CN106446935A - Kernel sparse representation and spatial constraint-based polarimetric SAR image classification method - Google Patents

Abstract

The invention discloses a kernel sparse representation and spatial constraint-based polarimetric SAR image classification method and belongs to the technical field of polarimetric SAR image classification. The method is used for solving the problem of low polarimetric SAR image classification efficiency caused by the fact that a pixel-based polarimetric SAR remote sensing image classification method has a high dimension characteristic and an excessively large calculation amount. The method comprises the classification steps of preprocessing an original polarimetric SAR image data to obtain to-be-classified polarimetric SAR image data; determining image types and training samples; performing polarimetric SAR image feature extraction based on a multicomponent scattering model, and eigenvalue decomposition and gray-level co-concurrence matrixes; constructing an over-complete dictionary; obtaining optimal sparse coefficients of the training samples of the image types; and performing signal reconstruction by utilizing the optimal sparse coefficients, and determining the image types according to reconstructed signals of the training samples of the image types and errors of to-be-classified polarimetric SAR images, thereby realizing the classification of the to-be-classified polarimetric SAR images. The method is used for the polarimetric SAR image classification.

Description

Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint

Technical field

The present invention relates to the Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint, belong to polarization SAR figure As sorting technique field.

Background technology

Polarimetric synthetic aperture radar (SAR) as a kind of advanced microwave remote sensing means, have round-the-clock, round-the-clock, point The advantage that resolution is high, large area covers, it passes through the echo information under observation different transmitting-receiving polarization combination, distinguishes the careful of object The parameters such as structure, target sensing and material composition carry out the backscattering characteristic that more adding system comprehensively reflects target, thus obtaining Obtain the terrestrial object information more fully enriching, have broad application prospects in remote sensing fields.

Come into operation with increasing polarization SAR system, the polarimetric SAR image data of acquisition is more and more abundanter, such as What is made to these view data and quickly and accurately interpreting, a difficult problem always in the urgent need to address.Polarimetric SAR Image Classification refers to the polarization SAR Interpretation Technology classified of atural object occurring in scene, merged image procossing, pattern recognition, The research of the multiple fields such as artificial intelligence.For the classification of atural object, mainly include supervised classification and two kinds of unsupervised classification.Supervision Classification is classification to be previously set according to the comparison diagram of scattered information in existing atural object classification figure or Polarimetric SAR Image, and The training sample choosing each class is trained.Unsupervised classification does not have human intervention for atural object classification, and program is according to certain Criterion carries out cluster and obtains classification results.

Sparse representation theory is the important tool that data efficient represents, is the once breakthrough Theory Advance that signal represents, The rarefaction representation of signal can be realized by excessively complete dictionary, be significant in the epoch of information-intensive society data explosion. At present, in recognition of face, the aspect such as classification hyperspectral imagery and SAR automatic target detection achieves significantly rarefaction representation Achievement.

With the raising of SAR system data retrieval capabilities and image resolution ratio, in image, target type is more finely various, Point target in low resolution SAR image becomes target area in high-definition picture, is provided with region and Texture eigenvalue.? In image classification and interpretation, except the scattering propertiess of target itself are in addition it is also necessary to consider its spatial relationship.Research shows, in remote sensing In image, neighbor tends to belong to same category, and its Electromagnetic Scattering Characteristics and other features often have larger similarity. Therefore, during rarefaction representation in addition to limiting sparse condition and reconstruction accuracy, it should also be taken into account that the space of neighbor Constraint.Meet hypothesis below：For the adjacent pixel in space, approximately linear can be carried out with identical training sample and represent, But the weight coefficient of corresponding training sample is different.The i.e. support of the atom in excessively complete dictionary in the rarefaction representation of neighbor Collection is identical, and different is only weight coefficient.

Higher-dimension that existing sorting technique based on pixel exists and the excessive defect of amount of calculation, and its specification area one Cause property is poor, has had a strong impact on the classification effectiveness of Polarimetric SAR Image.

Content of the invention

The invention aims to solve existing based on the area based on polarimetric SAR image classification method of pixel exist higher-dimension and The excessive defect of amount of calculation, causes the low problem of Classification of Polarimetric SAR Image efficiency, there is provided one kind is based on nuclear sparse expression and sky Between constraint Classification of Polarimetric SAR Image method.

Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint of the present invention, it includes following step Suddenly：

Step one：Collection original polarization SAR image data, carries out pretreatment, obtains polarimetric SAR image data to be sorted；

Step 2：Determine the image category of polarimetric SAR image data to be sorted and the training sample of each image category；

Step 3：Multicomponent scattering model, feature are based on successively to Polarimetric SAR Image to be sorted according to described image classification Value is decomposed and gray level co-occurrence matrixes carry out Polarimetric SAR Image feature extraction：

A：Polarimetric SAR Image scattering signatures based on multicomponent scattering model extract：Polarimetric SAR Image to be sorted is carried out Polarization target decomposition, obtains the scattering that odd scattering, even scattering, volume scattering, line scattering and spiral scatter five kinds of scattering compositions Power；

B：The Polarimetric SAR Image polarization characteristic that feature based value is decomposed extracts：To Polarimetric SAR Image feature based to be sorted Value decomposes three eigenvalues of acquisition and Polarization scattering entropy, average scattering angle and anisotropy amount；

C：Polarimetric SAR Image texture feature extraction based on gray level co-occurrence matrixes：Energy is extracted to Polarimetric SAR Image to be sorted Amount and contrast textural characteristics；

Step 4：All features that in step 3, Polarimetric SAR Image to be sorted is carried out with feature extraction acquisition are carried out whole Close and kernel function mapping, by the use of each described image classification training sample characteristic vector as the atom of dictionary, built complete Standby dictionary；

Step 5：According to the excessively complete dictionary obtaining and space constraint relation, using synchronous orthogonal matching pursuit algorithm pair Polarimetric SAR Image to be sorted carries out rarefaction representation, obtains the optimum sparse coefficient of each image category training sample；

Step 6：Optimum sparse coefficient using each the image category training sample obtaining in step 5 carries out signal weight Build, the image class belonging to error decision of the reconstruction signal according to each image category training sample and Polarimetric SAR Image to be sorted Not, realize the classification to Polarimetric SAR Image to be sorted.

Advantages of the present invention：The inventive method is applied to field of remote sensing image processing, realizes the classification of Polarimetric SAR Image. The polarization characteristic of Polarimetric SAR Image and textural characteristics are combined by it, preferably describe characters of ground object, and are realized by nuclear mapping Non-linear transfer, based on sparse representation theory and space constraint, makes full use of the similarity of adjacent space, decreases the dimension of classification Degree and complexity, solve the problems, such as that the specification area concordance based on pixel is poor, improve the classification effect of Polarimetric SAR Image Rate.

Brief description

Fig. 1 is the flow chart of the Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint of the present invention；

Fig. 2 is the magnitude image of Polarimetric SAR Image hh passage to be sorted；

Fig. 3 is multicomponent goal decomposition result schematic diagram；

Fig. 4 is Eigenvalues Decomposition result schematic diagram；

Fig. 5 is the energy diagram of gray level co-occurrence matrixes；

Fig. 6 is gray level co-occurrence matrixes contrast schematic diagram；

Fig. 5 and Fig. 6 is as the textural characteristics schematic diagram of gray level co-occurrence matrixes；

Fig. 7 is the sparse representation model of space constraint；

Fig. 8 is the classification results schematic diagram of present invention Polarimetric SAR Image to be sorted.

Specific embodiment

Specific embodiment one：With reference to Fig. 1 to Fig. 8, present embodiment is described, is based on core described in present embodiment dilute Relieving the exterior syndrome shows the Classification of Polarimetric SAR Image method with space constraint, and it comprises the following steps：

Step one：Collection original polarization SAR image data, carries out pretreatment, obtains polarimetric SAR image data to be sorted；

Step 2：Determine the image category of polarimetric SAR image data to be sorted and the training sample of each image category；

Step 3：Multicomponent scattering model, feature are based on successively to Polarimetric SAR Image to be sorted according to described image classification Value is decomposed and gray level co-occurrence matrixes carry out Polarimetric SAR Image feature extraction：

A：Polarimetric SAR Image scattering signatures based on multicomponent scattering model extract：Polarimetric SAR Image to be sorted is carried out Polarization target decomposition, obtains the scattering that odd scattering, even scattering, volume scattering, line scattering and spiral scatter five kinds of scattering compositions Power；

B：The Polarimetric SAR Image polarization characteristic that feature based value is decomposed extracts：To Polarimetric SAR Image feature based to be sorted Value decomposes three eigenvalues of acquisition and Polarization scattering entropy, average scattering angle and anisotropy amount；

C：Polarimetric SAR Image texture feature extraction based on gray level co-occurrence matrixes：Energy is extracted to Polarimetric SAR Image to be sorted Amount and contrast textural characteristics；

Step 4：All features that in step 3, Polarimetric SAR Image to be sorted is carried out with feature extraction acquisition are carried out whole Close and kernel function mapping, by the use of each described image classification training sample characteristic vector as the atom of dictionary, built complete Standby dictionary；

Step 5：According to the excessively complete dictionary obtaining and space constraint relation, using synchronous orthogonal matching pursuit algorithm pair Polarimetric SAR Image to be sorted carries out rarefaction representation, obtains the optimum sparse coefficient of each image category training sample；

Step 6：Optimum sparse coefficient using each the image category training sample obtaining in step 5 carries out signal weight Build, the image class belonging to error decision of the reconstruction signal according to each image category training sample and Polarimetric SAR Image to be sorted Not, realize the classification to Polarimetric SAR Image to be sorted.

