CN107451961A - The restoration methods of picture rich in detail under several fuzzy noise images - Google Patents
The restoration methods of picture rich in detail under several fuzzy noise images Download PDFInfo
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Abstract
A kind of restoration methods of picture rich in detail under several fuzzy noise images are claimed in the present invention; belong to fuzzy and noise image the method for reconstructing of true nature circle; research finds that fuzzy core and picture rich in detail all have rarefaction representation form in number of domains, and organize sparse domain has more preferable rarefaction representation form by exploring local and non-local information.The present invention is solved by using this of fuzzy core and picture rich in detail feature tectonic syntaxis optimization method by respective algorithms.By showing that the algorithm performance of proposition is more superior to algorithm progress theory analysis and simulation analysis of computer, there is good application prospect in the fields such as signal transacting, image procossing.
Description
Technical field
Fuzzy and noise algorithm is removed for realistic blur noise image the invention belongs to a kind of, is specially that several are fuzzy
By exploring the openness of fuzzy core and picture rich in detail under image, realize and recover to obtain while picture rich in detail for fuzzy core essence
The method really estimated.
Background technology
Image deblurring is the classical problem in image restoration technology, has been carried out extensively both at home and abroad for the problem all
More related technical research.The diversity of natural image causes image deblurring processing work to become relative difficulty, due to fuzzy
The complexity of image degradation process, image degradation model is established generally according to objective hypothesis constraints.At present, it is widely recognized as
Primary image degradation model be represented by, the convolution of picture rich in detail and degenrate function (point spread function) adds the shadow of noise
Ring.Image deblurring handles the inverse process that can regard this computing as.According to the acquisition situation of priori, at image deblurring
Reason can be divided into non-blind processing and blind processing.Non-blind processing is in feelings known to fuzzy core or image degradation model priori
, it is necessary to recover original image in blurred picture from, conventional method has Wiener filtering and Richardson- under condition
Lucy (RL) regularization algorithm, but its restoration result can produce serious ringing effect.But when actually restoring, and it is impossible
Know in advance and grasp so much knowledge on image degradation model, so the restored image effect that this algorithm obtains can not also allow
People is satisfied with.In real life, people are really it is desirable that special by combining existing image to the blurred picture observed
Knowledge is levied, fuzzy core and the priori of noise is made full use of, recovers the process of original image, the process i.e. Image Blind
The basic thought and essential meaning of processing.
Fergus in 2006[1]Spatial domain prior model is based on etc. one kind is proposed, PSF can be effectively estimated and remove multiple
Miscellaneous camera shake faintly method, but only with RL deconvolution reconstruction images, ringing effect is notable in restoration result.Go into business within 2007
Jia Ya[2]Propose a kind of new method that PSF is estimated with images transparent degree figure.Shan in 2008[3]Propose a kind of PSF estimation with
The blind restoration method that image restoration is carried out simultaneously, works well.And Joshi[4]With Cho and Lee[5]Deng then taking simplified Gauss first
Model is tested by the prediction to image clearly border, carrys out ambiguous estimation core, it is possible to achieve rapid solving, but influence of noise is excessive.
Levin[6]Existing deconvolution deblurring algorithm is summarized, has been drawn with Maximun Posterior Probability Estimation Method (Maximum a
Posteriori, MAP) while solve the problems, such as that fuzzy core and hidden image are insecure conclusions, it is proposed that it is general with maximum a posteriori
The method of the independent ambiguous estimation core of rate method.Li Xu in 2010[7]It is based on selecting that there is informedness border and ISD Deng proposition one kind
The initialization of fuzzy core and the detailed structure extraction of fuzzy core are separated progress, carried by the fuzzy core algorithm for estimating of algorithm, this method
More real fuzzy core is taken out.Hui Ji[8]Gone Deng a kind of image more sane in the case where fuzzy core has error condition of proposition
Blur method, while ambiguous estimation core and recover image, achieve better effects.Yuan in 2008[9]It is a kind of referred to as gradually Deng proposition
Between the yardstick entered and yardstick in non-blind image deconvolution method.They utilize Fergus in 2006 method ambiguous estimation image
PSF, devise a non-blind deconvolution method of the multiple dimensioned iteration that can effectively reduce ring distortion in de-blurred image.2009
Year Joshi[10]Noise is removed Deng local double-colored priori is combined, this method uses iteration weighted least-squares method solution by no means
Linear most effectiveization problem.Uwe Schmidt in 2011[11]Propose a kind of non-blind based on the sampling of Bayes's least mean-square error
The algorithm of noise and hidden image is estimated in deconvolution, obtains preferable effect.In the last few years, rarefaction representation was in image processing field
In it is more and more popular, it has what can not be despised in fields such as image repair, image noise reduction, super-resolution rebuilding, pattern-recognitions
Status.Zhang Jian in 2014[12]Etc. a kind of base unit represented by the use of structure group as image sparse is proposed, structure group is established
Sparse representation model solve the problems, such as image restoration, achieve good effect.
