CN102509263A - K-SVD (K-means singular value decomposition) speckle inhibiting method based on SAR (synthetic aperture radar) image local statistic characteristic - Google Patents

Abstract

The invention discloses a K-SVD (K-means singular value decomposition) speckle inhibiting method based on SAR (synthetic aperture radar) image local statistic characteristic, mainly solving the problem that detail information such as edge, texture and the like is fuzzy in the traditional speckle inhibiting method. The method is realized in the following processes of: inputting an SAR image, extracting overlapped blocks in the SAR image to obtain an overlapped block vector set; then randomly sampling the overlapped block vector set to obtain a training sample set; carrying out SAR_KSVD dictionary training on a training sample to obtain a final training dictionary; carrying out SAR_OMP sparse coding on the overlapped block vector set under the condition of the final training dictionary to obtain a sparse coding coefficient; and obtaining a speckle inhibited image by utilizing the final training dictionary and the sparse coding coefficient according to the redundant sparse representation image noise inhibiting theory. By applying the method disclosed by the invention, speckle noise in a homogenous region can be effectively inhibited, brightness and edge texture of a target at a strong reflection point can be well maintained to be clear, and the method disclosed by the invention can be applicable to SAR images in the fields such as land resource monitoring, natural disaster analysis and the like.

Description

Based on the relevant speckle suppression method of the K-SVD of SAR image local statistical property

Technical field

The invention belongs to technical field of image processing; Be the relevant speckle suppression method of a kind of dictionary training K-SVD specifically, can be used for the synthetic-aperture radar SAR graphical analysis of numerous areas such as land resource monitoring, disaster analysis, urban development planning based on SAR image local statistical property.

Background technology

Coherent speckle noise is the inherent characteristic of SAR image, and the coherent spot of these random scatters in the SAR image can be entrained in less ground object target, has a strong impact on the quality of image, and the automatic decipher of SAR image is caused very big difficulty.Therefore, in the SAR Flame Image Process, SAR image coherent spot suppresses to become key, also be follow-up SAR image characteristics extraction, cut apart, the basis of work such as identification.The target that coherent spot suppresses technology is exactly: when satisfying radiometric resolution, how to keep necessary spatial resolution, so in the filtering speckle noise, protect detailed information such as texture, edge.Will accomplish following 4 points so the SAR image of " good " presses down spot method: the speckle noise in the even scene is effectively removed in (1); (2) keep edge and textural characteristics in the image; (3) do not produce pseudo-Gibbs' effect; (4) the radar emission characteristic of maintenance image.

In the SAR imaging processing in early stage, adopt looked treatment technology more and suppressed coherent speckle noise more, though this technology is simple, but is cost with the sacrifice image resolution ratio.Therefore, be the basis, the SAR image after the imaging is carried out the main flow that coherent speckle noise suppresses to have become the high resolution SAR Flame Image Process with various filtering techniques.Filtering technique after the imaging can be divided into airspace filter technology and transform domain filtering technique at present.Wherein the airspace filter method comprises enhanced Lee filtering, Frost filtering and Gamma Map filtering etc.; These methods are difficult to keep the minutia of image usually; Can cause the fuzzy of image border and linear goal, the quality of filtering performance largely depends on the size of selected filter window.The transform domain method mainly contains wavelet transformation, stationary wavelet conversion, Bandelet conversion, Curvelet conversion and non-downsampling Contourlet conversion etc.These transform domain filtering methods are compared classical airspace filter method, and the hold facility of edge of image and linear goal has had large increase, but mostly the coefficient of transform domain are done certain statistical hypothesis, and these hypothesis are experimental, the gear shaper without theoretical foundation.And noise has similar frequency characteristic with the image border, promptly all is high-frequency signal, and pseudo-Gibbs' effect appears near image regular meeting homogeneous area and edge that therefore presses down behind the spot.

