CN105551000B - Remote sensing images method for reconstructing based on the constraint of reference image and the constraint of non-convex low-rank - Google Patents
Remote sensing images method for reconstructing based on the constraint of reference image and the constraint of non-convex low-rank Download PDFInfo
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Abstract
The invention discloses a kind of remote sensing images method for reconstructing constrained based on the constraint of reference image structure and non-convex low-rank, include the following steps: to initially set up target image constraint similar with structure of the reference image after high-grade filting, then replaces compressed sensing with non-convex low-rank appropriate constraintsNorm carrys out constrained objective image sparse coefficient, establishes the sparse optimized reconstruction model of remote sensing images and solves.The invention has the benefit that using the high-order structures feature vector of reference image as prior-constrained, it is constrained the non-convex low-rank nuclear norm of broad sense as target image sparse coefficient, image reconstruction model is established using the two complementary advantage, improves the reconstruction precision of target image.
Description
Technical field
The present invention relates to the signal reconstruction methods of multi-source Remote Sensing Images data, it particularly relates to a kind of based on reference to shadow
As the remote sensing images method for reconstructing of constraint and the constraint of non-convex low-rank.
Background technique
In remote sensing fields, the same area generally comprises the image of multi-source, multidate, these remote sensing images have different light
Spectral property, temporal resolution and spatial resolution.In some remote sensing applications, we only have some observed images, can not obtain
The original image of a certain area sometime needs the method by reconstruction if we need the information of these original images
To carry out remote sensing images reconstruction.Redundancy of the corresponding remote sensing image in spatial position on spectrum and time scale facilitates weight
It builds.The different sensors carried in same satellite have spectra overlapping or similar Object reflection to each other, cause to shoot
Image exist very big similitude.Simultaneously as the migration of ground terrestrial object information is slow, the different historical junctures are shot same
The image of position also has very big similitude.Their this similitude be embodied in structure it is similar on, i.e., the side in image
The detailed information such as edge, profile.The structure change feature of these multi-source Remote Sensing Images is sparse as being added to reference to constraint information
The reconstruction precision of target image can be improved in the reconstruction process of restricted coefficients of equation and target image.
The typical method for extracting structural information is use direction filter, such as gradient operator, Gabor filter.But it uses
There should be maximum universality in the filter for extracting structural information, that is, be generally applicable to various images.Meet this requirement
Theory be independent component analysis, it can separate different picture materials by extracting the structural information of image, while can
Train the filter for projective transformation.Expert based on independent component analysis thought and high-order Markov random field theory
Field model has trained two groups of filters by extracting 20,000 width image patch from Berkeley partitioned data set, is 8 respectively
The filter of the filter of a 3x3 and 24 5x5, shows universality.Compared to other filters, these filters have reason
By support, structural information can be preferably extracted.
It is using the structural information of remote sensing image as the main deficiency for being injected into reconstruction image with reference to constraint information merely: note
Enter process be it is indiscriminate, can not accurately portray each partial structurtes of spectrum picture, ignore sparse coefficient correlation, can not
The local degree of rarefication of picture engraving introduces the problems such as Gibbs' effect.It is approached based on the sparse low-rank of group and is solved with non-convex expression
It has determined and general rarefaction representation and has been introduced as these problems existing for remote sensing images algorithm for reconstructing with reference to constraint information, it can be to avoid
With reference to the excessive injection of constraint information, keep the marginal texture information of injection more reasonable, obtains more preferably remote sensing image grain details
Restore.
For the problems in the relevant technologies, currently no effective solution has been proposed.
Summary of the invention
For above-mentioned technical problem in the related technology, the present invention proposes a kind of based on reference to image constraint and non-convex low-rank
The remote sensing images method for reconstructing of constraint.
To realize the above-mentioned technical purpose, the technical scheme of the present invention is realized as follows:
A kind of remote sensing images method for reconstructing based on the constraint of reference image and the constraint of non-convex low-rank, includes the following steps:
It includes following steps: target image constraint similar with structure of the reference image after high-grade filting is initially set up, then with non-convex low
Order appropriate constraints replace the l of compressed sensing1Norm carrys out constrained objective image sparse coefficient, establishes the sparse optimized reconstruction of remote sensing images
Model simultaneously solves.