In the A of step 3, the Polarimetric SAR Image scattering signatures extraction detailed process based on multicomponent scattering model is：

The covariance matrix of Polarimetric SAR Image to be sorted is decomposed into odd scattering, even scattering, volume scattering, spiral dissipate Penetrate the weighted sum scattering five kinds of basic scattering mechanisms with line：

C=f_oddC_odd+f_doubleC_double+f_volumeC_volume+f_helixC_helix+f_wireC_wire, (1)

In formula, C is the covariance matrix of Polarimetric SAR Image to be sorted, C_oddScatter covariance matrix, C for odd_doubleFor Even scatters covariance matrix, C_volumeFor volume scattering covariance matrix, C_helixScatter covariance matrix, C for spiral_wireFor line Scattering covariance matrix, f_oddFor the weight coefficient of odd scattering, f_doubleFor the weight coefficient of even scattering, f_volumeDissipate for body The weight coefficient penetrated, f_helixFor the weight coefficient of spiral scattering, f_wireWeight coefficient for line scattering；

The covariance matrix of Polarimetric SAR Image to be sorted<C>For：

Each element S in formula_pq(p, q=h v) represent that, with the transmitting of q polarization mode, target when p-polarization mode receives is backward Complex scattering coefficients,<>Represent spacial average；

Make formula (1) equal sign left and right sides items correspondent equal, that is,：

In formula, β is the ratio of hh backscattering coefficient in odd scattering and vv backscattering coefficient, and α is hh in even scattering Backscattering coefficient and the ratio of vv backscattering coefficient, γ is the ratio of hh polarization and vv polarization backscattering coefficient in line scattering Value, ρ is the ratio of hv polarization in line scattering and vv polarization backscattering coefficient；

Solve the weight coefficient f that above formula obtains five kinds of scattering mechanisms_odd、f_double、f_volume、f_helixAnd f_wire, and then solve Obtain scattered power P of odd scattering_odd, even scattering scattered power P_double, scattered power P of volume scattering_volume, spiral Scattered power P of scattering_helix, line scattering scattered power P_wireAnd total scattering power P：

Thus Polarimetric SAR Image to be sorted is decomposed into the power of five kinds of Polarization scattering mechanism as Polarization scattering feature.

The Polarimetric SAR Image polarization characteristic that in the B of step 3, feature based value is decomposed extracts detailed process：

The coherence matrix of Polarimetric SAR Image to be sorted<T>Eigenvalues Decomposition be expressed as follows：

In formula, H is Matrix Conjugate transposition, and T is matrix transpose, Λ=diag { λ₁,λ₂,λ₃, it is characterized value diagonal matrix, should The diagonal of eigenvalue diagonal matrix is three eigenvalues of coherence matrix, λ₁≥λ₂≥λ₃>=0,It is characterized arrow Moment matrix, its column vector corresponds to<T>Orthogonal characteristic vectorWithCharacteristic vector is expressed as：

α in formula_iRepresent the internal degree of freedom of scattering object, span is 0 °≤α_i≤90°；β_iFor scattering object with respect to thunder Reach the deflection of sight line, span is -180 °≤β_i≤180°；δ_iFor the first scattering phase angle of scattering object, γ_iFor scattering Second scattering phase angle of body；

Define Polarization scattering entropy H, average scattering angle according to three eigenvaluesWith anisotropy amount A, respectively：

P in formula_iFor：p_i=λ_i/ ∑ λ, wherein λ=λ₁+λ₂+λ₃；

For Polarization scattering entropy H, 0≤H≤1, reflection Polarimetric SAR Image dissipates from isotropic scatterning H=0 to completely random Penetrate the unordered degree of statistics of H=1；Average scattering angle Represent the scattering mechanism of Polarimetric SAR Image；Each to different Property amount A reflect the size of second, third eigenvalue, be the supplementary parameter of scattering entropy.

In the C of step 3, the Polarimetric SAR Image texture feature extraction detailed process based on gray level co-occurrence matrixes is：

Based on Probability p (a, the b) computing formula of gray level co-occurrence matrixes it is：

Above formula represents that on a position in Polarimetric SAR Image to be sorted, gray level is the pixel of a to give apart from d and side To θ on another location gray level be b pixel occur Probability p (a, b | θ, d)；

The matrix form of gray level co-occurrence matrixes GLCM is：

In formula, L is gradation of image series；

ENERGY E NY based on gray level co-occurrence matrixes and contrast C ON are used for describing the texture spy of Polarimetric SAR Image to be sorted Levy, be defined as：

ENERGY E NY represents the uniformity of intensity profile in Polarimetric SAR Image to be sorted；

Contrast C ON represents the definition of Polarimetric SAR Image to be sorted.

