CN105427264B - A kind of image reconstructing method based on the estimation of group's sparse coefficient - Google Patents
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Abstract
The invention discloses a kind of image reconstructing methods based on the estimation of group's sparse coefficient.Belong to digital image processing techniques field.It is a kind of image reconstructing method based on the estimation of similar set of blocks sparse coefficient.Similar image block is found by Euclidean distance first, and carry out part and non-local sparse to similar image set of blocks to indicate, to obtain more sparse more accurate coefficient.Reconstruction model further is solved using the graceful iterative algorithm of Burger, and sparse coefficient is estimated using linear MMSE criterion, to guarantee the accurate estimation to the small coefficient comprising image texture detailed information.The present invention carries out Linear Minimum Mean-Square Error Estimation to similar image set of blocks rarefaction representation coefficient, not only repair and in terms of effect it is obvious, image after making reconstruct simultaneously possesses more abundant detailed information, whole visual effect is more clear, and can be used for optical imagery reparation and deblurring.
Description
Technical field
The invention belongs to digital image processing techniques field, the image reconstruction that it is in particular to estimated based on group's sparse coefficient
Method is handled for optical imagery reparation and deblurring.
Background technique
In recent years, rarefaction representation and dictionary learning have become a research hotspot, and are widely used in image procossing and meter
Calculation machine visual field, such as image denoising, reparation and color editor etc..The rarefaction representation of image is by the used complete dictionary of image
Linear combination is carried out to reconstruct, rarefaction representation is achieved the purpose that by using limited reconstructed sample number.
Traditional images rarefaction representation utilizes the sparse characteristic of true picture in the transform domain as illustrated, has effectively achieved in transform domain
The rarefaction representation of image real information.The key of this method is how dictionary makes actual signal corresponding to tectonic transition
It is more sparse in the transform domain as illustrated, and in the transform domain as illustrated preferably restore actual signal.Nearest transform domain rarefaction representation
New breakthrough is achieved with the reconstructing method that non local similitude combines, as non local similar image block is combined by BM3D method
Then 3D rendering block group carries out 3D wavelet transformation to 3D rendering block group, and estimates true coefficient using hard -threshold or Wiener filtering,
Image area finally is changed into coefficient contravariant, it had not only been utilized correlation in block but also correlation between block is utilized, and had obtained relatively good
Effect.But the threshold filter method based on sparse coefficient cannot achieve the accurate estimation to sparse coefficient, in resulting result
It is difficult to reflect the detail textures information of image.It can be obtained than threshold value comparison method more based on Linear Minimum Mean-Square Error Estimation method
Add accurate estimation, and the graceful iterative algorithm of Burger can fast and effeciently solve reconstruction model.
Summary of the invention
It is an object of the invention to be directed in existing optical image reconstruction to deficiency existing for threshold estimation coefficient, one is proposed
The image reconstructing method that kind is estimated based on group's sparse coefficient.This method has fully considered between the local similarity of image block and block
Similar image set of blocks is carried out the local and non local group's rarefaction representation combined simultaneously, it is dilute to obtain group by non local similitude
Sparse coefficient, and the sparse estimation coefficient of final group is fast and effeciently solved using the graceful iterative algorithm of Burger, and then use and be based on
The coefficient estimation method of linear minimum mean-squared error improves the precision of estimation coefficient, more accurately and effectively to estimate true
Coefficient, the final image finally reconstructed using the unusual value coefficient of estimation.Therefore, this method is when realizing image reconstruction
It can obtain the result closer to true picture.The following steps are included:
Step 1: similar image set of blocks group's rarefaction representation
After image is carried out image block extraction, image block collection is obtained using the similarity measurement method based on Euclidean distance
It closes, local rarefaction representation are as follows:
Xi=D α=[d1, d2…dm]·[α1, α2…αL] formula (1)
Wherein d1, d2…dmFor the atom in dictionary D, α1, α2…αLIt is image block x1,x2…xLSparse volume on dictionary D
Code coefficient, non-local sparse indicate are as follows:
Xi=β ΦT=[β1, β2…βn]T·[φ1, φ2…φm]TFormula (2)
Wherein φ1, φ2…φmFor the atom of dictionary Φ, β1, β2…βnIt is similar set of blocks XiMiddle row vector is in dictionary Φ
On sparse coding coefficient.Group's rarefaction representation of similar image set of blocks can be obtained by formula (1) and formula (2):
Xi=D γ ΦTFormula (3)
Wherein D is the sparse corresponding premultiplication dictionary in part, and Φ is that the corresponding right side of non-local sparse multiplies dictionary, and γ is while wrapping
The sparse coding coefficient of relevant information between the column element of set of rows containing similar block.
