficient is calculated using hard -threshold operator, and then method of the application based on iterative shrinkage threshold value carries out Efficient Solution to the model for proposing.Multiple dimensioned group of Sparse methods substantially increase sparse degree of the image in sparse domain.Test result indicate that, compressed sensing reconstructing method proposed by the present invention compared with the conventional method, can effectively lift the quality reconstruction of image.
Description
【Technical field】The invention discloses a kind of based on the multiple dimensioned group of compressed sensing Image Reconstruction side of sparse model
Method, belongs to signal transacting and rarefaction representation technical field, and in particular to a kind of image reconstructing method for being applied to compressed sensing.
【Background technology】The signal compressed after compressed sensing (Compressive Sensing, CS) and traditional sampling is adopted
Mode set is different, and by using certain redundancy of signal generally existing, it makes sampling and compression while carrying out, and breach how
The limitation of Qwest's sampling thheorem.Compressive sensing theory proves, if signal have in itself it is openness (or dilute on certain transform domain
Dredge), then signal can be reconstructed from little sampling.In compressive sensing theory, the weight of the sparse degree of signal to signal
Structure effect has significant impact.The sparse degree of signal is higher, then the quality for reconstructing is better.Therefore, how to find one it is dilute
Dredge domain so that projection of the signal in the domain is more sparse, is all the time the pass to be solved in compressed sensing restructuring procedure
Key problem.Due to the unstability of natural image generally existing, in fact and in the absence of a general sparse domain so that all
Projection of the signal in the domain is all sparse, and traditional compressed sensing reconstructing method is generally (such as discrete using fixed sparse domain
Cosine transform, wavelet transformation, profile wave convert, gradient field etc.), this sparse domain does not adapt to different signal kinds, thus
Usual quality reconstruction is poor.
In recent years, the method based on localized mass rarefaction representation achieves preferable sparse effect, and this method is generally utilized
From natural image learning to dictionary rarefaction representation is carried out to image.Compared with fixed dictionary, learning-oriented dictionary for
Image has more preferable adaptability, after sparse transformation, can to a greater degree improve the openness of image.But dictionary learning is usual
It is an extensive problem, and along with computation complexity higher.Meanwhile, traditional dictionary learning method independently considers figure
Each block of picture, so as to have ignored contacting between block and block.
Openness except image, J.Mairal and A.Buades et al. are by another significant properties of image --- non-office
Portion's self-similarity has been applied among image recovery, and the characteristic describes the texture that natural image shows in non local region
With the repeatability of structure, this repeatability can be effectively retained the edge of image with acutance to keep the non local consistent of image
Property.
Present invention introduces the Multi-scale model group sparse characteristic of image, it is proposed that one kind is based on multiple dimensioned group of sparse model
Compressed sensing image reconstructing method, the method make use of the openness and self-similarity of natural image simultaneously, from many of image
Build structural self similarity group in the sparse domain of yardstick, and train so that projection of the image in sparse domain is more sparse,
On the basis of this, we using based on iterative shrinkage threshold value (Iterative Shrinkage/Thresholding Algorithm,
ISTA method) is solved to corresponding optimization problem.Test result indicate that, compressed sensing reconstruct side proposed by the present invention
Method compared with the conventional method, can effectively lift the quality reconstruction of image, and with preferable convergence.
【The content of the invention】It is an object of the invention to multi-scale self-similarity is combined with group sparse characteristic, one is proposed
Plant based on the multiple dimensioned group of compressed sensing image reconstructing method of sparse model.
It is different from traditional block-based sparse representation model, the present invention simultaneously using image self-similarity with it is sparse
Property, multiple dimensioned group of sparse model is introduced, each group from multi-scale image concentration by selecting with the non local of similar structure
Image block is constituted, and adaptively learns corresponding sparse dictionary from each group afterwards.Be described in detail below multiple dimensioned group it is sparse
The learning method of model and self-adapting dictionary.
