CN105551000A - Remote sensing image reconstruction method based on reference image structure constraint and non-convex low rank constraint - Google Patents
Remote sensing image reconstruction method based on reference image structure constraint and non-convex low rank constraint 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 constraints
Norm 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 method of multi-source Remote Sensing Images data, specifically, relate to a kind of based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank.
Background technology
At remote sensing fields, the same area comprises the image of multi-source, multidate usually, and these remote sensing images have different spectral characteristics, temporal resolution and spatial resolution.In some remote sensing applications, we only have some observed images, cannot obtain a certain area original image sometime, if we need the information of these original images, need the method by rebuilding to carry out remote sensing images reconstruction.The redundant information of remote sensing image on spectrum and time scale corresponding to locus contributes to rebuilding.The different sensors of carrying in same satellite, has spectra overlapping or similar Object reflection to each other, causes the image of shooting to there is very large similarity.Meanwhile, because the migration of ground terrestrial object information is slow, the image of the same position of different historical juncture shooting also has very large similarity.Their this similarity be embodied in structure similar on, the detailed information such as the edge namely in image, profile.Using the structure variation characteristic of these multi-source Remote Sensing Images as the process of reconstruction joining sparse coefficient constraint and target image with reference to constraint information, the reconstruction precision of target image can be improved.
The typical method extracting structural information uses anisotropic filter, as gradient operator, Gabor filter.But, maximum universality should be had for the wave filter extracting structural information, namely generally be applicable to various image.The theory meeting this requirement is independent component analysis, and it can be separated different picture materials by the structural information extracting image, can train the wave filter for projective transformation simultaneously.Expert's field model based on independent component analysis thought and high-order Markov random field theory extracts 20,000 width image patch trained two groups of wave filters by concentrating from Berkeley partition data, be the wave filter of 8 3x3 and the wave filter of 24 5x5 respectively, show universality.Compare other wave filter, these wave filters have theories integration, can extract structural information better.
Using the structural information of remote sensing image as being injected into the main deficiency of rebuilding image with reference to constraint information be merely: injection process is indiscriminate, accurately cannot portray each partial structurtes of spectrum picture, ignore sparse coefficient correlativity, cannot picture engraving local degree of rarefication, introduce the problems such as Gibbs' effect.Approach to express with non-convex based on the low-rank that cohort is sparse and solve general rarefaction representation and be introduced as these problems that the remote sensing images reconstruction algorithm with reference to constraint information exists, the excessive injection with reference to constraint information can be avoided, make the marginal texture information of injection more reasonable, obtain more excellent remote sensing image grain details and recover.
For the problem in correlation technique, at present effective solution is not yet proposed.
Summary of the invention
For the above-mentioned technical matters in correlation technique, the present invention proposes a kind of based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank.
For realizing above-mentioned technical purpose, technical scheme of the present invention is achieved in that
A kind of based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank, comprise the steps: first to set up target image and the similar constraint of the reference structure of image after high-grade filting, then replace the l of compressed sensing with non-convex low-rank appropriate constraints
1norm carrys out constrained objective image sparse coefficient, sets up the sparse optimized reconstruction model of remote sensing images and solves.
Further, the expert field bank of filters that one group of size is 5x5 or 3x3 is used to do two-dimensional filtering to reference picture, calculate the sparse coefficient of the reference image matched with target image, similar as constraint condition to the expert field filter factor with reference to image using target image.
Further, by non-convex low-rank nuclear norm constrained objective image sparse coefficient, join in the sparse coefficient of target image by similar for the coefficient after the filter filtering of expert field, establishing target function.
Further, by the non local image reconstruction model of conjugate gradient algorithm, Taylor's first approximation and svd iterative band target image low-rank prior imformation.
Further, use match by moment method to upgrade average and the standard deviation of reference picture, make it consistent with reconstruction image.
Further, use higher order filter to extract structural information, its wave filter used concentrates extraction 20000 width image patch from Berkeley partition data and trained by expert's field model to obtain.
Further, when obtaining low-rank similar matrix, the position relationship of used similar image block matrix obtains from reference picture.
Further, by non-convex low-rank nuclear norm constrained objective image sparse coefficient, similarity is joined in the sparse coefficient of target image and upgrades, construct the objective function of reconstruction model:
Wherein, in model, Section 1 ensures that reconstructed results and observation data keep matching constraint; Section 2 is the structural constraint item of high-grade filting coefficient, H
kfor representing with the matrix operation of a kth filter filtering process equivalence, λ
kfor the Regularization adjustment factor for a kth wave filter; Section 3 is the regular terms that image carries out the sparse and similar piece of low-rank constraint of cohort, and λ represents the sparse level of image block, and η represents the weight of image block similarity degree matching.
