CN102509263B - 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

The relevant speckle suppression method of K-SVD based on 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 based on SAR image local statistical property specifically, can be used for the synthetic-aperture radar SAR graphical analysis of the numerous areas such as land resource monitoring, disaster analysis, urban development planning.

Background technology

Coherent speckle noise is the inherent characteristic of SAR image, together with the coherent spot of these random scatters in SAR image can be entrained in less ground object target, has a strong impact on the quality of image, and the automatic interpretation of SAR image is caused to very large difficulty.Therefore, in SAR image is processed, SAR image coherent spot suppresses to become key, be also follow-up SAR image characteristics extraction, cut apart, the basis of the work such as identification.The target of Speckle Suppression Technology is exactly: in meeting radiometric resolution, how to keep necessary spatial resolution, so in filtering speckle noise, protect the detailed information such as texture, edge.Therefore pressing down spot method, the SAR image of " good " to accomplish following 4 points: (1) effectively removes the speckle noise in even scene; (2) retain edge and textural characteristics in image; (3) do not produce pseudo-Gibbs' effect; (4) radar radiation characteristic of maintenance image.

In SAR imaging processing in earlier stage, adopt looked treatment technology inhibition coherent speckle noise more more, although this technology is simple, but taking sacrifice image resolution ratio as cost.Therefore,, taking various filtering techniques as basis, the SAR image after imaging is carried out to Speckle noise removal and become the main flow of High Resolution SAR Images processing.Filtering technique after imaging at present can be divided into airspace filter technology and transform domain filtering technique.Wherein airspace filter method comprises enhanced Lee filtering, Frost filtering and Gamma Map filtering etc., these methods are difficult to keep the minutia of image conventionally, can cause the fuzzy of image border and linear goal, the quality of filtering performance largely depends on the size of selected filter window.Transform domain method mainly contains wavelet transformation, Stationary Wavelet Transform, Bandelet conversion, Curvelet conversion and non-downsampling Contourlet conversion etc.These transform domain filtering methods are compared classical airspace filter method, and the edge of image and the hold facility of linear goal have had large increase, but mostly the coefficient of transform domain are done to certain statistical hypothesis, and these hypothesis are experimental, gear shaper without theoretical foundation.And noise has similar frequency characteristic with image border, be all high-frequency signal, the image therefore pressing down after spot often there will be pseudo-Gibbs' effect near homogeneous area and edge.

At present, a kind of emerging " dictionary learning method " obtained studying widely and applying in image is processed, and its core is the training process of dictionary, is called K-SVD algorithm.First this algorithm is proposed by the people such as Aharon, Elad.Research shows: K-SVD method has not only effectively suppressed additive white Gaussian noise, and the important information such as edge and texture all obtained good reservation, especially better to the result of texture image processing.The most important thing is that the method is a kind of Active Learning process, has good adaptability.But K-SVD algorithm is for additive noise design, and the coherent spot of SAR image is multiplicative noise, directly K-SVD algorithm application be there will be to level and smooth phenomenon in SAR image speckle.In order to overcome this shortcoming, a lot of scholars have adopted the strategy of log-transformation, first SAR image are carried out to log-transformation, change Multiplicative noise model into additivity, and then log image is carried out to denoising with K-SVD algorithm, finally carry out inverse transformation and can obtain pressing down SAR image after spot." but Statistical Properties of Logarithmically Transformed Speckle " literary composition is pointed out, SAR image is after log-transformation, its noise is not zero-mean, this causes image there will be but before and after spot, average differs larger, can not well keep the radiation characteristic of original SAR image.In addition, this also not meet noise in K-SVD algorithm be the requirement of zero-mean additive Gaussian noise.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 to weighting and improved and press down spot effect.But the method is concerning looking the lower SAR images of number, and because speckle noise can affect the training of dictionary, so final result still exists a large amount of speckle noises, and edge can be fuzzy.

Summary of the invention

The object of the invention is to overcome the deficiency of above-mentioned existing SAR image Speckle Suppression Technology, the relevant speckle suppression method of a kind of K-SVD based on SAR image local statistical property has been proposed, effectively to suppress the coherent spot of SAR image, the radiation characteristic of keep the edge information, grain details information and image preferably.