The detailed process building complete dictionary in step 4 is：

All features that Polarimetric SAR Image to be sorted in step 3 is carried out feature extraction acquisition are integrated, and acquisition is retouched State the characteristic vector of training sample, recycle l₂Norm method is normalized, and the characteristic vector after normalization is carried out kernel function Space reflection, the atom as dictionary built complete dictionary；

Set image category number as Q, for classification i, i=1,2 ..., Q, the N of selection_iThe M Wei Te of individual training sample Levy vector to be normalized, obtain N_iIndividual characteristic vectorExcessively complete dictionary as atomic building classification i

If being mapped as φ from data space to higher dimensional space, carried out in characteristic space vector using gaussian radial basis function The long-pending kernel function calculatingFor：

In formula, σ is constant；For space pixel p in Polarimetric SAR Image to be sorted_mCharacteristic vector,For polarization to be sorted Space pixel p in SAR image_nCharacteristic vector；

Mapped by kernel function, atomIt is each mapped toCross complete dictionary D_iIt is mapped as D_φi, the excessively complete dictionary of all categoriesAfter being mapped by kernel function, composition mapped complete dictionary D_φ：D_φ=[D_φ1,…,D_φQ]∈R^M*N(N=N₁+…+N_Q).

The detailed process obtaining the optimum sparse coefficient of each image category training sample in step 5 is：

If Polarimetric SAR Image spatial neighborhood pixels p to be sorted_mAnd p_n, the characteristic vector of extraction is respectivelyWithKernel function is mapped asWithFor classification i,By excessively complete dictionary D_φiRarefaction representation is：

In formula,It is characterized vectorKernel function mapping vector,For rarefaction representation Coefficient vector, x_im1,x_im2,L,For dictionary D excessively complete during rarefaction representation_φiIn each atom weight coefficient, wherein non-zero The subscript collection of coefficient is combined into

According to space constraint relation, neighbor p_nThe characteristic vector extractingNuclear mapping vectorFor classification i, use Pixel p_mIdentical atomBut different coefficients carry out linear expression：

It is set with u spatial neighborhood pixels, the eigenmatrix that the feature of extraction builds after kernel function mapping isFor classification i, by excessively complete dictionary D_φiRarefaction representation is：

In formula, coefficient matrix X_iMiddle nonzero term has identical bottom to mark

Therefore, the sparse representation model of space constraintFor：

In formula, | | X | |_{OK, 0}Represent coefficient matrix X_iIn non-zero row number, referred to as degree of rarefication K；

The sparse representation model of space constraint is converted into using degree of rarefication K as relaxation condition：

In formula | | | |_FFor Frobenius norm,Optimum sparse coefficient training sample tried to achieve for classification i.

Realize in step 6 to the detailed process of the classification of all Polarimetric SAR Images to be sorted be：

Q excessively complete dictionary D of Q class image category composition₁,D₂,...D_Q, after kernel function mapping, obtain each class respectively The optimum sparse coefficient of other training sampleAgain solve acquisition Polarimetric SAR Image to be sorted with different classes of Error r of excellent sparse coefficient reconstruction signal_i(Φ_φ)：

In formula | | | |₂For norm；

Polarimetric SAR Image generic to be sorted is judged by minimum residual method, chooses residual with Polarimetric SAR Image to be sorted The minimum classification representated by reconstruction signal of difference is as affiliated image category Class (Φ) of this Polarimetric SAR Image to be sorted：

In present embodiment, orthogonal characteristic vectorWithCan be understood as certain scattering mechanism.α_iCorresponding certain Scattering mechanism type, unrelated with the direction of scattering object；β_iRelevant with the rotation of sensor coordinate system, if adopting Pauli base Vector quantization is carried out to collision matrix, then β_iFor scattering object with respect to radar line of sight deflection.In described polarization SAR to be sorted In image, the rill of texture is deeper, then its contrast C ON is bigger, and the visual effect of image is clear.Constant σ practical application When take appropriate value as needed.

According to space constraint relation, the adjacent pixel in space can carry out approximately linear with identical training sample and represent, But corresponding weight coefficient is different, and that is, in the rarefaction representation of neighbor, the atom in excessively complete dictionary is identical, different It is only weight coefficient.

Embodiment 1：The effect of the present invention can be further illustrated by following experiment.