The content of the invention
Present invention seek to address that above problem of the prior art.Propose a kind of several moulds for obtaining more preferable recovery effect
Paste the restoration methods of picture rich in detail under noise image.Technical scheme is as follows：
The restoration methods of picture rich in detail under several a kind of fuzzy noise images, it comprises the following steps：
1) several observation blurred pictures Y, is obtainedl, construct following optimization method formula：
Wherein wlWeight coefficient is represented, | | | |1L1 norms are represented, for constraining sparse solution, HlRepresent fuzzy nuclear matrix, ax、
aHlRepresent picture rich in detail X and fuzzy core matrix HlRarefaction representation, λ, βiL1 norm constraint coefficients are represented, then image recovers
Problem has reformed into solution ax, aHlThe problem of；
2), structural matrix DxAnd DHl, DxRepresent the picture rich in detail X sparse domain of group, matrix DHlRepresent the group of fuzzy nuclear matrix
Sparse domain, for Dx DHlConstruction using the method for dictionary learning, then formula (3) can be to be expressed as：
WhereinFor representing the sparse form of group；
3), iteration renewal determines weight coefficient wl；Determine the similar block in picture rich in detail X and fuzzy the nuclear matrix sparse domain of group
To determine match block；
4), using the optimization method of the graceful iterative algorithm iterative step 2) of SBI separate type Donald Braggs, fuzzy nuclear moment is obtained
Battle arrayBe restored image.
Further, several observation blurred pictures Yl=HlX+Nl, l=1,2 ..., L (2), wherein Yl, X, NlRespectively
Represent yl, x, nlColumn vector form, yl=hl*x+nl, l=1,2 ..., L (1) wherein ylThe damaged image captured is represented,
hlUnknown fuzzy core is represented, different subscripts represents different fuzzy cores, nlGaussian noise is represented, L represents the image of capture
Quantity, HlRepresent fuzzy nuclear matrix.
Further, step 3) the weight coefficient wlSelection specifically include：
Weight coefficient is defined as：
WhereinThe estimation of fuzzy core and picture rich in detail is represented respectively, and ε is expressed as avoiding dividend from setting for 0
A very little numerical value, therefore, in kth iteration, weight coefficient is updated to：
WhereinThe estimation of fuzzy core and picture rich in detail in kth time iteration is illustrated respectively in, weight coefficient
It is initialized as unit 1.
Further, the similar block is expressed as by Euclidean distance：
Wherein x represents object block, introduces Lp norms as distance measure, is expressed as：
In order to eliminate the influence of noise, noise variance is introduced into, and then Lp norms distance modification is：
Wherein, s represents the standard variance of x in sample sequence.
Further, as p=2, Mahalanobis generalised distance has just been simplified to, has been calculated by equation below:
Wherein N represents the length of sample ordered series of numbers,Represent the average value of sample ordered series of numbers, xiRepresent sample number column element.
Further, the SBI algorithms are for solving following problem：
SBI represents the norm equation on variable u solving variable u therein, v, f (u) in a manner of loop iteration,
Norm equation of g (v) expressions on variable v, the relational expression between G expression variables u, v, specific solution procedure are as follows：
Represent two
Individual extension Lagrangian；bk+1Kth+1
The error residue of secondary iteration, obtained by the soft-decision thresholding of componentwise, solution draws paste nuclear matrix Obtain extensive
Complex pattern.