Further, two-dimensional filtering is done to reference picture using the expert filter group that one group of size is 5x5 or 3x3,
The sparse coefficient of the reference image to match with target image is calculated, with target image and with reference to the expert filter factor of image
It is similar to be used as constraint condition.
Further, with non-convex low-rank nuclear norm constrained objective image sparse coefficient, after expert filter filtering
Coefficient is similar to be added in the sparse coefficient of target image, and objective function is constructed.
Further, band target image is iteratively solved by conjugate gradient algorithms, Taylor's first approximation and singular value decomposition
The non local image reconstruction model of low-rank prior information.
Further, the mean value and standard deviation that reference picture is updated using match by moment method, keep it consistent with reconstruction image.
Further, structural information is extracted using higher order filter, used filter is divided from Berkeley
20000 width image patch are extracted in data set and are trained to obtain by expert's field model.
Further, when obtaining low-rank similar matrix, the positional relationship of used similar image block matrix is from reference
It is obtained in image.
Further, with non-convex low-rank nuclear norm constrained objective image sparse coefficient, similarity is added to target image
Sparse coefficient in be updated, construct the objective function of reconstruction model:
Wherein, first item guarantees that reconstructed results and observation data keep matching constraint in model；Section 2 is high-grade filting
The structural constraint item of coefficient, HkTo be indicated with the matrix operation of k-th of filter filtering process equivalence, λkTo be filtered for k-th
The Regularization adjustment factor of device；Section 3 is that image carries out the sparse regular terms with the constraint of similar block low-rank of group, and λ indicates image
The sparse level of block, η indicate the weight of image block similarity degree fitting.
Beneficial effects of the present invention: the present invention can will be obtained with reference to image and reconstruction image through expert filter filtering
Sparse coefficient it is similar as prior-constrained, constrained the non-convex low-rank nuclear norm of broad sense as target image sparse coefficient, utilization
The two complementary advantage establishes remote sensing images reconstruction model, improves the reconstruction precision of target image.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention
Example, for those of ordinary skill in the art, without creative efforts, can also obtain according to these attached drawings
Obtain other attached drawings.
Fig. 1 is the remote sensing images weight based on the constraint of reference image and the constraint of non-convex low-rank described according to embodiments of the present invention
The operating procedure block diagram of construction method；
Fig. 2 is the remote sensing images weight based on the constraint of reference image and the constraint of non-convex low-rank described according to embodiments of the present invention
The flow chart of construction method.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art's every other embodiment obtained belong to what the present invention protected
Range.
As shown in Figure 1, a kind of based on the constraint of reference image and the constraint of non-convex low-rank described according to embodiments of the present invention
Remote sensing images method for reconstructing, includes the following steps:
Step 1 carries out at two-dimensional filtering reference image using the expert filter group that one group of size is 5x5 or 3x3
Reason calculates the sparse coefficient of the reference image to match with target image, and with target image and with reference to the sparse system of image
Number is similar to be used as constraint condition；
Step 2 constructs the objective function of reconstruction model, wherein utilizes the dilute of non-convex low-rank nuclear norm constrained objective image
The sparse coefficient that image is referred to obtained in step 1 is added in the sparse coefficient of target image to construct and rebuild by sparse coefficient
The objective function of model；
It is low to iteratively solve band target image by conjugate gradient algorithms, Taylor's first approximation and singular value decomposition for step 3
The non local image reconstruction model of order prior information；
Step 4 is updated the mean value and standard deviation for referring to image by match by moment method, keeps it consistent with reconstruction image；
Step 5, iteration execute step 1 to step 4.
Wherein, in step 1, using higher order filter extract structural information, used filter be from
It extracts 20000 width image patch in Berkeley partitioned data set and is trained by expert's field model, the target
The similarity of the structural eigenvector of the structural eigenvector and reference image of image is after higher order filter filtering with l2Model
Several forms carries out cost evaluation.
In step 2, during constructing objective function, similar image block square used in low-rank similar matrix is obtained
The positional relationship of battle array in reference image by obtaining.