For achieving the above object, relevant speckle suppression method of the present invention, comprises the steps:

(1) to size be sAR image I carry out overlapping block extraction, and by its vectorization, obtain the set of overlapping block vector wherein N is number of pixels all in image I, y _ibe an overlapping block vector, M is the number of overlapping block vector;

(2) to the set of overlapping block vector choose at random, obtain training sample set wherein any one training sample m ' is training sample number, and meets the positive integer of 0 < M '≤M;

(3), based on SAR image local statistical property, according to redundancy rarefaction representation image denoising theory, obtain coherent spot and suppress objective function f ₁;

(4) use training sample set to training dictionary, D carries out the training of following SAR_K-SVD dictionary, obtains 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 iterations;

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

(4.3) i the training sample y to training sample set Y ' _i' carry out following SAR_OMP sparse coding, obtain y _i' sparse coding factor 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 wherein d _kthe k row of dictionary D, d _ktransposition, right ask absolute value;

(4.3d) will in step (4.3c), try to achieve more new formula of substitution indexed set in, obtain the indexed set I ' after upgrading;

(4.3e) by the I ' substitution rarefaction representation coefficient update formula α trying to achieve in step (4.3d) _i=(D _{i '}) ⁺y _i' in, obtain the rarefaction representation coefficient after upgrading, wherein D _{i '}the submatrix of dictionary D, (D _{i '}) ⁺to matrix D _{i '}ask matrix inversion operation;

(4.3f) by the α trying to achieve in step (4.3e) _isubstitution residual error is new formula r '=y more _i'-D _{i '}α _iin, obtain the residual error r ' after upgrading;

(4.3g) according to the sparse coding objective function f in step (4.2) ₂, build error update formula wherein r ' is the residual error after upgrading, D _{i '}the submatrix of the training dictionary D after upgrading, α _iit is the rarefaction representation coefficient after upgrading;

(4.3h) by the α trying to achieve in step (4.3e), (4.3f) _i, in the error update formula in r ' substitution step (4.3g), obtain upgrade after error E ';

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

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

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

(4.5) the row subscript k=k+1 of order training dictionary D, D=D '; If k≤T, proceeds to step (4.6), otherwise proceed to step (4.7), 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 ' proceeds to step (4.8), otherwise proceeds to step (4.9), and wherein M ' is training sample number;

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

(4.9) make iterations P=P+1, if P≤J proceeds to step (4.10), otherwise obtain final training dictionary wherein D is the training dictionary in iterative process, and J is maximum iteration time;

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

(5), according to redundancy rarefaction representation image denoising theory, utilize the final training dictionary obtaining in step (4) all overlapping block vector set Y are carried out to squelch, obtain coherent spot and suppress rear 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 spatial domain, original image is pressed down to spot, so overcome the deficiency of log-transformation K-SVD method, can better keep the radiation characteristic of original image;

(2) utilized the partial statistics characteristic of SAR image itself due to the present invention, and combine the advantage of dictionary training K-SVD in image denoising, so the brightness that can well keep strong reflection spot target in the speckle noise that effectively suppresses homogeneous region, and Edge texture is clear;

(3) used the SAR_K-SVD dictionary training of an Active Learning process due to the present invention, therefore there is higher adaptive ability;

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

Brief description of the drawings

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

Fig. 2 is a width true amplitude SAR image;

Fig. 3 is a width actual strength SAR image;

Fig. 4 is the present invention and the Simulation results figure of existing method to Fig. 2;

Fig. 5 is the present invention and the Simulation results figure of existing method to Fig. 3.

Embodiment

With reference to Fig. 1, of the present invention being implemented as follows:

Step 1, getting slippage factor is s=1, size is window, to input size be sAR image I, as shown in Figures 2 and 3, carry out doubling of the image piece and extract operation, obtain overlapping block vector set wherein y _ibe i overlapping block vector, M is the number of overlapping block vector, and

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

Step 2, to the set of overlapping block vector carry out random sampling, obtain training sample set wherein y _i' be i training sample, M ' is the number of training sample, and 0 < M '≤M.