Advantages of the present invention and have the beneficial effect that：
The dictionary that tradition carries out rarefaction representation acquisition by fixed transform domain lacks adaptivity, in some cases very
Hardly possible obtains more preferable sparse characteristic.The dictionary of adaptive learning acquisition can be carried out using signal own characteristic on rarefaction representation
Advantageously.Traditional method that rarefaction representation is carried out using image block as base unit, although adaptive dictionary can be obtained,
But the process for establishing dictionary is complicated and amount of calculation is huge, and during sparse coding, each image block is taken as one
Individual independent object considers, have ignored existing similitude between image block, and the sparse coding coefficient for causing to obtain not is very
Accurately.In the present invention, the image sparse sparse based on group of foundation represents that model replaces passing using image group structure as base unit
The image block of system, learn to obtain its adaptive dictionary for each image group structure, existed using fuzzy core and original image
The sparse characteristic in the sparse domain of group, tectonic syntaxis Estimation Optimization equation, while realizing that elimination is fuzzy, obtains estimating fuzzy core
Meter, and obtain most accurately solving by iterative algorithm, in the case where fully preserving image detail, blurred picture is answered
It is former.
The present invention is organizing the sparse characteristic in sparse domain, structure on the basis of existing technology, using fuzzy core and original image
Combined estimator optimization method formula is made, while realizing that elimination is fuzzy, obtains the estimation to fuzzy core, and obtain by iterative algorithm
Most accurate solution, in the case where fully preserving image detail, restores to blurred picture, preferably restores effect to obtain
Fruit.
Brief description of the drawings
Fig. 1 is the shadow for proposing Lp norm difference values when match block selects in algorithm that the present invention provides preferred embodiment
Ring.
Fig. 2 proposes that (2a-2c is respectively original image to recovery effects of the algorithm in emulating image, and two width are different fuzzy
The recovery effects of image and proposed algorithm).
Fig. 3 proposes repairing effect of the algorithm for realistic blur image.
Fig. 4 image degradations and restoration model.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, detailed
Carefully describe.Described embodiment is only the part of the embodiment of the present invention.
The present invention solve above-mentioned technical problem technical scheme be：
Known signal model is as follows：
yl=hl*x+nl, l=1,2 ..., L (1)
Wherein ylRepresent the damaged image captured, hlUnknown fuzzy core is represented, different subscripts may represent difference
Fuzzy core, nlGaussian noise is represented, L represents the amount of images of capture.
It is expressed as with column vector form：
Yl=Hl X+Nl, l=1,2 ..., L (2)
Wherein Yl, X, NlY is represented respectivelyl, x, nlColumn vector form, HlRepresent fuzzy nuclear matrix.Image
That recovers aims in the case where fuzzy core is unknown, from several observation blurred pictures YlMiddle acquisition is potential clear
Clear image.
In the present invention, in order to realize blind image deconvolution, a joint obscures the method that kernel estimates recover with picture rich in detail
It is suggested.
Inspired by this, construct following optimization method formula：
Wherein wlWeight coefficient is represented, will hereinafter be solved, | | | |1L1 norms are represented, for constraining sparse solution,
ax,Represent picture rich in detail X and fuzzy core matrix HlRarefaction representation, then image recover the problem of reformed into solution ax,The problem of.
According to signal reconstruction rule, in order to obtain rarefaction representation, it is necessary to known transition domain, then matrix Dx,It is used to
The sparse domain of expression group respectively, then above formula can be to be expressed as：
WhereinFor representing the sparse form of group.
Observation finds that optimization method formula is on two variable ax,Non-convex optimization equation, in order to effectively solve this
Problem, the method for a two step iteration are suggested：
The first step：Fuzzy core is initialized, solves equation below：
WhereinRepresent the fuzzy nuclear matrix of initialization or estimation.
Second step：The result estimated using the first step, solve equation below：
WhereinRepresent the picture rich in detail estimated in the first step.
Loop iteration, which is known, between the first step and second step meets stop condition.
The embodiment of above-mentioned fuzzy noise image deblurring and Noise Algorithm is specifically described below.