Step 2: the image reconstruction based on group's rarefaction representation
Image reconstruction model based on group's rarefaction representation are as follows:
Formula (4)
Wherein y is observed image, and H is degenerate matrix, D and ΦTRespectively the premultiplication of group's rarefaction representation and the right side multiply matrix, γi
For the rarefaction representation coefficient of i-th of similar image set of blocks, | | γi||pFor p norm constraint；It can be expressed as optimal under restrictive condition
Change form:
Formula (5)
For image reconstruction model, the graceful iterative algorithm of Burger be may be expressed as:
Formula (6)
Formula (7)
b(t+1)=b(t)-(x(t+1)-Dγ(t+1)ΦT) formula (8)
Wherein x(0)=0, γ(0)=0, b(0)=0.It is iteratively solved by above formula (6) to formula (8) come to image reconstruction mould
Type is solved.
Step 3: group's sparse coefficient is estimated
After image reconstruction model determines, coefficient estimates model are as follows:
Formula (9)
Wherein w is current iteration reconstructed image, w-z=v, z=D γ ΦT, z is true picture, and v is noise；For observation
Its coefficient, is expressed as by the similar set of blocks W of image first:
γW=γZ+γVFormula (10)
Wherein γW, γZRespectively indicate noisy unusual value coefficient and the unusual value coefficient of actual signal, γVIndicate additive noise
Coefficient；Then the unusual value coefficient of actual signal is estimated using linear MMSE criterion:
Formula (11)
Wherein E [] indicates expectation, Cov (γZ) indicate γWCovariance matrix, Cov (γZ,γW) indicate γZWith γW
Cross-covariance；Obtaining x(t+1)And γ(t+1)Afterwards, b is updated(t+1)；Loop iteration x(t+1), γ(t+1)And b(t+1), work as Burger
When graceful iterative algorithm meets termination condition, utilize
Formula (12)
The true picture block coefficient that will be estimatedIt is reconstructed into final image.
Innovative point of the invention is part and the non-local sparse characteristic that image is utilized in image reconstruction procedure；It will figure
The part of picture and non-local sparse characteristic are converted to the rarefaction representation of the unusual value coefficient of similar image set of blocks；It is graceful repeatedly using Burger
Reconstruction model is quickly and efficiently solved for algorithm, and estimates true picture singular value system using linear MMSE criterion
Number, to further increase estimated accuracy, and is used for optical imagery reparation and deblurring for this method.
Beneficial effects of the present invention: it is combined with non-local sparse by the part of image is sparse, improves rarefaction representation
Performance；Group's rarefaction representation is carried out to similar image set of blocks, obtained being more suitable for expressing similar image set of blocks row and column from
Dictionary is adapted to, and simultaneously includes the original image sparse coefficient of ranks relevant information；Reconstruct is solved using the graceful iterative algorithm of Burger
Model more efficient can be quickly obtained reconstruction result；True picture is estimated using the method for Linear Minimum Mean-Square Error Estimation
Corresponding sparse coefficient preferably protects image texture details corresponding small coefficient while capable of accurately estimating larger coefficient,
Therefore not only overall effect also retains image grain details abundant closer to true picture to the image after reconstructing.
The method that the present invention mainly uses emulation experiment is verified, and all steps, conclusion are all verified on MATLAB8.0
Correctly.