First, willImage x with step-lengthIt is divided intoFigure
As block, and it is expressed as xk, k=1,2 ..., n.Then, for each image block xk, from the correspondence of the multi-scale image collection of image x
The c image block for most matching, composition set are selected in neighborhood windowWillIn each image block arranged by row, then xkIt is right
The group answeredFinally, for each groupIts corresponding sparse dictionary is defined for Dk,Can be represented asUse αxRepresent αkSet, i.e.,So, CS reconstructions
Can be expressed as：
min||αx||0S.t.b=Ax (1)
Penalty factor λ is introduced, model can be converted into
ISTA algorithm frames are introduced below, then problem to be optimized can be converted into two following step iterative problems：
r(j)=x(j)-ρAT(Ax(j)- b), (3)
Here ρ represents constant step-length, and j represents that iterations (hereinafter omits iterations j).Obviously, (2) formula is solved
It is critical only that solution (4) formula.Introducing group sparse theory, makes x, r ∈ RN,Just like drawing a conclusion：For any ε
＞ 0,WithMeet
Wherein P () represents probability, M=Bs×c×n.Then (4) formula can be converted into
Wherein τ=λ M/N.(6) formula can be decomposed into n optimization subproblem：
Below to each groupCorresponding dictionary Dk makes definition.It is rightIt is approximateCarry out singular value decomposition：
OrderThen in (8) formulaIt is a diagonal matrix, diagonal element
Element is γkIn element be arranged in order,It is respectively matrixWithRow, then can defineCorresponding word
Allusion quotation DkIn atomEasily demonstrate,proveThen (7) formula can
It is written as
The analytic solutions that so can directly write out (9) formula are
Here hard () represents hard -threshold operator.Then the solution of each subproblem is represented byBy what is obtained
EachIn image block put back to its original position add and and seek weighted average, you can obtain the solution of (4) formula.
【Advantages and positive effects of the present invention】Compared with prior art, the invention has the advantages that and good effect：
First, using the openness and self-similarity combined reconstruction of image.Invention introduces structural group of rarefaction representation
Model, make use of the openness and self-similarity of image simultaneously under compressed sensing framework, greatly limit compressed sensing problem
Solution space, the reconstruct mode based on iterative shrinkage threshold value is developed on this basis new Optimized model is efficiently asked
Solution, ensure that preferable convergence while reconstruction property is improved；
Second, introduce Multi-scale model group sparse model.The present invention, will on the basis of structural group of sparse representation model
Former problem extend to multiple dimensioned group of sparse domain, and using the method study self-adapting dictionary of singular value decomposition, this method and biography
The CS reconstructing methods of system compare the reconstruction quality for greatly improving image.
【Brief description of the drawings】Fig. 1 is the set constructor method schematic diagram based on Multi-scale model self similarity proposed by the present invention；
【Specific embodiment】To make embodiment of the present invention state apparent with meaning advantage, with reference to
Drawings and Examples, are described in more detail to the present invention hereinafter.
Step 1, the compression sampling based on piecemeal CS：Set block size as 32 × 32 in the present invention, initiation parameter λ,
ρ, current iteration number of times j and maximum iteration Max_iter, and initialization survey matrix A is gaussian random projection matrix, it is right
Original image x carries out piecemeal sampling, obtains measured value b；
Step 2, initialization：According to measured value b and calculation matrix A, initialization x's is estimated as x(0)；
Step 3, the approximate r for calculating x(j)：r(j)=x(j)-ρAT(Ax(j)- b), hereinafter omit iterations footmark (j)；
Step 4, construction Multi-scale model self similarity group：Using the multi-scale image of the method construct r of arest neighbors interpolation
Collection, willImage r with step-lengthIt is divided intoImage block, for every
It is individualImage block, concentrate the most like blocks of search c in multi-scale image, thus construct Multi-scale model from
Similar groupWhereinAs shown in figure 1, remembering r herek=Rk
(r), k=1, wherein 2 ..., n, Rk() is by image block rkThe operator extracted from image r, and its transpositionThen represent the operator that image block is put back in reconstructed image (remaining position zero padding)；
Step 5, for each groupTraining self-adapting dictionary Dk：To each groupCarry out singular value decomposition,OrderThen whereinIt is a diagonal matrix, diagonal element is γkIn element be arranged in order,It is respectively matrixWithRow, then self-adapting dictionary DkIn i-th atom
Step 6, calculating sparse coefficientIt is i.e. rightSolution is optimized, is directly drawn
Enter hard -threshold operator hard (), then the analytic solutions of above formula are
Wherein τ=λ (Bs×c×n)/N；
Step 7, each group is reconstructed：
Step 8, renewal x(j)：By obtain eachIn image block put back to its original where position add and and ask plus
Weight average value, you can obtain x(j)：
Whether step 9, judgement iterations are equal to Max_iter, if being not equal to, iterations j=j+1, and return to step
Rapid 3；If being equal to, final reconstruction result is obtained
Emulation experiment of the invention is in Intel (R) Xeon (R) [email protected] CPU, Red Hat
Run under the simulated conditions of (Santiago) operating systems of Enterprise Linux Server release 6.5, emulation
Software uses MATLAB.