At present, a kind of emerging " dictionary learning method " obtained extensive studies and application in Flame Image Process, and its core is the training process of dictionary, is called the K-SVD algorithm.This algorithm is at first proposed by people such as Aharon, Elad.Research shows: the K-SVD method has not only effectively suppressed additive white Gaussian noise, and important informations such as edge and texture have all obtained preferably keeping, and is especially better to the texture image process result.The most important thing is that the method is a kind of active learning process, has excellent adaptability.But the K-SVD algorithm is to the additive noise design, and the coherent spot of SAR image is a multiplicative noise, directly the K-SVD algorithm application level and smooth phenomenon can be occurred in the SAR image speckle.In order to overcome this shortcoming; A lot of scholars have adopted the strategy of log-transformation, promptly earlier the SAR image are carried out log-transformation, change the multiplicative noise model into additivity; And then the log image is carried out denoising with the K-SVD algorithm, carry out inverse transformation at last and can obtain pressing down SAR image behind the spot." but Statistical Properties of Logarithmically Transformed Speckle " literary composition is pointed out; The SAR image is after log-transformation; Its noise is not a zero-mean; This causes image to occur but average differs bigger before and after the spot, can not well keep the radiation characteristic of original SAR image.In addition, this does not satisfy that noise is the requirement of zero-mean additive Gaussian noise in the K-SVD algorithm yet.Samuel Foucher is in " SAR Image Filtering via Learned Dictionaries and Sparse Representations " for this reason, the objective function of K-SVD algorithm carried out weighting improved and press down the spot effect.But the method is concerning looking the lower SAR image of number, because speckle noise can influence the training of dictionary, so still there is a large amount of speckle noises in final result, and the edge can blur.

Summary of the invention

The objective of the invention is to overcome the deficiency of above-mentioned existing SAR image coherent spot inhibition technology; The relevant speckle suppression method of a kind of K-SVD based on SAR image local statistical property has been proposed; With the coherent spot of effective inhibition SAR image, keep the radiation characteristic of edge, grain details information and image preferably.

For realizing above-mentioned purpose, relevant speckle suppression method of the present invention comprises the steps:

(1) to size does

The SAR image I carry out overlapping block and extract, and, obtain the set of overlapping block vector with its vectorization

Wherein N is a number of pixels all in the image I, y _iBe an overlapping block vector, M is the number of overlapping block vector;

(2) picked at random is carried out in overlapping block vector set

; Obtaining training sample set

wherein any training sample M ' is the training sample number, and satisfies the positive integer of 0＜M '≤M;

(3) based on SAR image local statistical property, suppress theoretical according to redundant rarefaction representation picture noise, obtain coherent spot and suppress objective function f ₁

(4) with training sample set

training dictionary D is carried out the training of following SAR_K-SVD dictionary, obtain final training dictionary

(4.1) make i=1, k=1, P=1, wherein i is training sample y _i' subscript, k is the k row d of dictionary D _kSubscript, P is an iterations;

(4.2) suppress objective function f according to the coherent spot in the step (3) ₁, keeping obtaining being applicable to the sparse coding objective function f of SAR image under the constant situation of training dictionary D ₂

(4.3) to i the training sample y of training sample set Y ' _i' carry out following SAR_OMP sparse coding, obtain y _i' the sparse coding alpha _i:

(4.3a) make initial indexed set I ⁰=(), initial residual error r ⁰=y _i', initial rarefaction representation coefficient

Initial error

(4.3b) make residual error r '=r ⁰, indexed set I '=I ⁰, sparse degree j=0;

(4.3c) according to formula

Try to achieve best subscript D wherein _kBe the k row of dictionary D,

Be d _kTransposition, Be right

Ask absolute value;

(4.3d) with

the substitution indexed set of trying to achieve in the step (4.3c) more in the new formula

, the indexed set I ' after obtaining upgrading;

(4.3e) with the I ' substitution rarefaction representation coefficient update formula α that tries to achieve in the step (4.3d) _i=(D _{I '}) ⁺y _i' in, the rarefaction representation coefficient after obtaining upgrading, wherein D _{I '}Be the submatrix of dictionary D, (D _{I '}) ⁺Be to matrix D _{I '}Ask matrix inversion operation;

(4.3f) with the α that tries to achieve in the step (4.3e) _iThe substitution residual error is new formula r '=y more _i'-D _{I '}α _iIn, the residual error r ' after obtaining upgrading;

(4.3g) according to the sparse coding objective function f in the step (4.2) ₂, make up the error update formula

Wherein r ' is the residual error after upgrading, D _{I '}Be the submatrix of the training dictionary D after upgrading, α _iIt is the rarefaction representation coefficient after upgrading;

(4.3h) with the α that tries to achieve among step (4.3e), (4.3f) _i, in the error update formula in the r ' substitution step (4.3g), the error E after obtaining upgrading ';

(4.3i) make sparse degree j=j+1, indexed set I ⁰=I ', if E '＞ε and j＜L then change step (4.3j) over to, otherwise α _iBe training sample y _i' the sparse coding coefficient, wherein ε is a departure, L is maximum sparse degree;

(4.3j) repeated execution of steps (4.3c)-(4.3h);

(4.4) utilize the sparse coding alpha that obtains in the step (4.3) _i, adopt the k row d of singular value decomposition method SVD to dictionary D _kUpgrade the dictionary D ' after obtaining upgrading;