Beneficial effect of the present invention: the present invention can be similar as prior-constrained using the sparse coefficient obtained through expert field filter filtering with reference to image and reconstruction image, broad sense non-convex low-rank nuclear norm is retrained as target image sparse coefficient, both utilizations complementary advantage sets up remote sensing images reconstruction model, improves the reconstruction precision of target image.
Accompanying drawing explanation
In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.
Fig. 1 is the operation steps block diagram based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank according to the embodiment of the present invention.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, be clearly and completely described the technical scheme in the embodiment of the present invention, obviously, described embodiment is only the present invention's part embodiment, instead of whole embodiments.Based on the embodiment in the present invention, the every other embodiment that those of ordinary skill in the art obtain, all belongs to the scope of protection of the invention.
As shown in Figure 1, a kind of remote sensing images method for reconstructing based on retraining with reference to image structure constraint and non-convex low-rank according to the embodiment of the present invention, comprises the steps:
Step one, the expert field bank of filters that one group of size is 5x5 or 3x3 is used to carry out two-dimensional filtering process to reference to image, calculate the sparse coefficient of the reference image matched with target image, and similar as constraint condition to the sparse coefficient with reference to image using target image;
Step 2, build the objective function of reconstruction model, wherein, utilize the sparse coefficient of non-convex low-rank nuclear norm constrained objective image, the sparse coefficient of the reference image obtained in step one is joined in the sparse coefficient of target image to build the objective function of reconstruction model;
Step 3, by the non local image reconstruction model of conjugate gradient algorithm, Taylor's first approximation and svd iterative band target image low-rank prior imformation;
Step 4, upgrades average and the standard deviation of reference image by match by moment method, make it consistent with reconstruction image;
Step 5, iteration performs step one to step 4.
Wherein, in step, higher order filter is used to extract structural information, its wave filter used is concentrated extraction 20000 width image patch from Berkeley partition data and is trained by expert's field model and obtains, the similarity of the structural eigenvector of described target image and the structural eigenvector with reference to image after this higher order filter filtering with l
2the form of norm carries out cost evaluation.
In step 2, in the process of establishing target function, the position relationship obtaining the similar image block matrix used by low-rank similar matrix obtains by with reference in image.
The objective function of the reconstruction model built in step 2 is:
Wherein, in model, Section 1 ensures that reconstructed results and observation data keep matching constraint; Section 2 is the structural constraint item of high-grade filting coefficient, H
kfor representing with the matrix operation of a kth filter filtering process equivalence, λ
kfor the Regularization adjustment factor for a kth wave filter; Section 3 is the regular terms that image carries out the sparse and similar piece of low-rank constraint of cohort, and λ represents the sparse level of image block, and η represents the weight of image block similarity degree matching.
The non-convex function of similar piece in solution procedure three, and with the objective function of conjugate gradient algorithm, local minimum Taylor first approximation and singular value decomposition algorithm iterative band non-convex G-function prior imformation constraint.
In step 4, use match by moment method to upgrade average and the standard deviation of reference image, make it consistent with reconstruction image.
The step one mentioned in step 5 is 2 or 3 times to the iterations of step 4, can obtain net result.
Described expert field wave filter is the expert field wave filter of one group of 5x5 or 3x3.
Conveniently understand technique scheme of the present invention, below by way of in concrete use-pattern, technique scheme of the present invention is described in detail.
When specifically using, according to of the present invention based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank, first for reference picture, on each picture position, the image block matrix similar to current block is extracted in its neighborhood, mark this position, and this labeling process is converted to matrix representation;
Set up the common constraint observing item fidelity with reference picture structural information phase Sihe, solve this constraint with conjugate gradient algorithm, try to achieve preliminary reconstruction image;
Foundation extracts the leaching process that similar block matrix uses on a reference, and the image after step 1 is rebuild extracts the identical non local similar block matrix of analogous location relation non local to reference picture;
Use non-convex low-rank nuclear norm to retrain the openness of this matrix, and use Taylor's first approximation and soft-threshold svd to try to achieve low-rank matrix corresponding to block matrix similar with this;
Set up the common constraint observing item fidelity with low-rank matrix phase Sihe, solve this constraint with conjugate gradient algorithm, try to achieve the reconstruction image of single iteration;
Use match by moment method correction reference picture, make its average consistent with reconstruction image with standard deviation;
When not obtaining result, re-establishing the common constraint observing item fidelity with reference picture structural information phase Sihe, solving this constraint with conjugate gradient algorithm, try to achieve preliminary reconstruction image, repeat above-mentioned steps.