Step 3, according to redundancy rarefaction representation image denoising theory, 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 refers to that the gray-scale value of SAR image pixel in smaller homogeneous region obeys certain probability distribution, and C is a constant;

(3b) based on SAR image local statistical property, obtain rarefaction representation factor alpha _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) by speckle noise n _iafter deducting 1, obtain stochastic variable n _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 _ispeckle noise, and n _i>=1, L is the number of looking of SAR image, L ^lthat a truth of a matter is the exponential that L, index are L, (n _i-1) ^l-1that a truth of a matter is (n _i-1), the index exponential that is L-1, that a truth of a matter is that e, index are-L (n _i-1) exponential, Γ () is gamma function;

(3d) by the p (x in step (3a) and 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 _ithe true atural object reflection coefficient of SAR image, n _ispeckle noise, and x _iand n _iseparate, p (x _i) be true atural object reflection coefficient x _iprobability density function, p (n _i-1) be stochastic variable n _i-1 probability density function, SAR image coherent spot model refers to y _i=x _in _i, its non-logarithmic form refers to y _ithe actual measured value of SAR image, the additive noise under non-logarithmic form, and

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

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

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 step (3e), finally trained dictionary D and rarefaction representation coefficient maximum likelihood estimation formulas as follows:

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

$=\arg \underset{D}{\max }\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{{\mathrm{\&alpha;}}_i}{\max }\left\{p(n_i-1)p\left({\mathrm{\&alpha;}}_i\right)\right\}$

Wherein, Y is the set of overlapping block vector, y _ithe actual measured value of SAR image, p (y _i| D) be overlapping block vector y _iconditional probability under training dictionary D, D and α _irespectively training dictionary and the rarefaction representation coefficient in training process, with be respectively finally to train dictionary and rarefaction representation coefficient, M is the number of all overlapping block vectors, be by with the optimum solution set forming, p (α _i) be sparse coding factor alpha _iprobability density function, p (n _i-1) be stochastic variable n _i-1 probability density function;

(3g) by the sparse coding factor alpha in step (3b) and step (3c) _iprobability density function p (α _i) and stochastic variable n _i-1 probability density function p (n _i-1), substitution maximum likelihood estimation formulas in, calculate through simplifying, obtain coherent spot and suppress objective function f ₁as follows:

$f_1=\{\hat{D},{\widehat{\mathrm{\&alpha;}}}_i\}=\arg \underset{D,{\mathrm{\&alpha;}}_i}{\min }{\left|\right|{\mathrm{\&alpha;}}_i\left|\right|}_0+\mathrm{\&lambda;}{\left|\right|y_i-D{\mathrm{\&alpha;}}_i\left|\right|}_2^2\&CenterDot;\frac{1}{{\left|\right|D{\mathrm{\&alpha;}}_i\left|\right|}_2^2},$

Wherein, y _ithe actual measured value of SAR image, D and α _irespectively training dictionary and the rarefaction representation coefficient in training process, with respectively finally to train dictionary and rarefaction representation coefficient, be by with the optimum solution set forming, λ is Lagrange multiplier, || || ₀0 norm, 2 norms.

Step 4, uses training sample set to training dictionary, D carries out the training of following SAR_K-SVD dictionary, obtains 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 iterations;

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

$f_2={\widehat{\mathrm{\&alpha;}}}_i=\arg \underset{{\mathrm{\&alpha;}}_i}{\min }{\left|\right|{\mathrm{\&alpha;}}_i\left|\right|}_0+\mathrm{\&lambda;}{\left|\right|y_i-D{\mathrm{\&alpha;}}_i\left|\right|}_2^2\&CenterDot;\frac{1}{{\left|\right|D{\mathrm{\&alpha;}}_i\left|\right|}_2^2},$

Wherein, y _ibe the actual measured value of SAR image, D is the training dictionary remaining unchanged, α _ithe rarefaction representation coefficient in sparse coding process, be final rarefaction representation coefficient, λ is Lagrange multiplier, || || ₀0 norm, 2 norms.