1st, experimental data

The present invention experiment used by data be EMISAR Foulum area Polarimetric SAR Image, image size be 886 × 1100 pixels.This area has the multiformity of atural object, and its hh channel amplitude image is as shown in Fig. 2 cut according on Google Maps The optical picture taking understand Foulum area atural object can be divided into forest, city, bare area, thin through crop, broad leaf crop five class.Described The optical picture the intercepting same time non-with polarization SAR data obtains.

2nd, experiment content and analysis

To Polarimetric SAR Image, classified based on the Classification of Polarimetric SAR Image method of nuclear sparse expression and space constraint, Result is as shown in Figure 8.

For test sample, the nicety of grading of the Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint Confusion matrix is as shown in table 1.Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint and dividing based on SVM Class classification Comparative result is as shown in table 2.

Table 1

Table 2

By the classification results of Fig. 8 it can be seen that Classification of Polarimetric SAR Image side based on nuclear sparse expression and space constraint Method can obtain classification results well, especially homogeneous area, due to space constraint, atural object can be had and more comprehensively retouch State, it is possible to reduce the noise of classification results, thus further increase classifying quality.From table 2 it can be seen that except improving classification Precision, in terms of classification effectiveness, the inventive method takes as 241s, and is taken based on the rarefaction representation sorting technique of pixel and be 1154s.This is because combining the rarefaction representation of space constraint in categorizing process, the rarefaction representation process of neighbor is simultaneously Carry out, and in the categorizing process of rarefaction representation, rarefaction representation is carried out based on single pixel.Therefore, based on sparse table Show that the Classification of Polarimetric SAR Image method with space constraint not only make use of spatial information, improves nicety of grading consistent with region Property, and classification effectiveness is greatly improved.

Claims (7)

1. a kind of Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint it is characterised in that it include following Step：

Step one：Collection original polarization SAR image data, carries out pretreatment, obtains polarimetric SAR image data to be sorted；

Step 2：Determine the image category of polarimetric SAR image data to be sorted and the training sample of each image category；

Step 3：Multicomponent scattering model is based on successively to Polarimetric SAR Image to be sorted according to described image classification, eigenvalue divides Solution and gray level co-occurrence matrixes carry out Polarimetric SAR Image feature extraction：

A：Polarimetric SAR Image scattering signatures based on multicomponent scattering model extract：Polarimetric SAR Image to be sorted is polarized Goal decomposition, obtains the scattered power that odd scattering, even scattering, volume scattering, line scattering and spiral scatter five kinds of scattering compositions；

B：The Polarimetric SAR Image polarization characteristic that feature based value is decomposed extracts：Polarimetric SAR Image feature based value to be sorted is divided Solution obtains three eigenvalues and Polarization scattering entropy, average scattering angle and anisotropy amount；

C：Polarimetric SAR Image texture feature extraction based on gray level co-occurrence matrixes：To Polarimetric SAR Image to be sorted extract energy and Contrast textural characteristics；

Step 4：All features that in step 3, Polarimetric SAR Image to be sorted is carried out with feature extraction acquisition are integrated and Kernel function map, by the use of each described image classification training sample characteristic vector as the atom of dictionary, built complete word Allusion quotation；

Step 5：According to the excessively complete dictionary obtaining and space constraint relation, treated point using synchronous orthogonal matching pursuit algorithm Class Polarimetric SAR Image carries out rarefaction representation, obtains the optimum sparse coefficient of each image category training sample；

Step 6：Optimum sparse coefficient using each the image category training sample obtaining in step 5 carries out signal reconstruction, The image category belonging to error decision of the reconstruction signal according to each image category training sample and Polarimetric SAR Image to be sorted, Realize the classification to Polarimetric SAR Image to be sorted.

2. the Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint according to claim 1, its feature It is, in the A of step 3, the Polarimetric SAR Image scattering signatures extraction detailed process based on multicomponent scattering model is：

By the covariance matrix of Polarimetric SAR Image to be sorted be decomposed into odd scattering, even scattering, volume scattering, spiral scattering and Line scatters the weighted sum of five kinds of basic scattering mechanisms：

C=f_oddC_odd+f_doubleC_double+f_volumeC_volume+f_helixC_helix+f_wireC_wire, (1)

In formula, C is the covariance matrix of Polarimetric SAR Image to be sorted, C_oddScatter covariance matrix, C for odd_doubleFor even Scattering covariance matrix, C_volumeFor volume scattering covariance matrix, C_helixScatter covariance matrix, C for spiral_wireFor line scattering Covariance matrix, f_oddFor the weight coefficient of odd scattering, f_doubleFor the weight coefficient of even scattering, f_volumeFor volume scattering Weight coefficient, f_helixFor the weight coefficient of spiral scattering, f_wireWeight coefficient for line scattering；