The objective function of the reconstruction model constructed in step 2 are as follows:
Wherein, first item guarantees that reconstructed results and observation data keep matching constraint in model；Section 2 is high-grade filting
The structural constraint item of coefficient, HkTo be indicated with the matrix operation of k-th of filter filtering process equivalence, λkTo be filtered for k-th
The Regularization adjustment factor of device；Section 3 is that image carries out the sparse regular terms with the constraint of similar block low-rank of group, and λ indicates image
The sparse level of block, η indicate the weight of image block similarity degree fitting.
The non-convex function of similar block in solution procedure three, and with conjugate gradient algorithms, local minimum Taylor's first approximation
The objective function constrained with non-convex G-function prior information is iteratively solved with singular value decomposition algorithm.
In step 4, the mean value and standard deviation for referring to image are updated using match by moment method, keeps it consistent with reconstruction image.
The number of iterations of the step of mentioning in step 5 one to step 4 is 2 or 3 times, and final result can be obtained.
The expert filter that the expert filter is one group of 5x5 or 3x3.
In order to facilitate understanding above-mentioned technical proposal of the invention, below by way of in specifically used mode to of the invention above-mentioned
Technical solution is described in detail.
When specifically used, the remote sensing images according to the present invention based on the constraint of reference image and the constraint of non-convex low-rank
Method for reconstructing on each picture position, extracts image similar with current block first against reference picture in its neighborhood
Block matrix marks the position, and the labeling process is converted to matrix to indicate；
The common constraint with reference picture structural information phase Sihe observation item fidelity is established, solving with conjugate gradient algorithms should
Constraint, acquires preliminary reconstruction image；
Foundation extracts extraction process used in similar block matrix on a reference, on the image after step 1 reconstruction
It extracts and the identical non local similar block matrix of the non local analogous location relationship of reference picture；
The sparsity of the matrix is constrained using non-convex low-rank nuclear norm, and uses Taylor's first approximation and soft-threshold singular value
Decomposition acquires low-rank matrix corresponding with the similar block matrix；
The common constraint with low-rank matrix phase Sihe observation item fidelity is established, the constraint is solved with conjugate gradient algorithms, asks
Obtain the reconstruction image of single iteration；
Reference picture is corrected using match by moment method, keeps its mean value and standard deviation consistent with reconstruction image；
When not obtaining result, the common constraint with reference picture structural information phase Sihe observation item fidelity is re-established,
The constraint is solved with conjugate gradient algorithms, preliminary reconstruction image is acquired, repeats the above steps.
In one embodiment, it is achieved by the steps of:
1, on reference image, it is assumed that one piece of sample block at the i of positionSize isIn image
It is middle in other positions to there is much image blocks similar with its.Under this assumption, a thresholding is set, each sample block is carried out
K neighborhood search obtains the low-rank matrix of similar image block composition, and the low-rank prior information structure based on non local similar image block
It builds low-rank and approaches form:
Wherein, T is the threshold value pre-set, xi,Indicate image block, HiIndicate to meet this threshold condition with figure
As block xiThe pixel position index value of similar image block.The process for extracting similar block matrix based on reference picture is represented by square
Battle array operation, with matrix BiIt indicates.
2, it establishes and is constrained as follows for the cost of reconstruction image:
Wherein, X is image to be reconstructed, and Y is observation data, and R is the transformation that can be can be carried out, and M is observing matrix；In model
One guarantee reconstructed results and observation data keep matching constraint；Section 2 is the structural constraint item of high-grade filting coefficient, HkFor
With the matrix operation expression of k-th of filter filtering process equivalence, λkFor the Regularization adjustment factor for k-th of filter.
Above-mentioned constraint can be converted to following least square problem, and be solved using conjugate gradient:
Extract convolutional filtering matrix H used in structural informationkIt can be realized, can be saved interior with the form of filter convolution
It deposits, realizes the processing to larger image.In this specification, filter uses the expert filter that one group of size is 5x5 or 3x3
Group does two-dimensional filtering to reference picture, using target image it is similar to expert's least square of filter factor with reference to image as
Constraint condition.There are three types of situations for the filter of specific choice: 8 3x3 filters, 24 5x5 filters, or uses 8 simultaneously
A 3x3 filter and 24 5x5 filters.