(4.5) the row subscript k=k+1 of order training dictionary D, D=D '; If k≤T then changes step (4.6) over to, otherwise change step (4.7) over to, wherein T is the column number of dictionary;

(4.6) repeated execution of steps (4.3)-(4.5);

(4.7) the row subscript k=1 of order training dictionary D, training sample subscript i=i+1 if i≤M ' then changes step (4.8) over to, otherwise changes step (4.9) over to, and wherein M ' is the training sample number;

(4.8) repeated execution of steps (4.3)-(4.7);

(4.9) make iterations P=P+1; If P≤J; Then change step (4.10) over to; Otherwise obtain final training dictionary

wherein D be the training dictionary in the iterative process, J is a maximum iteration time;

(4.10) repeated execution of steps (4.3)-(4.8);

(5) suppress theoretical according to redundant rarefaction representation picture noise; Utilize the final training dictionary that obtains in the step (4) that all overlapping block vector set Y are carried out squelch, obtain coherent spot and suppress back image

The present invention has the following advantages compared with prior art:

(1) because the present invention does not do any pre-service to original SAR image, but directly in the spatial domain, original image is pressed down spot,, can better keep the radiation characteristic of original image so overcome the deficiency of log-transformation K-SVD method;

(2) because the present invention has utilized the partial statistics characteristic of SAR image itself; And in conjunction with the advantage of dictionary training K-SVD in picture noise suppresses; So the brightness that can in the speckle noise that suppresses homogeneous region effectively, well keep the strong reflection point target, and edge clean mark;

(3) because the present invention has used an initiatively SAR_K-SVD dictionary training of learning process, so have higher adaptive ability;

(4) because the present invention is based on the relevant speckle suppression method that the statistical property of SAR image intensity figure and map of magnitudes obtains, suppress so be suitable for the coherent spot of SAR magnitude image and intensity image, wider applicability is arranged.

Description of drawings

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is a width of cloth true amplitude SAR image;

Fig. 3 is a width of cloth actual strength SAR image;

Fig. 4 is the present invention and existing method to the experiment simulation of Fig. 2 figure as a result;

Fig. 5 is the present invention and existing method to the experiment simulation of Fig. 3 figure as a result.

Embodiment

With reference to Fig. 1, enforcement of the present invention is following:

Step 1, getting slippage factor is s=1, size does

Window, to the input size do

The SAR image I, as shown in Figures 2 and 3, carry out doubling of the image piece and extract operation, obtain the set of overlapping block vector

Y wherein _iBe i overlapping block vector, M is the number of overlapping block vector, and

$M={(\sqrt{N}-\sqrt{n}+1)}^2.$

Step 2 is to the set of overlapping block vector

Carry out random sampling, obtain the training sample set Y wherein _i' be i training sample, M ' is the number of training sample, and 0＜M '≤M.

Step 3 suppresses theoretical according to redundant rarefaction representation picture noise, obtains coherent spot and suppresses objective function f ₁

(3a) based on SAR image local statistical property, obtain the true atural object reflection coefficient x of SAR image _iProbability density function p (x _i) as follows:

p(x _i)＝C

Wherein, SAR image local statistical property is meant the certain probability distribution of gray-scale value obedience of SAR image pixel in smaller homogeneous region, and C is a constant;

(3b), obtain the rarefaction representation alpha based on SAR image local statistical property _iProbability density function p (α _i) as follows:

p(α _i)＝exp(-λ||α _i||)

Wherein λ is a constant, and exp (λ || α _i||) be an exponential function;

(3c) with speckle noise n _iObtain stochastic variable n after deducting 1 _i-1, based on SAR image local statistical property, obtain stochastic variable n _i-1 probability density function p (n _i-1) as follows:

Wherein, n _iBe speckle noise, and n _i>=1, L is the number of looking of SAR image, L ^LBe that a truth of a matter is that L, index are the exponential of L, (n _i-1) ^L-1Be that a truth of a matter is (n _i-1), index is the exponential of L-1,

Be that a truth of a matter is that e, index are-L (n _i-1) exponential, Γ () is a gamma function;

(3d) with the p (x in step (3a) and the step (3c) _i) and p (n _i-1), the additive noise under the non-logarithmic form of substitution SAR image coherent spot model

Probability density function in, try to achieve additive noise

Probability density function

Wherein, x _iBe the true atural object reflection coefficient of SAR image, n _iBe speckle noise, and x _iAnd n _iSeparate, p (x _i) be true atural object reflection coefficient x _iProbability density function, p (n _i-1) is stochastic variable n _i-1 probability density function, SAR image coherent spot model is meant y _i=x _iN _i, its non-logarithmic form is meant

y _iBe the actual measured value of SAR image,

Be the additive noise under the non-logarithmic form, and

(3e) suppose all overlapping block vector y _i, i=1, L, M are separate, then obtain the likelihood function p (Y|D) of overlapping block vector set Y under training dictionary D as follows:

$p\left(Y\right|D)=\underset{i=1}{\overset{M}{\mathrm{\Π}}}p\left(y_i\right|D),$

Wherein, p (y _i| D) be overlapping block vector y _iConditional probability under training dictionary D, M is the number of all overlapping block vectors;

(3f) to likelihood function p (Y|D) maximizing in the step (3e), finally trained the maximum likelihood estimation formulas of dictionary D and rarefaction representation coefficient

following:

$\{\hat{D},\widehat{\mathrm{\α}}\}=\arg \underset{D}{\max }p\left(Y\right|D)=\arg \underset{D}{\max }\underset{i=1}{\overset{M}{\mathrm{\Σ}}}p\left(y_i\right|D),$

$=\arg \underset{D}{\max }\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\underset{{\mathrm{\α}}_i}{\max }\left\{p(n_i-1)p\left({\mathrm{\α}}_i\right)\right\}$

Wherein, Y is the set of overlapping block vector, y _iBe the actual measured value of SAR image, p (y _i| D) be overlapping block vector y _iConditional probability under training dictionary D, D and α _iBe respectively training dictionary and the rarefaction representation coefficient in the training process,

With

Be respectively that finally to train dictionary and rarefaction representation coefficient, M be the numbers of all overlapping blocks vector,

Be by

With The optimum solution set that constitutes, p (α _i) be the sparse coding alpha _iProbability density function, p (n _i-1) is stochastic variable n _i-1 probability density function;

(3g) with the sparse coding alpha in step (3b) and the step (3c) _iProbability density function p (α _i) and stochastic variable n _i-1 probability density function p (n _i-1), substitution

The maximum likelihood estimation formulas in, through simplify calculating, obtaining coherent spot and suppressing objective function f ₁As follows:

$f_1=\{\hat{D},{\widehat{\mathrm{\α}}}_i\}=\arg \underset{D,{\mathrm{\α}}_i}{\min }{\left|\right|{\mathrm{\α}}_i\left|\right|}_0+\mathrm{\λ}{\left|\right|y_i-D{\mathrm{\α}}_i\left|\right|}_2^2\·\frac{1}{{\left|\right|D{\mathrm{\α}}_i\left|\right|}_2^2},$

Wherein, y _iBe the actual measured value of SAR image, D and α _iBe respectively training dictionary and the rarefaction representation coefficient in the training process,

With Be respectively finally to train dictionary and rarefaction representation coefficient,

Be by

With The optimum solution set that constitutes, λ is a Lagrange multiplier, || || ₀Be 0 norm,

Be 2 norms.

Step 4; With training sample set

training dictionary D is carried out the training of following SAR_K-SVD dictionary, obtain final training dictionary

(4.1) make i=1, k=1, P=1, wherein i is training sample y _i' subscript, k is the k row d of dictionary D _kSubscript, P is an iterations;

(4.2) suppress objective function f according to the coherent spot in the step (3) ₁, keeping obtaining being applicable to the sparse coding objective function f of SAR image under the constant situation of training dictionary D ₂As follows:

$f_2={\widehat{\mathrm{\α}}}_i=\arg \underset{{\mathrm{\α}}_i}{\min }{\left|\right|{\mathrm{\α}}_i\left|\right|}_0+\mathrm{\λ}{\left|\right|y_i-D{\mathrm{\α}}_i\left|\right|}_2^2\·\frac{1}{{\left|\right|D{\mathrm{\α}}_i\left|\right|}_2^2},$

Wherein, y _iBe the actual measured value of SAR image, D is the training dictionary that remains unchanged, α _iBe the rarefaction representation coefficient in the sparse coding process,

Be final rarefaction representation coefficient, λ is a Lagrange multiplier, || || ₀Be 0 norm,

Be 2 norms.