Detailed description of the invention
Fig. 1 is workflow block diagram of the invention；
Fig. 2 is complex pattern to be repaired used in present invention emulation；
Fig. 3 is used in present invention emulation to de-blurred image；
Fig. 4 is the result figure to each restorative procedure of Fig. 2；
Fig. 5 is the result figure to each deblurring method of Fig. 3.
Specific embodiment
Referring to Fig.1, the present invention is based on the image reconstructing method of group's sparse coefficient estimation, specific steps include the following:
Step 1: similar image set of blocks group's rarefaction representation
Firstly, acquiring its Euclidean distance using formula (13) after image block is extracted:
Formula (13)
Wherein xjFor arbitrary image block in search window,For two norm squareds, d (xi,xj) value show two figures more greatly
The similar image set of blocks X of L similar image set of blocks is obtained as the similarity between block is smaller, then by formula (14)i:
Formula (14)
WhereinIt indicates similar block extraction operation, obtained similar image set of blocks is subjected to group's sparse table by formula (3)
Show, so as to later reconstitution.
Step 2: the image reconstruction based on group's rarefaction representation
Image reconstruction realizes that formula (6) can be further indicated that using the graceful iterative algorithm of Burger are as follows:
Formula (15)
Wherein γ and b is obtained known quantity after preceding an iteration.This is quadratic minimization problem, and closed solution can indicate
Are as follows:
Formula (16)
Wherein A=HTy+η(DγΦT+ b)/2, I is unit matrix.In the case where given x and b, formula (7) can simplify are as follows:
Formula (17)
Wherein w=x-b.Obtaining updateWithAfterwards, it is updated using formula (8)After meeting condition, using final
Updated value obtains final image.
Step 3: group's sparse coefficient is estimated
Group's sparse coefficient provides its estimation models by formula (11), and since similar image block is uncorrelated to its noise, then it becomes
It is also uncorrelated to change rear coefficient, therefore formula (11) can simplify are as follows:
Formula (18)
If γZ, γVFor diagonal matrix, thenIn i-th of coefficient can be estimated by formula (19):
Formula (19)
Wherein noise singular varianceIt may be expressed as:
Formula (20)
Wherein σ2The noise variance contained for input picture w.In the t times iterative process, σ2It is updated by formula (21):
Formula (21)
WhereinFor the noise variance that observed image contains, μ is control parameter.According to two-way variance estimation theory, really
Signal singular values varianceSingle Sample Maximal possibility predication may be expressed as:
Formula (22)
Wherein γiFor i-th of singular value of W, k is singular value number.When the graceful iterative algorithm of Burger meets termination condition,
The true picture block coefficient that will be estimated using formula (12)It is reconstructed into final image.
Effect of the invention can be further illustrated by following emulation experiment:
One, experiment condition and content
Experiment condition: testing the input picture that uses is Fig. 2 and Fig. 3, and wherein Fig. 2 is that (ratio is complex pattern to be repaired
20%), Fig. 3 is to de-blurred image (its fuzzy core is 9 × 9uniform core), and pixel size is 256 × 256.In experiment
Each reconstructing method all uses MATLAB Programming with Pascal Language to realize.
Experiment content: it under these experimental conditions, repairs image and uses SALAS method, BPFA method and FoE method and this
Inventive method compares, de-blurred image using L0_ABS method, IDDBM3D method, NCSR method and the method for the present invention into
Row comparison.Reconstruct reducing power objectively evaluates result structural similarity SSIM measurement.
Experiment 1: weight is carried out to Fig. 2 respectively with the method for the present invention and existing SALAS method, BPFA method and FoE method
Structure.Wherein SALAS method is a kind of quick TV image repair method, and reconstruction result is Fig. 4 (a)；BPFA method utilizes one kind
Beta-Bernoulli process training dictionary is truncated image to be reconstructed, reconstruction result is Fig. 4 (b)；And FoE method will
Modulus Model is combined with Bayesian Estimation, automatic adjusument parameter therein, and reconstruction result is Fig. 4 (c).This hair in experiment
Tile size is arranged in bright methodThe image block number L that similar image set of blocks includes, image block extract sliding distance s points
It is not arranged are as follows:L=60, s=4；Final reconstruction result is Fig. 4 (d).