(4.3) i the training sample y to training sample set Y ' _i' carry out following SAR orthogonal matching pursuit SAR_OMP sparse coding, obtain y _i' sparse coding factor 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 wherein d _kthe k row of dictionary D, d _ktransposition, right ask absolute value;

(4.3d) will in step (4.3c), try to achieve more new formula of substitution indexed set in, obtain the indexed set I ' after upgrading;

(4.3e) by the I ' substitution rarefaction representation coefficient update formula α trying to achieve in step (4.3d) _i=(D _{i '}) ⁺y _i' in, obtain the rarefaction representation factor alpha after upgrading _i, wherein D _{i '}the submatrix of dictionary D, (D _{i '}) ⁺to matrix D _{i '}ask matrix inversion operation;

(4.3f) by the α trying to achieve in step (4.3e) _isubstitution residual error is new formula r '=y more _i'-D _{i '}α _iin, obtain the residual error r ' after upgrading;

(4.3g) according to the sparse coding objective function f in step (4.2) ₂, build error update formula wherein r ' is the residual error after upgrading, D _{i '}the submatrix of the training dictionary D after upgrading, α _iit is the rarefaction representation coefficient after upgrading;

(4.3h) by the α trying to achieve in step (4.3e), (4.3f) _i, in the error update formula in r ' substitution step (4.3g), obtain upgrade after error E ';

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

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

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

(4.5) the row subscript k=k+1 of order training dictionary D, D=D '; If k≤T, proceeds to step (4.6), otherwise proceed to step (4.7), 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 ' proceeds to step (4.8), otherwise proceeds to step (4.9), and wherein M ' is training sample number;

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

(4.9) make iterations P=P+1, if P≤J proceeds to step (4.10), otherwise obtain final training dictionary wherein D is the training dictionary in iterative process, and J is maximum iteration time;

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

Step 5, according to redundancy rarefaction representation image denoising theory, utilizes final training dictionary all overlapping block vector set Y are carried out to squelch, obtain coherent spot and suppress rear image

(5a) utilize final training dictionary to all overlapping block vector set carry out SAR_OMP sparse coding, obtain sparse coding matrix of coefficients

(5b) by the sparse coding matrix of coefficients obtaining in step (Sa) the estimator of substitution overlapping block vector set Y in, obtain the estimation of overlapping block vector set Y

(5c) estimation to overlapping block vector set Y according to following formula be weighted on average, obtain SAR image coherent spot and suppress rear image

$\hat{I}={(\mathrm{\&lambda;I}+\underset{i,j}{\mathrm{\&Sigma;}}{R}_{\mathrm{ij}}^T{R}_{\mathrm{ij}})}^{-1}(\mathrm{\&lambda;}\hat{Y}+\underset{i,j}{\mathrm{\&Sigma;}}{R}_{\mathrm{ij}}^T\hat{D}{\widehat{\mathrm{\&alpha;}}}_{\mathrm{ij}}^{\&prime;}),$

Wherein, λ is Lagrange multiplier, and I is original SAR image array, R _ijoverlapping block operations factor, the transposition of overlapping block operations factor, the estimation of overlapping block vector set Y, right inversion operation, finally to train dictionary, it is sparse coding matrix of coefficients the element of the capable j of i row, be image after coherent spot suppresses, first redundancy rarefaction representation image denoising theory refers to one group of redundancy basis representation for image, obtains redundancy rarefaction representation coefficient, and then redundancy rarefaction representation coefficient is obtained to the image after squelch do inverse transformation.

Effect of the present invention can further illustrate by following experimental result and analysis:

1. experimental data

Experimental data of the present invention is the true SAR image of two width, and a width 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 is that original image is the ku wave band that is positioned at Albuquerque area, the New Mexico 4 apparent intensity SAR images 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 log_K-SVD that scholar Samuel Foucher proposes for 2008 in article " SAR Image Filtering via Learned Dictionaries and Sparse Representations ";

Method 3: the inventive method.

3. experiment content and interpretation of result

The true SAR view data of two width is as shown in Figures 2 and 3 carried out to coherent spot inhibition with distinct methods, the result obtaining as shown in Figure 4 and Figure 5, the coherent spot that wherein Fig. 4 (a) and Fig. 5 (a) obtain for existing method 1 suppresses result figure, the coherent spot that Fig. 4 (b) and Fig. 5 (b) obtain for existing method 2 suppresses result figure, the coherent spot inhibition result figure that Fig. 4 (c) and Fig. 5 (c) obtain for the inventive method.As can be seen from Figure 4 and Figure 5, the speckle noise in existing method 1 result figure has obtained filtering effectively, and texture information also obtained certain reservation, but obvious cut effect has appearred in homogeneous region, edge and strong reflection spot objective fuzzy; In the result figure of existing method 2, the detailed information such as edge, texture has obtained good reservation, but still quite a large amount of existing of speckle noise in homogeneous region, and can not well keep the radiation characteristic of original image; The inventive method has significantly been improved result, not only effectively suppressed the speckle noise of homogeneous region, well kept point target and Edge texture information, and effectively suppressed homogeneous region cut effect, well kept the radiation characteristic of original image.