The filter of 8 3x3 sizes:
The filter of 24 5x5 sizes:
3, the similar block position on each position in neighborhood has been extracted according to the structural similarity of reference picture, rebuild
On image, similar block will be put together according to this positional relationship, one can be formed for the similar block on a position
Set, and matrix is expressed as in the form of column vector, obtain similar block matrix
4, similar block matrix XiIt can be corroded by some noises.For preferably reconstruction image, by XiTwo parts are resolved into,
That is Xi=Li+Wi, wherein LiAnd WiIt is low-rank matrix and Gaussian noise respectively.It rewrites as follows:
Wherein rank (Li) representing matrix LiOrder, with matrix LiNon-zero singular value number it is identical；WhereinIt indicates
Fobenius norm,Indicate the variance of additive Gaussian noise.
With the convex approximate norm of non-convex kernel function G approximate matrix order, the following formula is obtained:
E (X, ε)=Gdet (X+ ε I)
Wherein Gdet (X)=θ X, (X >=0), ε are the parameters of a very little.And for general matrix
?Above formula obtains
Wherein Σ isEigenvalue matrix, i.e.,no=min (n, m), σj(Li) indicate LiJth
A singular value, and Σ1/2It is a diagonal matrix, the element on it is diagonal is matrix LiSingular value.
Accordingly, for each similar block matrix Xi, obtain the low-rank prior information building based on non local similar image block
The non-convex low-rank restricted model of broad sense:
Above-mentioned belt restraining inequality is converted into below without constraint equation:
It can be obtained using local minimum Taylor first approximation
The η of τ=λ/2 is defined,The nuclear norm of weight is usedIt indicates, can rewrite as follows:
It is iterating through following formula in (k+1) step threshold process is weighted to singular value decomposition and obtain reconstruction image block:
WhereinIndicate XiSingular value decomposition, (x)+=max { x, 0 }.Although it is not Global optimal solution, it
Locally always make target function value monotone decreasing.
5, with non-convex low-rank nuclear norm constrained objective image, the objective function for being directed to reconstruction image is constructed:
Wherein, first item guarantees that reconstructed results and observation data keep matching constraint in model；Section 2 is image progress
The sparse regular terms with the constraint of similar block low-rank of group, λ indicate the sparse level of image block, and η indicates that image block similarity degree is quasi-
The weight of conjunction, BiIndicate the extraction matrix that similar block matrix is extracted based on reference picture.
Above-mentioned constraint can be converted to following least square problem, and be solved using conjugate gradient:
Wherein, ∑iBi TBiIndicate the quantity of overlapping block on each position, ∑iBi TLiIndicate block average result.
6, the mean value and standard deviation for calculating reconstruction image are respectively μ1And σ1, mean value and the standard deviation difference of reference picture X
For μrefAnd σref, then reference picture X adjusts DN value according to following formula:
G=σ1/σref
B=μ1-g·μref
X=gX+b
7, step 2 needs iterative processing to step 6, and iteration need to execute 2 to 3 times altogether, that is, can converge to final result.
In conclusion carrying out constrained objective shadow in the texture information with reference to image by means of above-mentioned technical proposal of the invention
As on the basis of, a kind of remote sensing images method for reconstructing based on the constraint of reference image texture and the non-convex low-rank constraint of broad sense is proposed,
By using for reference human visual system to the treatment process of image, calculating target image and reference image texture first is in wavelet coefficient
In statistical nature, corresponding feature vector is constructed respectively, with the building of the similarity degree of feature vector with reference to constraint, then with non-convex
Low-rank appropriate constraints replace the sparse coefficient of the L1 norm constraint target image of compressed sensing, establish the sparse optimization weight of remote sensing images
Established model simultaneously solves, and can efficiently reduce sampled data, improves the precision of reconstructed image.
Specifically, the embodiment of the present invention is based on reference picture texture constraint and the non-convex kernel function low-rank of broad sense is constrained and changed
It establishes in the remote sensing images algorithm for reconstructing method that generation solves based on the non local similar image block low-rank prior information of reference image
Data reconstruction mathematical model, it is first based on band low-rank using the iterative solution of conjugate gradient method, Taylor's first approximation and singular value decomposition
The non-convex kernel function of broad sense for testing the low-rank matrix of the non local iconic model of information, obtains similar image block.The present invention have compared with
Strong texture structure holding capacity, while comparison and other methods, experiment also indicate that proposed method can be in less survey
Remote sensing image is more accurately rebuild under amount, is reduced the artifact of reconstructed image, is more rationally restored the texture structure of remote sensing images.