(4.3) to i the training sample y of training sample set Y ' _i' carry out following SAR orthogonal matching pursuit SAR_OMP sparse coding, obtain y _i' the sparse coding alpha _i:

(4.3a) make initial indexed set I ⁰=(), initial residual error r ⁰=y _i', initial rarefaction representation coefficient

Initial error

(4.3b) make residual error r '=r ⁰, indexed set I '=I ⁰, sparse degree j=0;

(4.3c) according to formula

Try to achieve best subscript

D wherein _kBe the k row of dictionary D,

Be d _kTransposition,

Be right Ask absolute value;

(4.3d) with

the substitution indexed set of trying to achieve in the step (4.3c) more in the new formula

, the indexed set I ' after obtaining upgrading;

(4.3e) with the I ' substitution rarefaction representation coefficient update formula α that tries to achieve in the step (4.3d) _i=(D _{I '}) ⁺y _i' in, the rarefaction representation alpha after obtaining upgrading _i, D wherein _{I '}Be the submatrix of dictionary D, (D _{I '}) ⁺Be to matrix D _{I '}Ask matrix inversion operation;

(4.3f) with the α that tries to achieve in the step (4.3e) _iThe substitution residual error is new formula r '=y more _i'-D _{I '}α _iIn, the residual error r ' after obtaining upgrading;

(4.3g) according to the sparse coding objective function f in the step (4.2) ₂, make up the error update formula

Wherein r ' is the residual error after upgrading, D _{I '}Be the submatrix of the training dictionary D after upgrading, α _iIt is the rarefaction representation coefficient after upgrading;

(4.3h) with the α that tries to achieve among step (4.3e), (4.3f) _i, in the error update formula in the r ' substitution step (4.3g), the error E after obtaining upgrading ';

(4.3i) make sparse degree j=j+1, indexed set I ⁰=I ', if E '＞ε and j＜L then change step (4.3j) over to, otherwise α _iBe training sample y _i' the sparse coding coefficient, wherein ε is a departure, L is maximum sparse degree;

(4.3j) repeated execution of steps (4.3c)-(4.3h);

(4.4) utilize the sparse coding alpha that obtains in the step (4.3) _i, adopt the k row d of singular value decomposition method SVD to dictionary D _kUpgrade the dictionary D ' after obtaining upgrading;

(4.5) the row subscript k=k+1 of order training dictionary D, D=D '; If k≤T then changes step (4.6) over to, otherwise change step (4.7) over to, wherein T is the column number of dictionary;

(4.6) repeated execution of steps (4.3)-(4.5);

(4.7) the row subscript k=1 of order training dictionary D, training sample subscript i=i+1 if i≤M ' then changes step (4.8) over to, otherwise changes step (4.9) over to, and wherein M ' is the training sample number;

(4.8) repeated execution of steps (4.3)-(4.7);

(4.9) make iterations P=P+1; If P≤J; Then change step (4.10) over to; Otherwise obtain final training dictionary

wherein D be the training dictionary in the iterative process, J is a maximum iteration time;

(4.10) repeated execution of steps (4.3)-(4.8);

Step 5; Suppress theoretical according to redundant rarefaction representation picture noise; Utilize final training dictionary

that all overlapping block vector set Y are carried out squelch, obtain coherent spot and suppress back image

(5a) utilize final training dictionary

that the SAR_OMP sparse coding is carried out in all overlapping block vector set

, obtain sparse coding matrix of coefficients

(5b) in the estimator

with the sparse coding matrix of coefficients that obtains in the step (Sa) substitution overlapping block vector set Y, obtain the estimation

of overlapping block vector set Y

(5c) weighted mean is carried out in the estimation of overlapping block vector set Y, obtain SAR image coherent spot and suppress back image according to following formula

$\hat{I}={(\mathrm{\λI}+\underset{i,j}{\mathrm{\Σ}}{R}_{\mathrm{ij}}^T{R}_{\mathrm{ij}})}^{-1}(\mathrm{\λ}\hat{Y}+\underset{i,j}{\mathrm{\Σ}}{R}_{\mathrm{ij}}^T\hat{D}{\widehat{\mathrm{\α}}}_{\mathrm{ij}}^{\′}),$

Wherein, λ is a Lagrange multiplier, and I is original SAR image array, R _IjBe the overlapping block operations factor,

Be the transposition of overlapping block operations factor,

Be the estimation of overlapping block vector set Y,

Be right

Inversion operation, Be finally to train dictionary,

It is the sparse coding matrix of coefficients The element of the capable j of i row,

Be that coherent spot suppresses the back image, redundant rarefaction representation picture noise suppresses theory and is meant at first image and obtains redundant rarefaction representation coefficient with one group of redundancy basis representation, and then redundant rarefaction representation coefficient is obtained the image after the squelch do inverse transformation.

Effect of the present invention can further specify through following experimental result and analysis:

1. experimental data

Experimental data of the present invention is the true SAR images of two width of cloth, and a width of cloth is that original image is that the X-band 2 that is positioned at Britain Bedfordshire area of 256 * 256 pixel sizes is looked amplitude SAR image, and its resolution is 3m; Another width of cloth is that original image is the ku wave band 4 apparent intensity SAR images that are positioned at New Mexico Albuquerque area of 256 * 256 pixel sizes, and its resolution is 1m.