Experiment coherent spot is suppressed to result and carry out quantitative test, some homogeneous regions as shown in white rectangle in Fig. 2 and Fig. 3, are selected, adopt average MRI and the edge of equivalent number ENL, ratio images to keep the performance index such as index E PD-ROA to evaluate coherent spot inhibition, result as shown in Table 1 and Table 2.

Table 1. suppresses evaluation of result index to the coherent spot of Fig. 2

Table 2. suppresses evaluation of result index to the coherent spot of Fig. 3

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

Claims (1)

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 be sAR image I carry out overlapping block extraction, and by its vectorization, obtain the set of overlapping block vector wherein N is number of pixels all in image I, y _ibe an overlapping block vector, M is the number of overlapping block vector;

(2) to the set of overlapping block vector choose at random, obtain training sample set wherein any one training sample m ' is training sample number, and meets the positive integer of 0 < M '≤M;

(3), based on SAR image local statistical property, according to redundancy rarefaction representation image denoising theory, obtain suppressing objective function f based on the K-SVD coherent spot of SAR image local statistical property 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 C is a constant;

(3b) based on SAR image local statistical property, obtain rarefaction representation factor alpha _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 exponential function;

(3c) by speckle noise n _iafter deducting 1, obtain stochastic variable n _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 _ispeckle noise, and n _i>=1, L is the number of looking of SAR image, L ^lthat a truth of a matter is the exponential that L, index are L, (n _i-1) ^l-1that a truth of a matter is (n _i-1), the index exponential that is L-1, that a truth of a matter is that e, index are-L (n _i-1) exponential, Γ () is gamma function;

(3d) by the p (x in step (3a) and 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

$p\left({\tilde{n}}_i\right)=p\left(x_i(n_i-1)\right)=p\left(x_i\right)\&CenterDot;p(n_i-1),$

Wherein, x _ithe true atural object reflection coefficient of SAR image, n _ispeckle noise, and x _iand n _iseparate, p (x _i) be true atural object reflection coefficient x _iprobability density function, p (n _i-1) be stochastic variable n _i-1 probability density function;

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

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

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 step (3e), finally trained dictionary with final rarefaction representation coefficient maximum likelihood estimation formulas as follows:

$\begin{array}{c}\{\hat{D},\widehat{\mathrm{\&alpha;}}\}=\arg \underset{D}{\max }p\left(Y\right|D)=\arg \underset{D}{\max }\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}p\left(y_i\right|D)\\ =\arg \underset{D}{\max }\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{{\mathrm{\&alpha;}}_i}{\max }\left\{p(n_i-1)p\left({\mathrm{\&alpha;}}_i\right)\right\}\end{array},$

Wherein, Y is the set of overlapping block vector, y _ithe actual measured value of SAR image, p (y _i| D) be overlapping block vector y _iconditional probability under training dictionary D, D and α _irespectively training dictionary and the rarefaction representation coefficient in training process, with be respectively finally to train dictionary and final rarefaction representation coefficient, M is the number of all overlapping block vectors, be by with the optimum solution set forming, p (α _i) be sparse coding factor alpha _iprobability density function, p (n _i-1) be stochastic variable n _i-1 probability density function;

(3g) by the sparse coding factor alpha in step (3b) and step (3c) _iprobability density function p (α _i) and stochastic variable n _i-1 probability density function p (n _i-1), substitution maximum likelihood estimation formulas in, calculate through simplifying, obtain coherent spot and suppress objective function f ₁as follows:

$f_1=\{\hat{D},{\widehat{\mathrm{\&alpha;}}}_i\}=\arg \underset{D,{\mathrm{\&alpha;}}_i}{\min }{\left|\right|{\mathrm{\&alpha;}}_i\left|\right|}_0+\mathrm{\&lambda;}{\left|\right|y_i-{\mathrm{D\&alpha;}}_i\left|\right|}_2^2\&CenterDot;\frac{1}{{\left|\right|{\mathrm{D\&alpha;}}_i\left|\right|}_2^2},$