Comparison BPFA method, FoE method and the method for the present invention can be seen that SALAS method reconstruction result not only details line
Loss of learning is managed, and whole visual effect is bad；It can be seen that its detailed information and overall effect are excellent by BPFA method reconstruction result
In SALAS method, but still it is not satisfactory；The result of FoE method compares first two and improves a lot, and overall effect is preferable, but thin
It is still to be improved to save information；The method of the present invention combines rarefaction representation with the self similarity of image and non local similitude, and leads to
Linear MMSE criterion estimation sparse coefficient is crossed, and with the graceful iterative algorithm rapid solving reconstruction model of Burger, further
Its estimated accuracy is improved, so that not only whole visual effect is good for the image of reconstruct, but also detailed information is abundant.
The SSIM index of the different restorative procedures of table 1
| Image | SALAS method | BPFA method | FoE method | The method of the present invention |
| Barbara | 0.8916 | 0.9111 | 0.9335 | 0.9562 |
Table 1 gives the SSIM index situation to Fig. 2 each method being reconstructed, and wherein SSIM value improves more multilist and shows again
Structure effect is better.It can be seen that the method for the present invention comparison other methods improve a lot, this result and quality reconstruction figure kissing
It closes.
Above-mentioned experiment shows reconstructing method of the present invention, and not only reduction effect is obvious, but also reconstructed image is abundant in content, together
When visual effect and to objectively evaluate index all preferable, it can be seen that the present invention is effective to optical imagery reparation.
Experiment 2: with the method for the present invention and existing L0_ABS method, IDDBM3D method, NCSR method respectively to Fig. 3 into
Row reconstruct.Wherein L0_ABS is a kind of based on l0The image reconstructing method of norm rarefaction representation, reconstruction result are Fig. 5 (a)；
IDDBM3D is a kind of improved BM3D reconstructing method, and reconstruction result is Fig. 5 (b)；NCSR method is it is also contemplated that by the dilute of image
It dredges characteristic to combine with non local similitude, but the starting point of its combination and concrete model are all larger with context of methods difference,
Reconstruction result is Fig. 5 (c).Tile size is arranged in the method for the present invention in experimentThe image block that similar image set of blocks includes
Number L, image block extract sliding distance s and are respectively set are as follows:L=60, s=4, final reconstruction result are Fig. 5 (d).
Comparison IDDBM3D method, NCSR method and the method for the present invention can be seen that L0_ABS method reconstruction result details line
It is larger to manage loss of learning, and whole visual effect is bad；IDDBM3D method and NCSR method are current best deblurring method,
It can be seen that detailed information and overall effect are preferable by its reconstruction result；The method of the present invention and IDDBM3D method and NCSR method
It compares, the image overall visual effect and detailed information richness of reconstruct are close, visually reach higher level.
The SSIM index of the different deblurring methods of table 2
| Image | L0_ABS method | IDDBM3D method | NCSR method | The method of the present invention |
| Barbara | 0.8692 | 0.9014 | 0.9117 | 0.9170 |
Table 2 gives the SSIM index situation of Fig. 3 and each method that it is reconstructed, and wherein SSIM value, which improves, gets over multilist
Show that quality reconstruction is better.It can be seen that the method for the present invention comparison L0_ABS method improve a lot, and compare IDDBM3D method and
NCSR method also slightly improves, this result matches with quality reconstruction figure.
Above-mentioned experiment shows reconstructing method of the present invention, and not only reduction effect is obvious, but also reconstructed image is abundant in content, together
When visual effect and to objectively evaluate index all preferable, it can be seen that the present invention is effective to optical imagery deblurring.