2.1：Weight coefficient wlSelection：
Weight coefficient wlPurpose be to weigh the minimum variance of data distortion again, and then improve fuzzy core and clearly scheme
The estimation of picture, therefore weight coefficient should be inversely proportional with data distortion, then weight coefficient is defined as：
WhereinRepresent the estimation of fuzzy core and picture rich in detail respectively, ε represent to avoid dividend from being 0 one is very
Small numerical value.It is to recover problem for solving image due to going that, in constantly iterative process, it is meant that weight coefficient needs
To be continuously updated with each iteration, therefore, in kth iteration, weight coefficient is updated to：
WhereinIt is illustrated respectively in the estimation of fuzzy core and picture rich in detail in kth time iteration.It is noticeable
It is that the initialization of weight coefficient should be unit 1.
2.2：The searching of similar block：
The sparse domain of group used in the present invention, a method is provided to explore the part of image and non-local information,
The sparse domain of group is sufficiently learnt in units of group, and each group is formed by many similar block common combinations.Therefore, in group
In sparse, the searching of the similar block to match with object block is just particularly important.For purposes of simplicity, similar block is several by Europe
In distance determine, be expressed as：
Wherein x represents object block.In the present invention, in order to increase the robustness that matching selects soon, spy introduces Lp norms and made
For distance measure, it is expressed as：
Obviously, as p=2, just it is reduced to Euclidean distance.Furthermore, it is contemplated that the influence of noise may seriously be broken
The result that bad match block is found, in order to eliminate the influence of noise, noise variance is introduced into, and then Lp norms distance modification is：
As p=2, change has been simplified to Mahalanobis generalised distance, wherein, s represents x in sample sequencei, yiStandard side
Difference, it is calculated by equation below:
2.3：Algorithm for Solving：
Next it is the solution to algorithm optimization equation (4) with the determination that weight coefficient and match block select.In order to
Effectively solves above-mentioned optimization method, SBI algorithms are introduced into, and SBI algorithms are for solving following problem：
For SBI solving variable u, v therein in a manner of loop iteration, specific solution procedure is as follows：
TABLE I:Steps of SBI algorithm.
Wherein,
Represent two extension Lagrangians.
In order to utilize SBI algorithms, formula (5) (6) can be rewritten respectively to be done：
The first step：
Second step：
Obtained with SBI Algorithm for Solving:
The first step：For picture rich in detail：
Second step：Nuclear matrix is obscured for each：
Observation finds that formula (16) (17) has similar structure, is the solution of two word problems of u and a, then, I
Solved by taking (16) as an example, the solution for (17) is identical.
U subproblems in observation discovery formula (16) are actually the minimum variance optimization under a L2 norm constraint
Problem, it is easy to which the approximate form for trying to achieve solution is：
Wherein,It is worth noting that, in order to simplify the mark of the iteration in above formula
It is omitted.
For obtaining a subproblems in (16), if DXIt is a traditional sparse domain, such as wavelet field, tight wavelet field, this is excellent
Change problem can be to solve well by simple threshold judgement, but organizes the sparse domain D of group under rarefaction representationXIt is complicated
, it is multiple, it is impossible to threshold judgement to be applied directly to all groups, but once equation is set up in each iteration：
Wherein, Represent GiThe sparse domain of group of group, on this basis, for axSolution
Can be by being obtained for independent solve under each group, i.e.,：
Solving for above formula can be obtained by the soft-decision thresholding of componentwise, i.e.,：
Wherein, soft-decision thresholding T is defined as:
Optimization problem independent utility is to all groups in formula (20), and axSolution with cross combine it is allObtain
.
By formula (18) (21), the first step is effectively solved, and same process is used for solving second step.It is whole to calculate
The structure of method is given in the table below:
TABLE II:The proposed algorithm.
It is worth noting that, when the second step in upper table solves fuzzy nuclear matrix, the change in formula (18) (21)
Amount, which should substitute, changes fuzzy nuclear matrix accordingly
The above embodiment is interpreted as being merely to illustrate the present invention rather than limited the scope of the invention.
After the content for having read the record of the present invention, technical staff can make various changes or modifications to the present invention, these equivalent changes
Change and modification equally falls into the scope of the claims in the present invention.