In emulation experiment, experimental subjects is respectively House (256 × 256), Barbara (256 × 256), Leaves
(256 × 256), Monarch (256 × 256), Parrots (256 × 256), Vessels (96 × 96) image, respectively with it is existing
Discrete wavelet method (Discrete Wavelet Transform Method, DWT), profile wave method (Contourlet
Method, CT), the full calculus of variations (Total Variation, TV), assume method (Multi-hypothesis, MH), joint
Sparse methods (Collaborative Sparsity Method, Cos) are contrasted.
Sample rate is respectively set as 20%, 30% and 40% by us, and the block size of splits' positions sampling is set to 32 ×
32, the tile size in step 4It is set to 8 × 8, SlidingDis and is set to 4, the size L × L of search window sets
It is 10 × 10, the number of plies of multi-scale image collection is set to 4, the number c of image block is set to 50, ρ=1, λ=10 in each group.This hair
Bright parameter selection has certain universality, and 6 width images of this experiment have used same group of parameter, while this group of parameter also may be used
With in the restructuring procedure for expanding to other natural images.In the present invention, we use the result of MH algorithms as the initial value x of x(0).Table 1 is PSNR (the Peak Signal to Noise that various reconstructing methods reconstruct each image under different sample rates
Ratio, PSNR, unit dB), runic represents the maximum PSNR values of identical sample rate similarly hereinafter piece image.As can be seen that of the invention
The quality reconstruction of method is all higher than in most cases existing CS reconstructing methods, and the PSNR average values of 6 width images are in sampling
Rate is have 3.14dB, 2.91dB and 2.72dB respectively compared to the reconstruction result of CoS methods in the case of 20%, 30% and 40%
Lifting.In sum, the reconstructed image quality of the inventive method is higher, stability preferably, be a kind of effective compressed sensing
Image reconstructing method.
The PSNR comparing results (dB) of each method reconstructed image of table 1
Claims (3)
1. a kind of sparse set constructor method for being applied to compressed sensing restructuring procedure based on Multi-scale model self similarity, including
Following steps：
(1) initialize：Initiation parameter λ, ρ, current iteration number of times j and maximum iteration Max_iter, based on piecemeal CS, just
Beginningization calculation matrix A is gaussian random projection matrix, and piecemeal sampling is carried out to original image x, measured value b is obtained, according to measured value b
With calculation matrix A, initialization x's is estimated as x(0)；
(2) the approximate r of x is calculated(j)：r(j)=x(j)-ρAT(Ax(j)- b), hereinafter omit iterations footmark (j)；
(3) Multi-scale model self similarity group is constructed：Using the multi-scale image collection of the method construct r of arest neighbors interpolation, willImage r with step-lengthIt is divided intoImage block, for eachImage block, the most like blocks of c are searched in each search window of multi-scale image collection, so as to construct many
Mesostructure self similarity groupK=1,2 ..., n, whereinHere r is rememberedk=Rk
(r), k=1, wherein 2 ..., n, Rk() is by image block rkThe operator extracted from image r, and its transpositionThen represent the operator that image block is put back in reconstructed image (remaining position zero padding).
2. the sparse set constructor method of Multi-scale model according to claim 1, for each groupTraining self adaptation
Dictionary Dk, and calculate sparse coefficient
(1) train from each groupCorresponding adaptation dictionary Dk：To each groupCarry out singular value decomposition,OrderThen whereinIt is a diagonal matrix, diagonal element is γkIn element be arranged in order,It is respectively matrixWithRow, self-adapting dictionary DkIn i-th atomI=1,2 ..., m；
(2) sparse coefficient is calculatedIt is rightSolution is optimized, hard -threshold is introduced directly into
Operator hard (), the analytic solutions of above formula areWherein τ=λ
(Bs×c×n)/N。
3. according to the self-adapting dictionary D tried to achieve in claim 2kWith sparse coefficientObtain final result：
(1) each group is reconstructed：
(2) x is updated(j)：By eachIn image block put back to its originally where position add and and seek weighted average, obtain
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| CN110796625A (en) * | 2019-10-30 | 2020-02-14 | 重庆邮电大学 | Image compressed sensing reconstruction method based on group sparse representation and weighted total variation |
| CN113191948A (en) * | 2021-04-22 | 2021-07-30 | 中南民族大学 | Image compressed sensing reconstruction system with multi-resolution characteristic cross fusion and method thereof |
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