The covariance matrix of Polarimetric SAR Image to be sorted<C>For：

$<C>=\left[\begin{array}{ccc}<{\left|S_{hh}\right|}^2>& \sqrt{2}<S_{hh}{S}_{hv}^{*}>& <S_{hh}{S}_{vv}^{*}>\\ \sqrt{2}<S_{hv}{S}_{hh}^{*}>& 2<{\left|S_{hv}\right|}^2>& \sqrt{2}<S_{hv}{S}_{vv}^{*}>\\ <S_{vv}{S}_{hh}^{*}>& \sqrt{2}<S_{vv}{S}_{hv}^{*}>& <{\left|S_{vv}\right|}^2>\end{array}\right],---\left(2\right)$

Each element S in formula_pq(p, q=h v) represent that, with the transmitting of q polarization mode, target when p-polarization mode receives dissipates backward again Penetrate coefficient,<>Represent spacial average；

Make formula (1) equal sign left and right sides items correspondent equal, that is,：

$<{\left|S_{vv}\right|}^2>=f_{odd}+f_{double}+f_{volume}+\frac{1}{4}{f}_{helix}+f_{wire}$

$<S_{hh}{S}_{vv}^{*}>=f_{odd}\mathrm{\&beta;}+f_{double}\mathrm{\&alpha;}+\frac{1}{3}{f}_{volume}-\frac{1}{4}{f}_{helix}+f_{wire}\mathrm{\&gamma;}$

$<{\left|S_{hv}\right|}^2>=\frac{1}{3}{f}_{volume}+\frac{1}{4}{f}_{helix}+f_{wire}{\left|\mathrm{\&rho;}\right|}^2$

$<S_{hh}{S}_{hv}^{*}>=\&PlusMinus;j\frac{1}{4}{f}_{helix}+f_{wire}{\mathrm{\&gamma;\&rho;}}^{*}$

$<S_{hv}{S}_{vv}^{*}>=\&PlusMinus;j\frac{1}{4}{f}_{helix}+f_{wire}\mathrm{\&rho;},---\left(3\right)$

In formula, β is the ratio of hh backscattering coefficient in odd scattering and vv backscattering coefficient, and α is backward for hh in even scattering Scattering coefficient and the ratio of vv backscattering coefficient, γ is the ratio of hh polarization and vv polarization backscattering coefficient in line scattering, ρ Ratio for hv polarization in line scattering and vv polarization backscattering coefficient；

Solve the weight coefficient f that above formula obtains five kinds of scattering mechanisms_odd、f_double、f_volume、f_helixAnd f_wire, and then solve acquisition Scattered power P of odd scattering_odd, even scattering scattered power P_double, scattered power P of volume scattering_volume, spiral scattering Scattered power P_helix, line scattering scattered power P_wireAnd total scattering power P：

P_odd=f_odd(1+|β|²)

P_double=f_double(1+|α|²)

P_volume=8f_volume/ 3, (4) P_helix=f_helix

P_wire=f_wire(1+|γ|²+2|ρ|²)

P=P_odd+P_double+P_volume+P_helix+P_wire

Thus Polarimetric SAR Image to be sorted is decomposed into the power of five kinds of Polarization scattering mechanism as Polarization scattering feature.

3. the Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint according to claim 2, its feature It is, the Polarimetric SAR Image polarization characteristic that in the B of step 3, feature based value is decomposed extracts detailed process and is：

The coherence matrix of Polarimetric SAR Image to be sorted<T>Eigenvalues Decomposition be expressed as follows：

$<T>={\mathrm{U\&Lambda;U}}^H=\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{({\stackrel{r}{e}}_i\&CenterDot;{\stackrel{r}{e}}^T)}_i={\mathrm{\&lambda;}}_1({\stackrel{r}{e}}_1\&CenterDot;{{\stackrel{r}{e}}_1}^T)+{\mathrm{\&lambda;}}_2({\stackrel{r}{e}}_2\&CenterDot;{{\stackrel{r}{e}}_2}^T)+{\mathrm{\&lambda;}}_3({\stackrel{r}{e}}_3\&CenterDot;{{\stackrel{r}{e}}_3}^T),---\left(5\right)$

In formula, H is Matrix Conjugate transposition, and T is matrix transpose, Λ=diag { λ₁,λ₂,λ₃, it is characterized value diagonal matrix, this feature The diagonal of value diagonal matrix is three eigenvalues of coherence matrix, λ₁≥λ₂≥λ₃>=0,It is characterized vector moment Battle array, its column vector corresponds to<T>Orthogonal characteristic vectorWithCharacteristic vector is expressed as：