Wherein, y _ithe actual measured value of SAR image, D and α _irespectively training dictionary and the rarefaction representation coefficient in training process, with respectively finally to train dictionary and final rarefaction representation coefficient, be by with the optimum solution set forming, λ is Lagrange multiplier, || || ₀0 norm, 2 norms;

(4) use training sample set to training dictionary, D carries out the training of following SAR_K-SVD dictionary, obtains 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 iterations;

(4.2) suppress objective function f according to the coherent spot in step (3) ₁, in the situation that keeping training dictionary D constant, obtain being applicable to the K-SVD sparse coding objective function f based on SAR image local statistical property of SAR image ₂:

$f_2={\widehat{\mathrm{\&alpha;}}}_i=\arg \underset{{\mathrm{\&alpha;}}_i}{\min }{\left|\right|{\mathrm{\&alpha;}}_i\left|\right|}_0+\mathrm{\&lambda;}{\left|\right|y_i-{\mathrm{D\&alpha;}}_i\left|\right|}_2^2\&CenterDot;\frac{1}{{\left|\right|{\mathrm{D\&alpha;}}_i\left|\right|}_2^2},$

Wherein, y _ibe the actual measured value of SAR image, D is the training dictionary remaining unchanged, α _ithe rarefaction representation coefficient in sparse coding process, be final rarefaction representation coefficient, λ is Lagrange multiplier, || || ₀0 norm, 2 norms;

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

(4.3a) make initial indexed set I ⁰=(), initial residual error r ⁰=y _i', initial rarefaction representation coefficient initial error $E=\frac{\left|\right|r^0\left|\right|}{\left|\right|y_i^{\&prime;}\left|\right|};$

(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 wherein d _kthe k row of dictionary D, d _ktransposition, right ask absolute value;

(4.3d) will in step (4.3c), try to achieve more new formula of substitution indexed set in, obtain the indexed set I ' after upgrading;

(4.3e) by the I ' substitution rarefaction representation coefficient update formula of trying to achieve in step (4.3d) in, obtain the rarefaction representation factor alpha after upgrading _i, wherein the submatrix of dictionary D, to matrix ask matrix inversion operation;

(4.3f) by the α trying to achieve in step (4.3e) _imore new formula of substitution residual error in, obtain the residual error r ' after upgrading;

(4.3g) according to the sparse coding objective function f in step (4.2) ₂, build error update formula wherein r ' is the residual error after upgrading, the submatrix of the training dictionary D after upgrading, α _iit is the rarefaction representation coefficient after upgrading;

(4.3h) by the α trying to achieve in step (4.3e), (4.3f) _i, in the error update formula in r ' substitution step (4.3g), obtain upgrade after error E ';

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

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

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

(4.5) the row subscript k=k+1 of order training dictionary D, D=D '; If k≤T, proceeds to step (4.6), otherwise proceed to step (4.7), 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 ' proceeds to step (4.8), otherwise proceeds to step (4.9), and wherein M ' is training sample number;

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

(4.9) make iterations P=P+1, if P≤J proceeds to step (4.10), otherwise obtain final training dictionary wherein D is the training dictionary in iterative process, and J is maximum iteration time;

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

(5) according to the K-SVD redundancy rarefaction representation image denoising theory based on SAR image local statistical property, utilize the final training dictionary obtaining in step (4) all overlapping block vector set Y are carried out to squelch, obtain coherent spot and suppress rear image

(5a) utilize final training dictionary to all overlapping block vector set carry out SAR_OMP sparse coding, obtain sparse coding matrix of coefficients

(5b) by the sparse coding matrix of coefficients obtaining in step (5a) the estimator of substitution overlapping block vector set Y in, obtain the estimation of overlapping block vector set Y

(5c) estimation to overlapping block vector set Y according to following formula be weighted on average, obtain SAR image coherent spot and suppress rear image

Wherein, λ is Lagrange multiplier, and I is original SAR image array, R _ijoverlapping block operations factor, the transposition of overlapping block operations factor, the estimation of overlapping block vector set Y, right inversion operation, finally to train dictionary, it is sparse coding matrix of coefficients the element of the capable j of i row, it is image after coherent spot suppresses.