Claims (1)
1. a kind of image reconstructing method based on the estimation of group's sparse coefficient, it is characterised in that specific step is as follows:
Step 1: similar image set of blocks group's rarefaction representation
Image block extraction is carried out to observed image first and utilizes the similarity based on Euclidean distance then for target image block
Measurement selects the highest L-1 image block of similarity and object block to form similar image set of blocks in search space；It is finally right
Similar image set of blocks carries out local with the non local group's rarefaction representation combined simultaneously, obtains observed image similar image block collection
Group's rarefaction representation coefficient of conjunction；
Step 2: the image reconstruction based on group's rarefaction representation
Firstly, establishing the image reconstruction model based on group's rarefaction representation:
Wherein y is observed image, H degenerate matrix, D and ΦTRespectively the premultiplication of group's rarefaction representation and the right side multiply matrix, γiIt is i-th
The rarefaction representation coefficient of a similar image set of blocks, | | γi||pFor p norm constraint, form is optimized in restrictive condition and is ordered p=
0；Secondly above-mentioned reconstruction model is converted to two sub- optimization problems using the graceful iterative algorithm of Burger to iteratively solve: obtains this
Rarefaction representation coefficient is estimated using linear minimum mean-squared error method after the reconstructed image estimated in iteration, is being estimated
Sparse coefficient after combine observed image data y update reconstructed image；
Step 3: group's sparse coefficient is estimated
When reconstructed image determines, coefficient estimation model be may be expressed as:
Wherein w is current iteration reconstructed image, w-z=v, z=D γ ΦT, z is true picture, and v is noise；Utilize linear minimum
Mean square error estimation criterion estimation coefficientIts coefficient, is expressed as by set of blocks W similar for observed image first:
γW=γZ+γV
Wherein γW, γZRespectively indicate noisy unusual value coefficient and the unusual value coefficient of actual signal, γVIndicate additive noise；Then
Estimated using unusual value coefficient of the linear MMSE criterion to actual signal:
Wherein E [] indicates expectation, Cov (γW) indicate γWCovariance matrix, Cov (γZ,γW) indicate γZWith γWIt is mutual
Covariance matrix；When the graceful algorithm of Burger meets stopping criterion for iteration, utilize
The true picture block coefficient that will be estimatedIt is reconstructed into final image.
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| CN106683055A (en) * | 2016-12-09 | 2017-05-17 | 河海大学 | Degradation model and group sparse representation-based foggy day image restoration method |
| CN106875338B (en) * | 2017-02-16 | 2020-05-08 | 清华大学深圳研究生院 | Image super-resolution processing method based on group sparse processing |
| CN107256538B (en) * | 2017-06-08 | 2019-10-01 | 大连海事大学 | A kind of image repair method |
| CN107301631B (en) * | 2017-06-28 | 2020-09-18 | 重庆大学 | SAR image speckle reduction method based on non-convex weighted sparse constraint |
| CN107301632A (en) * | 2017-06-28 | 2017-10-27 | 重庆大学 | A kind of SAR image method for reducing speckle represented based on sequence joint sparse |
| CN107301629A (en) * | 2017-06-28 | 2017-10-27 | 重庆大学 | A kind of image reconstructing method represented based on transform domain joint sparse |
| CN107330950A (en) * | 2017-06-28 | 2017-11-07 | 重庆大学 | A kind of MRI image reconstructing method based on non local singular value decomposition with estimation |
| CN109146797B (en) * | 2018-06-15 | 2019-10-25 | 闽南师范大学 | A kind of impulsive noise ancient book image inpainting method sparse based on Lp pseudonorm and overlapping group |
| CN109816613B (en) * | 2019-02-28 | 2023-02-28 | 广州方硅信息技术有限公司 | Image completion method and device |
| CN110267049B (en) * | 2019-05-30 | 2021-09-07 | 西安交通大学 | Storage optimization method for sparse coding |
| CN113570497A (en) * | 2021-02-04 | 2021-10-29 | 腾讯科技（深圳）有限公司 | Image processing method, image processing device, computer equipment and storage medium |
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