${\stackrel{r}{e}}_i={\&lsqb;{\mathrm{cos\&alpha;}}_i,{\mathrm{sin\&alpha;}}_i{\mathrm{cos\&beta;}}_i{e}^{{\mathrm{i\&delta;}}_i},{\mathrm{sin\&alpha;}}_i{\mathrm{sin\&beta;}}_i{e}^{{\mathrm{i\&gamma;}}_i}\&rsqb;}^T,---\left(6\right)$

α in formula_iRepresent the internal degree of freedom of scattering object, span is 0 °≤α_i≤90°；β_iRegard with respect to radar for scattering object The deflection of line, span is -180 °≤β_i≤180°；δ_iFor the first scattering phase angle of scattering object, γ_iFor scattering object Second scattering phase angle；

Define Polarization scattering entropy H, average scattering angle according to three eigenvaluesWith anisotropy amount A, respectively：

$H=-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{p}_i{\log }_3{p}_i,---\left(7\right)$

$\stackrel{\&OverBar;}{\mathrm{\&alpha;}}=p_1{\mathrm{\&alpha;}}_1+p_2{\mathrm{\&alpha;}}_2+p_3{\mathrm{\&alpha;}}_3,---\left(8\right)$

$A=\frac{p_2-p_3}{p_2+p_3},---\left(9\right)$

P in formula_iFor：p_i=λ_i/ ∑ λ, wherein λ=λ₁+λ₂+λ₃；

For Polarization scattering entropy H, 0≤H≤1, reflection Polarimetric SAR Image scatters H from isotropic scatterning H=0 to completely random =1 unordered degree of statistics；Average scattering angle Represent the scattering mechanism of Polarimetric SAR Image；Anisotropy amount A reflects the size of second, third eigenvalue, is the supplementary parameter of scattering entropy.

4. the Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint according to claim 3, its feature It is, in the C of step 3, the Polarimetric SAR Image texture feature extraction detailed process based on gray level co-occurrence matrixes is：

Based on Probability p (a, the b) computing formula of gray level co-occurrence matrixes it is：

$p(a,b)=\frac{p(a,b,d,\mathrm{\&theta;})}{\underset{a=1}{\mathrm{\&Sigma;}}\underset{b=1}{\mathrm{\&Sigma;}}p(a,b,d,\mathrm{\&theta;})},---\left(10\right)$

Above formula represents that on a position in Polarimetric SAR Image to be sorted, gray level is the pixel of a to give apart from d and direction θ On another location gray level be b pixel occur Probability p (a, b | θ, d)；

The matrix form of gray level co-occurrence matrixes GLCM is：

${\mathrm{GLCM}}_{L\&times;L}=\left[\begin{array}{cccc}p(0,0)& p(0,1)& ...& p(0,L-1)\\ p(1,0)& p(1,1)& ...& p(1,L-1)\\ ...& ...& p(a,b)& ...\\ p(L-1,0)& p(L-1,1)& ...& p(L-1,L-1)\end{array}\right],---\left(11\right)$

In formula, L is gradation of image series；

ENERGY E NY based on gray level co-occurrence matrixes and contrast C ON are used for describing the textural characteristics of Polarimetric SAR Image to be sorted, It is defined as：

$ENY=\underset{a=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{b=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{p}^2(a,b),---\left(12\right)$

ENERGY E NY represents the uniformity of intensity profile in Polarimetric SAR Image to be sorted；

$CON=\underset{a=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{b=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{(a-b)}^{2}p(a,b),---\left(13\right)$

Contrast C ON represents the definition of Polarimetric SAR Image to be sorted.

5. the Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint according to claim 4, its feature It is, the detailed process building complete dictionary in step 4 is：

All features that Polarimetric SAR Image to be sorted in step 3 is carried out feature extraction acquisition are integrated, and obtain description instruction Practice the characteristic vector of sample, recycle l₂Norm method is normalized, and the characteristic vector after normalization is carried out kernel function space Mapping, the atom as dictionary built complete dictionary；

Set image category number as Q, for classification i, i=1,2 ..., Q, the N of selection_iThe M D feature vectors of individual training sample It is normalized, obtain N_iIndividual characteristic vectorExcessively complete dictionary as atomic building classification i

$D_i=\&lsqb;{\stackrel{r}{d}}_{i1},K,{\stackrel{r}{d}}_{ij},\mathrm{...},{\stackrel{r}{d}}_{{\mathrm{iN}}_i}\&rsqb;,(i=1,2,\mathrm{...},Q,j=1,2,\mathrm{...},N_i),---\left(14\right)$

If being mapped as φ from data space to higher dimensional space, characteristic space vector inner product meter is carried out using gaussian radial basis function The kernel function calculatedFor：