In one embodiment, realize as follows:
1, with reference on image, one piece of sample block at i place, position is supposed
size is
at a lot of image block similar to it of the upper existence in other position of image.Under this assumption, a thresholding is set, the low-rank matrix that k neighborhood search obtains similar image block composition is carried out to each sample block, and approach form based on the low-rank prior imformation structure low-rank of non local similar image block:
Wherein, T is the threshold value pre-set, x
i,
represent image block, H
irepresent meet this threshold condition with image block x
ithe pixel position index value of similar image block.The process extracting similar block matrix based on reference picture can be expressed as matrix operation, with matrix B
irepresent.
2, set up as follows for the cost constraint of rebuilding image:
Wherein, X is image to be reconstructed, and Y is observation data, and R is the conversion possible carried out, and M is observing matrix; In model, Section 1 ensures that reconstructed results and observation data keep matching constraint; Section 2 is the structural constraint item of high-grade filting coefficient, H
kfor representing with the matrix operation of a kth filter filtering process equivalence, λ
kfor the Regularization adjustment factor for a kth wave filter.
Above-mentioned constraint can be converted to following least square problem, and uses conjugate gradient to solve:
Extract the convolutional filtering matrix H that structural information is used
kcan realize by the form of wave filter convolution, can internal memory be saved, realize the process to larger image.In the application's book, wave filter uses the expert field bank of filters that one group of size is 5x5 or 3x3 to do two-dimensional filtering to reference picture, similar as constraint condition to the least square of the expert field filter factor with reference to image using target image.The wave filter of concrete selection has three kinds of situations: 8 3x3 wave filters, 24 5x5 wave filters, or uses 8 3x3 wave filters and 24 5x5 wave filters simultaneously.
The wave filter of 8 3x3 sizes:
The wave filter of 24 5x5 sizes:
3, the structural similarity of foundation reference picture has extracted similar piece of position on each position in neighborhood, on reconstruction image, according to this position relationship, similar piece will be put together, one can be formed for the similar set of blocks on a position, and be expressed as matrix with the form of column vector, obtain similar block matrix
4, similar block matrix X
ican be corroded by some noises.In order to rebuild image better, by X
iresolve into two parts, i.e. X
i=L
i+ W
i, wherein L
iand W
ilow-rank matrix and Gaussian noise respectively.Rewrite as follows:
Wherein rank (L
i) representing matrix L
iorder, with matrix L
inon-zero singular value number identical; Wherein
represent Fobenius norm,
represent the variance of additive Gaussian noise.
By the convex approximate norm of non-convex kernel function G approximate matrix order, obtain following formula:
E(X，ε)＝Gdet(X+εI)
Wherein Gdet (X)=θ X, (X >=0), ε is a very little parameter.And for general matrix
n≤m,
above formula obtains
Wherein ∑ is
eigenvalue matrix, namely
n
o=min (n, m), σ
j(L
i) represent L
ia jth singular value, and ∑
1/2be a diagonal matrix, the element on its diagonal angle is matrix L
isingular value.
Thus, for each similar block matrix X
i, obtain building broad sense non-convex low-rank restricted model based on the low-rank prior imformation of non local similar image block:
Without constraint equation below above-mentioned belt restraining inequality is converted to:
Local minimum Taylor first approximation is used to obtain
Definition τ=λ/2 η,
the nuclear norm of weight is used
represent, can rewrite as follows:
(k+1) step be iterating through following formula to svd be weighted threshold process obtain rebuild image block:
Wherein
represent X
isvd, (x)
+=max{x, 0}.Although it is not Global optimal solution, it always makes target function value monotone decreasing in local.
5, with non-convex low-rank nuclear norm constrained objective image, the objective function for rebuilding image is built:
Wherein, in model, Section 1 ensures that reconstructed results and observation data keep matching constraint; Section 2 is the regular terms that image carries out the sparse and similar piece of low-rank constraint of cohort, and λ represents the sparse level of image block, and η represents the weight of image block similarity degree matching, B
irepresent the extraction matrix extracting similar block matrix based on reference picture.
Above-mentioned constraint can be converted to following least square problem, and uses conjugate gradient to solve:
(R
TM
TMR+η∑
iB
i TB
i)X
(t)＝R
TM
TY+η∑
iB
i TL
i
Wherein, ∑
ib
i tb
irepresent the quantity of overlapping block on each position, ∑
ib
i tl
irepresent block average result.