2. experimental technique

Scholars such as method 1:Fabrizio Argent 2009 in article " LMMSE and MAP estimators forreduction of multiplicative noise in the nonsubsampled contourlet domain ", propose based on NSCT MAP filtering method;

Method 2: the relevant speckle suppression method of the log_K-SVD that scholar Samuel Foucher proposed in article " SAR Image Filtering via Learned Dictionaries and Sparse Representations " in 2008;

Method 3: the inventive method.

3. experiment content and interpretation of result

With distinct methods the true SAR view data of two width of cloth as shown in Figures 2 and 3 being carried out coherent spot suppresses; The result who obtains such as Fig. 4 and shown in Figure 5; Wherein Fig. 4 (a) and Fig. 5 (a) suppress figure as a result for the coherent spot that existing method 1 obtains; Fig. 4 (b) and Fig. 5 (b) suppress figure as a result for the coherent spot that existing method 2 obtains, and Fig. 4 (c) and Fig. 5 (c) suppress figure as a result for the coherent spot that the inventive method obtains.Can find out that from Fig. 4 and Fig. 5 existing method 1 speckle noise among the figure has as a result obtained filtering effectively, and texture information also obtained certain reservation, but tangible cut effect has appearred in homogeneous region, edge and strong reflection point target are blured; Detailed information such as edge, texture have obtained good reservation among the figure as a result of existing method 2, but still quite a large amount of the existing of the speckle noise in the homogeneous region, and can not well keep the radiation characteristic of original image; The inventive method has significantly been improved the result; Not only suppressed the speckle noise of homogeneous region effectively, well kept point target and edge texture information, and suppressed the cut effect of homogeneous region effectively, well kept the radiation characteristic of original image.

The experiment coherent spot is suppressed the result carry out quantitative test; Some homogeneous regions shown in white rectangle in Fig. 2 and Fig. 3, have been selected; Performance index such as the average MRI of employing equivalent number ENL, ratio image and edge maintenance index E PD-ROA are estimated coherent spot and are suppressed effect, and the result is shown in table 1 and table 2.

The coherent spot of table 1. couple Fig. 2 suppresses the evaluation of result index

The coherent spot of table 2. couple Fig. 3 suppresses the evaluation of result index

Can find out more intuitively that from table 1 and table 2 the present invention has all obtained result preferably at ENL, MRI and EPDROA, it is best that the coherent spot of comparing with other two kinds of existing methods suppresses effect.

Claims (4)

1. the relevant speckle suppression method of the dictionary training K-SVD based on SAR image local statistical property comprises the steps:

(1) to size does

The SAR image I carry out overlapping block and extract, and, obtain the set of overlapping block vector with its vectorization

Wherein N is a number of pixels all in the image I, y _iBe an overlapping block vector, M is the number of overlapping block vector;

(2) picked at random is carried out in overlapping block vector set

; Obtaining training sample set

wherein any training sample

M ' is the training sample number, and satisfies the positive integer of 0＜M '≤M;

(3) based on SAR image local statistical property, suppress theoretical according to redundant rarefaction representation picture noise, obtain coherent spot and suppress objective function f ₁

(4) with training sample set training dictionary D is carried out the training of following SAR_K-SVD dictionary, obtain final training dictionary

(4.1) make i=1, k=1, P=1, wherein i is training sample y _i' subscript, k is the k row d of dictionary D _kSubscript, P is an iterations;

(4.2) suppress objective function f according to the coherent spot in the step (3) ₁, keeping obtaining being applicable to the sparse coding objective function f of SAR image under the constant situation of training dictionary D ₂

(4.3) to i the training sample y of training sample set Y ' _i' carry out following SAR orthogonal matching pursuit SAR_OMP sparse coding, obtain y _i' the sparse coding alpha _i:

(4.3a) make initial indexed set I ⁰=(), initial residual error r ⁰=yi ', initial rarefaction representation coefficient

Initial error

(4.3b) make residual error r '=r ⁰, indexed set I '=I ⁰, sparse degree j=0;

(4.3c) according to formula

Try to achieve best subscript

D wherein _kBe the k row of dictionary D,

Be d _kTransposition,

Be right

Ask absolute value;

(4.3d) with

the substitution indexed set of trying to achieve in the step (4.3c) more in the new formula

, the indexed set I ' after obtaining upgrading;

(4.3e) with the I ' substitution rarefaction representation coefficient update formula α that tries to achieve in the step (4.3d) _i=(D _{I '}) ⁺y _i' in, the rarefaction representation alpha after obtaining upgrading _i, D wherein _{I '}Be the submatrix of dictionary D, (D _{I '}) ⁺Be to matrix D _{I '}Ask matrix inversion operation;