$\mathrm{\&kappa;}({\stackrel{r}{d}}_m,{\stackrel{r}{d}}_n)=\exp (-\frac{\left|\right|{\stackrel{r}{d}}_m-{\stackrel{r}{d}}_n|{|}_2^2}{2{\mathrm{\&sigma;}}^2}),---\left(15\right)$

In formula, σ is constant；For space pixel p in Polarimetric SAR Image to be sorted_mCharacteristic vector,For polarization SAR to be sorted Space pixel p in image_nCharacteristic vector；

Mapped by kernel function, atomIt is each mapped toCross complete dictionary D_iIt is mapped as D_φi, institute There is the excessively complete dictionary of classificationAfter being mapped by kernel function, composition mapped complete dictionary D_φ：D_φ= [D_φ1..., D_φQ]∈R^M*N（N=N₁++N_Q）.

6. the Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint according to claim 5, its feature It is, the detailed process obtaining the optimum sparse coefficient of each image category training sample in step 5 is：

If Polarimetric SAR Image spatial neighborhood pixels p to be sorted_mAnd p_n, the characteristic vector of extraction is respectivelyWith Kernel function is mapped asWithFor classification i,By excessively complete dictionary D_φiRarefaction representation is：

In formula,It is characterized vectorKernel function mapping vector,For rarefaction representation it is Number vector, x_im1,x_im2,L,For dictionary D excessively complete during rarefaction representation_φiIn each atom weight coefficient, wherein nonzero coefficient Subscript collection be combined into

According to space constraint relation, neighbor p_nThe characteristic vector extractingNuclear mapping vectorFor classification i, use pixel p_m Identical atomBut different coefficients carry out linear expression：

It is set with u spatial neighborhood pixels, the eigenmatrix that the feature of extraction builds after kernel function mapping isFor classification i, by excessively complete dictionary D_φiRarefaction representation is：

$\begin{array}{c}{\mathrm{\&Phi;}}_{\mathrm{\&phi;}}=\&lsqb;{\stackrel{r}{f}}_{\mathrm{\&phi;}1},{\stackrel{r}{f}}_{\mathrm{\&phi;}2},\mathrm{...},{\stackrel{r}{f}}_{\mathrm{\&phi;}u}\&rsqb;\\ \&ap;\&lsqb;D_{\mathrm{\&phi;}i}{\stackrel{r}{x}}_{i1},D_{\mathrm{\&phi;}i}{\stackrel{r}{x}}_{i2},\mathrm{...},D_{\mathrm{\&phi;}i}{\stackrel{r}{x}}_{iu}\&rsqb;=D_{\mathrm{\&phi;}i}\&lsqb;{\stackrel{r}{x}}_{i1},{\stackrel{r}{x}}_{i2},\mathrm{...},{\stackrel{r}{x}}_{iu}\&rsqb;=D_{\mathrm{\&phi;}i}{X}_i\end{array},---\left(18\right)$

In formula, coefficient matrix X_iMiddle nonzero term has identical bottom to mark

Therefore, the sparse representation model of space constraintFor：

In formula, | | X | |_{OK, 0}Represent coefficient matrix X_iIn non-zero row number, referred to as degree of rarefication K；

The sparse representation model of space constraint is converted into using degree of rarefication K as relaxation condition：

In formula | | | |_FFor Frobenius norm,Optimum sparse coefficient training sample tried to achieve for classification i.

7. the Classification of Polarimetric SAR Image method based on nuclear sparse expression and space constraint according to claim 6, its feature Be, realize in step 6 to the detailed process of the classification of all Polarimetric SAR Images to be sorted be：

Q excessively complete dictionary D of Q class image category composition₁,D₂,...D_Q, obtain each classification instruction after kernel function mapping respectively Practice the optimum sparse coefficient of sampleSolve acquisition Polarimetric SAR Image to be sorted diluter with different classes of optimum Error r of sparse coefficient reconstruction signal_i(Φ_φ)：

$r_i\left({\mathrm{\&Phi;}}_{\mathrm{\&phi;}}\right)={\left|\right|D_{\mathrm{\&phi;i}}{X}_i^{*}-{\mathrm{\&Phi;}}_{\mathrm{\&phi;}}\left|\right|}_2(i=\mathrm{1,2},...,Q),---\left(21\right)$

In formula | | | |₂For norm；

Polarimetric SAR Image generic to be sorted is judged by minimum residual method, chooses with Polarimetric SAR Image residual error to be sorted Classification representated by little reconstruction signal is as affiliated image category Class (Φ) of this Polarimetric SAR Image to be sorted：

$Class\left(\mathrm{\&Phi;}\right)=\underset{i=1,2,\mathrm{...},Q}{\mathrm{argmin}}{r}_i\left({\mathrm{\&Phi;}}_{\mathrm{\&phi;}}\right).---\left(22\right)$