6, the average and the standard deviation that calculate reconstruction image are respectively μ
1and σ
1, average and the standard deviation of reference picture X are respectively μ
refand σ
ref, then reference picture X is according to formula adjustment DN value below:
g＝σ
1/σ
ref
b＝μ
1-g·μ
ref
X＝g·X+b
7, the 2nd step needs iterative processing to the 6th step, and iteration need perform 2 to 3 times altogether, namely can converge to net result.
In sum, by means of technique scheme of the present invention, come on the basis of constrained objective image at the texture information with reference to image, propose a kind of based on the remote sensing images method for reconstructing with reference to image texture constraint and the constraint of broad sense non-convex low-rank, by using for reference human visual system to the processing procedure of image, first target image and the statistical nature of reference image texture in wavelet coefficient is calculated, build corresponding proper vector respectively, build with reference to constraint with the similarity degree of proper vector, the sparse coefficient of the L1 norm constraint target image of compressed sensing is replaced again with non-convex low-rank appropriate constraints, set up the sparse optimized reconstruction model of remote sensing images and solve, effectively can reduce sampled data, improve the precision of reconstructed image.
Specifically, the embodiment of the present invention retrains based on reference picture texture constraint and broad sense non-convex kernel function low-rank and sets up based on the data reconstruction mathematical model with reference to image non local similar image block low-rank prior imformation in the remote sensing images reconstruction algorithm method of iterative, adopt method of conjugate gradient, Taylor's first approximation and svd iterative based on the broad sense non-convex kernel function of the low-rank matrix of the non local iconic model of band low-rank prior imformation, obtain similar image block.The present invention has stronger texture structure hold facility, contrast and additive method simultaneously, experiment also shows that proposed method can rebuild remote sensing image more accurately under less measurement, reduces the artifact of reconstructed image, more rationally recovers the texture structure of remote sensing images.
The present invention proposes a kind of based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of broad sense non-convex low-rank, by using for reference human visual system to the processing procedure of image, first calculating target image and reference image texture are at the statistical nature after the filter filtering of expert field, build corresponding proper vector respectively, build with reference to constraint with the similarity degree of proper vector, then replace the l of compressed sensing with non-convex nuclear norm appropriate constraints
1the sparse coefficient of norm constraint target image, sets up the sparse optimized reconstruction model of remote sensing images and solves, effectively can reduce sampled data, improves the precision of reconstructed image.
The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.
Claims (8)
1. the remote sensing images method for reconstructing retrained based on the constraint of reference image structure and non-convex low-rank, it is characterized in that, comprise the steps: first to set up target image and with reference to the similar constraint of the structure of image after high-grade filting, then replace compressed sensing with non-convex low-rank appropriate constraints
norm carrys out constrained objective image sparse coefficient, sets up the sparse optimized reconstruction model of remote sensing images and solves.
2. according to claim 1 based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank, it is characterized in that: use the expert field bank of filters that one group of size is 5x5 or 3x3 to do two-dimensional filtering to reference picture, calculate the sparse coefficient of the reference image matched with target image, similar as constraint condition to the expert field filter factor with reference to image using target image.
3. according to claim 2 based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank, it is characterized in that: by non-convex low-rank nuclear norm constrained objective image sparse coefficient, join in the sparse coefficient of target image by similar for the coefficient after the filter filtering of expert field, establishing target function.
4. according to claim 3 based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank, it is characterized in that: by the non local image reconstruction model of conjugate gradient algorithm, Taylor's first approximation and svd iterative band target image low-rank prior imformation.
5. according to claim 4 based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank, it is characterized in that: use match by moment method to upgrade average and the standard deviation of reference picture, make it consistent with reconstruction image.
6. according to claim 2 based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank, it is characterized in that, use higher order filter to extract structural information, its wave filter used concentrates extraction 20000 width image patch from Berkeley partition data and trained by expert's field model to obtain.
7. according to claim 3 based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank, it is characterized in that, when obtaining low-rank similar matrix, the position relationship of used similar image block matrix obtains from reference picture.
8. according to claim 3 based on the remote sensing images method for reconstructing with reference to image structure constraint and the constraint of non-convex low-rank, it is characterized in that, by non-convex low-rank nuclear norm constrained objective image sparse coefficient, similarity is joined in the sparse coefficient of target image and upgrades, construct the objective function of reconstruction model:
Wherein, in model, Section 1 ensures that reconstructed results and observation data keep matching constraint; Section 2 is the structural constraint item of high-grade filting coefficient, H
kfor representing with the matrix operation of a kth filter filtering process equivalence,
for the Regularization adjustment factor for a kth wave filter; Section 3 is the regular terms that image carries out the sparse and similar piece of low-rank constraint of cohort,
represent the sparse level of image block,
represent the weight of image block similarity degree matching.
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