The present invention proposes a kind of remote sensing images reconstruction side based on the constraint of reference image structure and the non-convex low-rank constraint of broad sense
Method, by using for reference human visual system to the treatment process of image, calculating target image and reference image texture first is through special
Statistical nature after family's field filter filtering, constructs corresponding feature vector respectively, constructs ginseng with the similarity degree of feature vector
Constraint is examined, then replaces the l of compressed sensing with non-convex nuclear norm appropriate constraints1The sparse coefficient of norm constraint target image is established
The sparse optimized reconstruction model of remote sensing images simultaneously solves, and can efficiently reduce sampled data, improve the precision of reconstructed image.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Within mind and principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (4)
1. a kind of remote sensing images method for reconstructing based on the constraint of reference image and the constraint of non-convex low-rank, which is characterized in that including such as
Lower step: initially setting up target image constraint similar with structure of the reference image after high-grade filting, then close with non-convex low-rank
The l of compressed sensing is replaced like constraint1Norm carrys out constrained objective image sparse coefficient, establishes the sparse optimized reconstruction model of remote sensing images
And it solves；Wherein, two-dimensional filtering is done to reference picture using expert's filter group that one group of size is 5x5 or 3x3, calculate with
The sparse coefficient for the reference image that target image matches, with target image work similar to the expert filter factor with reference to image
For constraint condition；With non-convex low-rank nuclear norm constrained objective image sparse coefficient, by the coefficient phase after expert filter filtering
It is seemingly added in the sparse coefficient of target image, constructs objective function；Pass through conjugate gradient algorithms, Taylor's first approximation and unusual
It is worth Decomposition iteration and solves the non local image reconstruction model with target image low-rank prior information, wherein with non-convex low-rank core model
Number constrained objective image sparse coefficient, similarity is added in the sparse coefficient of target image and is updated, reconstruction is constructed
The objective function of model:
Wherein, first item guarantees that reconstructed results and observation data keep matching constraint in model；Section 2 is high-grade filting coefficient
Structural constraint item, Hk is and the matrix operation of k-th filter filtering process equivalence expression λkFor for k-th of filter
Regularization adjustment factor；Section 3 is that image carries out the sparse regular terms with the constraint of similar block low-rank of group, and λ indicates image block
Sparse level, η indicate image block similarity degree fitting weight.
2. the remote sensing images method for reconstructing according to claim 1 based on the constraint of reference image and the constraint of non-convex low-rank,
It is characterized in that: updating the mean value and standard deviation of reference picture using match by moment method, keep it consistent with reconstruction image.
3. the remote sensing images method for reconstructing according to claim 1 based on the constraint of reference image and the constraint of non-convex low-rank,
It is characterized in that, extracts structural information using higher order filter, used filter is from Berkeley partitioned data set
It extracts 20000 width image patch and is trained to obtain by expert's field model.
4. the remote sensing images method for reconstructing according to claim 1 based on the constraint of reference image and the constraint of non-convex low-rank,
It is characterized in that, when obtaining low-rank similar matrix, the positional relationship of used similar image block matrix is obtained from reference picture
?.
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| CN109102477B (en) * | 2018-08-31 | 2021-08-24 | 哈尔滨工业大学 | Hyperspectral remote sensing image recovery method based on non-convex low-rank sparse constraint |
| CN109658342A (en) * | 2018-10-30 | 2019-04-19 | 中国人民解放军战略支援部队信息工程大学 | The remote sensing image brightness disproportionation variation bearing calibration of double norm mixed constraints and system |
| CN110599466B (en) * | 2019-08-29 | 2022-04-29 | 武汉大学 | Hyperspectral anomaly detection method for component projection optimization separation |
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| CN113034635B (en) * | 2021-03-04 | 2022-08-23 | 重庆不贰科技(集团)有限公司 | Image reconstruction method for inhibiting industrial imaging step artifacts |
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