(4.3f) with the α that tries to achieve in the step (4.3e) _iThe substitution residual error is new formula r '=y more _i'-D _{I '}α _iIn, the residual error r ' after obtaining upgrading;

(4.3g) according to the sparse coding objective function f in the step (4.2) ₂, make up the error update formula

Wherein r ' is the residual error after upgrading, D _{I '}Be the submatrix of the training dictionary D after upgrading, α _iIt is the rarefaction representation coefficient after upgrading;

(4.3h) with the α that tries to achieve among step (4.3e), (4.3f) _i, in the error update formula in the r ' substitution step (4.3g), the error E after obtaining upgrading ';

(4.3i) make sparse degree j=j+1, indexed set I ⁰=I ', if E '＞ε and j＜L then change step (4.3j) over to, otherwise α _iBe training sample y _i' the sparse coding coefficient, wherein ε is a departure, L is maximum sparse degree;

(4.3j) repeated execution of steps (4.3c)-(4.3h);

(4.4) utilize the sparse coding alpha that obtains in the step (4.3) _i, adopt the k row d of singular value decomposition method SVD to dictionary D _kUpgrade the dictionary D ' after obtaining upgrading;

(4.5) the row subscript k=k+1 of order training dictionary D, D=D '; If k≤T then changes step (4.6) over to, otherwise change step (4.7) over to, wherein T is the column number of dictionary;

(4.6) repeated execution of steps (4.3)-(4.5);

(4.7) the row subscript k=1 of order training dictionary D, training sample subscript i=i+1 if i≤M ' then changes step (4.8) over to, otherwise changes step (4.9) over to, and wherein M ' is the training sample number;

(4.8) repeated execution of steps (4.3)-(4.7);

(4.9) make iterations P=P+1; If P≤J; Then change step (4.10) over to; Otherwise obtain final training dictionary

wherein D be the training dictionary in the iterative process, J is a maximum iteration time;

(4.10) repeated execution of steps (4.3)-(4.8);

(5) suppress theoretical according to redundant rarefaction representation picture noise; Utilize the final training dictionary

that obtains in the step (4) that all overlapping block vector set Y are carried out squelch, obtain coherent spot and suppress back image

2. the relevant speckle suppression method of the K-SVD based on SAR image local statistical property according to claim 1, wherein step (3) is described suppresses theoretical according to redundant rarefaction representation picture noise, obtains coherent spot and suppresses objective function f ₁, obtain as follows:

(3a) based on SAR image local statistical property, obtain the true atural object reflection coefficient x of SAR image _iProbability density function p (x _i) as follows:

p(x _i)＝C

Wherein C is a constant;

(3b), obtain the rarefaction representation alpha based on SAR image local statistical property _iProbability density function p (α _i) as follows:

p(α _i)＝exp(-λ||α _i||)

Wherein λ is a constant, and exp (λ || α _i||) be the index function;

(3c) with speckle noise n _iObtain stochastic variable n after deducting 1 _i-1, based on SAR image local statistical property, obtain stochastic variable n _i-1 probability density function p (n _i-1) as follows:

Wherein, n _iBe speckle noise, and n _i>=1, L is the number of looking of SAR image, L ^LBe that a truth of a matter is that L, index are the exponential of L, (n _i-1) ^L-1Be that a truth of a matter is (n _i-1), index is the exponential of L-1, Be that a truth of a matter is that e, index are-L (n _i-1) exponential, Γ () is a gamma function;

(3d) with the p (x in step (3a) and the step (3c) _i) and p (n _i-1), the additive noise under the non-logarithmic form of substitution SAR image coherent spot model

Probability density function in, try to achieve additive noise

Probability density function

Wherein, x _iBe the true atural object reflection coefficient of SAR image, n _iBe speckle noise, and x _iAnd n _iSeparate, p (x _i) be true atural object reflection coefficient x _iProbability density function, p (n _i-1) is stochastic variable n _i-1 probability density function;

(3e) suppose all overlapping block vector y _i, i=1, L, M are separate, then obtain the likelihood function p (Y|D) of overlapping block vector set Y under training dictionary D as follows:

$p\left(Y\right|D)=\underset{i=1}{\overset{M}{\mathrm{\Π}}}p\left(y_i\right|D),$

Wherein, p (y _i| D) be overlapping block vector y _iConditional probability under training dictionary D, M is the number of all overlapping block vectors;

(3f) to likelihood function p (Y|D) maximizing in the step (3e), finally trained the maximum likelihood estimation formulas of dictionary

and rarefaction representation coefficient

following:

$\{\hat{D},\widehat{\mathrm{\α}}\}=\arg \underset{D}{\max }p\left(Y\right|D)=\arg \underset{D}{\max }\underset{i=1}{\overset{M}{\mathrm{\Σ}}}p\left(y_i\right|D),$

$=\arg \underset{D}{\max }\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\underset{{\mathrm{\α}}_i}{\max }\left\{p(n_i-1)p\left({\mathrm{\α}}_i\right)\right\}$

Wherein, Y is the set of overlapping block vector, y _iBe the actual measured value of SAR image, p (y _i| D) be overlapping block vector y _iConditional probability under training dictionary D, D and α _iBe respectively training dictionary and the rarefaction representation coefficient in the training process,

With

Be respectively that finally to train dictionary and rarefaction representation coefficient, M be the numbers of all overlapping blocks vector,

Be by

With The optimum solution set that constitutes, p (α _i) be the sparse coding alpha _iProbability density function, p (n _i-1) is stochastic variable n _i-1 probability density function;

(3g) with the sparse coding alpha in step (3b) and the step (3c) _iProbability density function p (α _i) and stochastic variable n _i-1 probability density function p (n _i-1), substitution

The maximum likelihood estimation formulas in, through simplify calculating, obtaining coherent spot and suppressing objective function f ₁As follows:

$f_1=\{\hat{D},{\widehat{\mathrm{\α}}}_i\}=\arg \underset{D,{\mathrm{\α}}_i}{\min }{\left|\right|{\mathrm{\α}}_i\left|\right|}_0+\mathrm{\λ}{\left|\right|y_i-D{\mathrm{\α}}_i\left|\right|}_2^2\·\frac{1}{{\left|\right|D{\mathrm{\α}}_i\left|\right|}_2^2},$

Wherein, y _iBe the actual measured value of SAR image, D and α _iBe respectively training dictionary and the rarefaction representation coefficient in the training process,

With

Be respectively finally to train dictionary and rarefaction representation coefficient,

Be by With

The optimum solution set that constitutes, λ is a Lagrange multiplier, || || ₀Be 0 norm,

Be 2 norms.

3. the relevant speckle suppression method of the K-SVD based on SAR image local statistical property according to claim 1, the sparse coding objective function f in the wherein said step (4.2) ₂Represent as follows:

$f_2={\widehat{\mathrm{\α}}}_i=\arg \underset{{\mathrm{\α}}_i}{\min }{\left|\right|{\mathrm{\α}}_i\left|\right|}_0+\mathrm{\λ}{\left|\right|y_i-D{\mathrm{\α}}_i\left|\right|}_2^2\·\frac{1}{{\left|\right|D{\mathrm{\α}}_i\left|\right|}_2^2},$

Wherein, y _iBe the actual measured value of SAR image, D is the training dictionary that remains unchanged, α _iBe the rarefaction representation coefficient in the sparse coding process,

Be final rarefaction representation coefficient, λ is a Lagrange multiplier, || || ₀Be 0 norm,

Be 2 norms.

4. the relevant speckle suppression method of the K-SVD based on SAR image local statistical property according to claim 1; Wherein step (5) is described suppresses theoretical according to redundant rarefaction representation picture noise, obtains coherent spot inhibition back image

and carries out as follows:

(5a) utilize final training dictionary

that the SAR_OMP sparse coding is carried out in all overlapping block vector set

, obtain sparse coding matrix of coefficients

(5b) in the estimator

with the sparse coding matrix of coefficients that obtains in the step (5a) substitution overlapping block vector set Y, obtain the estimation

of overlapping block vector set Y

(5c) weighted mean is carried out in the estimation of overlapping block vector set Y, obtain SAR image coherent spot and suppress back image

according to following formula

$\hat{I}={(\mathrm{\λI}+\underset{i,j}{\mathrm{\Σ}}{R}_{\mathrm{ij}}^T{R}_{\mathrm{ij}})}^{-1}(\mathrm{\λ}\hat{Y}+\underset{i,j}{\mathrm{\Σ}}{R}_{\mathrm{ij}}^T\hat{D}{\widehat{\mathrm{\α}}}_{\mathrm{ij}}^{\′}),$

Wherein, λ is a Lagrange multiplier, and I is original SAR image array, R _IjBe the overlapping block operations factor,

Be the transposition of overlapping block operations factor,

Be the estimation of overlapping block vector set Y, Be right

Inversion operation,

Be finally to train dictionary,

It is the sparse coding matrix of coefficients

The element of the capable j of i row,

Be that coherent spot suppresses the back image.

Images