Claims (6)
1. the restoration methods of picture rich in detail under several a kind of fuzzy noise images, it is characterised in that comprise the following steps：
1) several observation blurred pictures Y, is obtainedl, construct following optimization method formula：
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Wherein wlWeight coefficient is represented, | | | |1L1 norms are represented, for constraining sparse solution, HlRepresent fuzzy nuclear matrix, ax、Table
Show picture rich in detail X and fuzzy core matrix HlRarefaction representation, λ, βiL1 norm constraint coefficients are represented, then the problem of image recovery
Solution a is reformed intox,The problem of；
2), structural matrix DxAndDxRepresent the picture rich in detail X sparse domain of group, matrixRepresent that the group of fuzzy nuclear matrix is dilute
Domain is dredged, forConstruction using the method for dictionary learning, then formula (3) can be to be expressed as：
WhereinFor representing the sparse form of group；
3), iteration renewal determines weight coefficient wl；Determine picture rich in detail X and fuzzy the nuclear matrix similar block in the sparse domain of group with true
Determine match block；
4), using the optimization method of the graceful iterative algorithm iterative step 2) of SBI separate type Donald Braggs, fuzzy nuclear matrix is obtainedBe restored image.
2. the restoration methods of picture rich in detail under several fuzzy noise images according to claim 1, it is characterised in that described
Several observation blurred pictures Yl=HlX+Nl, l=1,2 ..., L (2), wherein Yl, X, NlY is represented respectivelyl, x, nlColumn vector shape
Formula, yl=hl*x+nl, l=1,2 ..., L (1) wherein ylRepresent the damaged image captured, hlUnknown fuzzy core is represented, no
Same subscript represents different fuzzy cores, nlGaussian noise is represented, L represents the amount of images of capture, HlRepresent fuzzy nuclear moment
Battle array.
3. the restoration methods of picture rich in detail under several fuzzy noise images according to claim 1 or 2, it is characterised in that
Step 3) the weight coefficient wlSelection specifically include：
Weight coefficient is defined as：
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4. the restoration methods of picture rich in detail under several fuzzy noise images according to claim 3, it is characterised in that described
Similar block is expressed as by Euclidean distance：
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Wherein x represents object block, introduces Lp norms as distance measure, is expressed as：
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In order to eliminate the influence of noise, noise variance is introduced into, and then Lp norms distance modification is：
<mrow>
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mfrac>
<mrow>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mi>p</mi>
</msup>
</mrow>
<msup>
<mi>s</mi>
<mi>p</mi>
</msup>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, s represents the standard variance of x in sample sequence.
5. the restoration methods of picture rich in detail under several fuzzy noise images according to claim 4, it is characterised in that work as p
When=2, Mahalanobis generalised distance has just been simplified to, has been calculated by equation below:
<mrow>
<mi>s</mi>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein N represents the length of sample ordered series of numbers,Represent the average value of sample ordered series of numbers, xiRepresent sample number column element.
6. the restoration methods of picture rich in detail under several fuzzy noise images according to claim 4, it is characterised in that described
SBI algorithms are for solving following problem：
<mrow>
<mtable>
<mtr>
<mtd>
<munder>
<mi>min</mi>
<mrow>
<mi>u</mi>
<mo>&Element;</mo>
<msup>
<mi>R</mi>
<mi>N</mi>
</msup>
<mo>,</mo>
<mi>v</mi>
<mo>&Element;</mo>
<msup>
<mi>R</mi>
<mi>N</mi>
</msup>
</mrow>
</munder>
</mtd>
<mtd>
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>s</mi>
<mo>.</mo>
<mi>t</mi>
<mo>.</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>u</mi>
<mo>=</mo>
<mi>G</mi>
<mi>v</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
SBI represents the norm equation on variable u, g (v) solving variable u therein, v, f (u) in a manner of loop iteration
Norm equation of the expression on variable v, the relational expression between G expression variables u, v, specific solution procedure are as follows：
Represent two expansions
Open up Lagrangian；bk+1Kth+1 time is repeatedly
The error residue in generation, obtained by the soft-decision thresholding of componentwise, solution draws paste nuclear matrix Be restored figure
Picture.
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| CN113487491B (en) * | 2021-05-26 | 2024-04-26 | 辽宁工程技术大学 | Image restoration method based on sparsity and non-local mean self-similarity |
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