Remote sensing image classification method based on complex matrix and multi-feature collaborative learning

Abstract

The present invention discloses a remote sensing image classification method based on complex matrix and multi-feature collaborative learning, which reduces speckle noise and calculation time by introducing superpixels on the basis of Riemann RNRS classification method, and integrates complex matrix and multi-features into NRS classification framework through a collaborative learning method based on superpixels. The present invention can make full use of matrix information and polarization features, especially can perform accurate classification in heterogeneous areas, and obtain better classification results.

Description

Technical Field

[0001] The invention belongs to the field of image processing and remote sensing technology, and relates to a remote sensing image classification method based on complex matrix and multi-feature collaborative learning. Background Art

[0002] Fully polarimetric synthetic aperture radar is a microwave measurement device with multi-polarization modes, which can monitor the earth's surface during the day and night and in all-weather conditions. Compared with the synthetic aperture radar (SAR) SAR system, the polarimetric SAR system can obtain more target scattering in the stratum by transmitting and receiving electromagnetic waves in two orthogonal polarization modes. Therefore, four-channel polarimetric SAR data is obtained, providing more scattering information for terrain targets. In recent years, polarimetric SAR systems have received more and more attention, and many experts and scholars at home and abroad are engaged in research in this area. It has been widely used in image classification, crop monitoring, target recognition and other fields. However, for heterogeneous areas such as urban areas and forests, traditional target decomposition-based methods are difficult to divide images into semantically consistent ground object areas, which is also a challenge for polarimetric SAR image classification.

[0003] Polarimetric SAR image classification is an important task in radar image processing, in which feature learning is the key to classification. At present, the recently regularized subspace (NRS) method has achieved great success in the field of natural and remote sensing image processing. Recently, the regularized subspace method has been widely used in image classification as a popular representation learning method. This method is simple and effective because it can obtain an analytical solution through L2 norm regularization. However, the NRS method cannot learn polarimetric SAR data well because it is a complex Emilian matrix rather than a vector, and matrix vectorization will destroy the data structure and cross-polarization information. Later, the Riemann nearest subspace classification method (RNRS) was proposed on this basis, in which the original covariance matrix is ​​used to construct a data dictionary for each class. The original covariance matrix is ​​a complex matrix that gives a Riemann manifold space. The model can effectively learn polarimetric SAR raw data.

[0004] Although the above polarimetric SAR classification methods have greatly improved the classification performance, they still have several disadvantages: (1) RNRS classification is a pixel-level classification method, which is time-consuming and prone to misclassification due to speckle noise. In particular, in the RNRS method, some matrix operations are involved in the solution process, and the matrix operations of pixels are very time-consuming. (2) Polarimetric SAR data alone cannot classify terrain objects of heterogeneous origin well. Although the RNRS method can effectively learn complex matrix structures and channel information, it may cause misclassification in heterogeneous areas. This is because the scattering matrices within the same heterogeneous object are completely different. Specifically, adjacent pixels in the same class always produce completely different scattered echoes, and pixels in different classes may have similar non-uniform scattered echoes.

[0005] In summary, the existing polarimetric SAR image classification methods still have some defects and are easily disturbed by speckle noise, making it difficult to perform high-precision classification of heterogeneous surfaces. Summary of the invention

[0006] The purpose of the present invention is to provide a remote sensing image classification method based on complex matrix and multi-feature collaborative learning, which can perform accurate classification in heterogeneous areas and obtain better classification results.

[0007] The technical solution adopted by the present invention is:

[0008] The steps of the remote sensing image classification method based on complex matrix and multi-feature collaborative learning include:

[0009] Step 1, input the polarimetric SAR image to be classified, and perform refined Lee filtering preprocessing on the polarimetric SAR image;

[0010] Step 2, extracting the original complex matrix and multi-class features from the polarimetric SAR image, and constructing a polarimetric SAR complex matrix dictionary and a multi-feature dictionary respectively;

[0011] Step 3: Generate superpixels using a simple linear iterative clustering method for the polarimetric SAR image. For each superpixel, extract a complex matrix and multiple features to represent the superpixel.

[0012] Step 4, using the Riemann distance to measure the distance of the feature vectors in the polarimetric SAR complex matrix dictionary, constructing a superpixel-based Riemann nearest subspace model; using the Euclidean distance to measure the distance of the feature vectors in the multi-features;

[0013] Step 5, establish a first-order derivative optimization algorithm to solve the superpixel-based Riemann nearest subspace model in step 4 to obtain a coefficient matrix A;

[0014] Step 6, establishing a collaborative learning model through the complex matrix dictionary, the feature dictionary, the complex matrix of the superpixel obtained in step 3, and the multiple features, for jointly learning the complex matrix and the multiple features, and obtaining the representation coefficient B of the multiple features;

[0015] Step 7: Based on the coefficient A in step 5 and the coefficient B in step 6, a classification result of the polarimetric SAR image is obtained.

[0016] The present invention is also characterized in that:

[0017] Step 2 is as follows:

[0018] Polarimetric SAR data contains more scattering information than conventional SAR data because its scattered echoes come from four channels according to different transmission and reception modes. Polarimetric data is represented as an S matrix, i.e., a polarimetric scattering matrix. The polarimetric scattering matrix contains all polarization information of the target. Usually, it has a complex form. The polarimetric scattering matrix S is represented as:

[0019] S=[S hh , S hv , S vh , S vv ] (1)

[0020] Where h and v are horizontal and vertical transmission and reception modes respectively. Under the condition of reciprocity, S hv =S vh ; S hh Indicates the echo data of the horizontally transmitted polarized wave received horizontally, S hv is the echo data of the horizontally transmitted polarized wave received vertically, S vv is the echo data of the vertically transmitted polarized wave received vertically; the S matrix is ​​expressed by the scattering vector K as follows:

[0021]

[0022] Through multi-view processing, each pixel is represented by a covariance matrix C. The polarization covariance matrix is ​​also called a complex Emilite matrix. The polarization covariance matrix C is written as:

[0023]

[0024] The covariance matrix C is a complex matrix with real diagonal elements and complex off-diagonal elements; (.) * Refers to the conjugate transpose.

[0025] The method of complex matrix dictionary in step 3 is: randomly select N from each category of polarization SAR data kpixels; each pixel is represented by a covariance matrix C through multi-view processing, where C is a complex matrix, and each selected complex matrix is ​​placed in a dictionary set D to form a complex matrix dictionary, which is represented by D = {D 1 , D 2 , …D c}, where c is the number of classes.

[0026] The multiple features in step 3 include the following feature vectors:

[0027] Based on the polarization data representation, 16-dimensional feature vectors of polarization SAR images are extracted respectively; including 6-dimensional features of polarization scattering matrix S, 9-dimensional features of coherence matrix T, and 1-dimensional features of SPAN map;

[0028] Based on polarization target decomposition, 17-dimensional feature vectors of polarization SAR images are extracted respectively; including 3-dimensional features obtained by Cloude-Pottier decomposition, 3-dimensional features obtained by Freeman decomposition, and 9-dimensional features obtained by Huynen decomposition {A 0 , B 0 , C 0 , D 0 , E 0 , F 0 , G 0 , H 0 , I 0} and 2D characteristics of polarization parameters;

[0029] Among them A 0 Indicates the target symmetry, B 0 -C 0 Indicates the target asymmetry, B 0 +C 0 Indicates the irregularity of the target, D 0 represents the target linear characteristic, E 0 represents the local curvature difference, F 0 Indicates the surface torsion, G 0 represents the target helicity, H 0 Represents the symmetric and asymmetric adhesion, I 0 Indicates the target direction;

[0030] Based on image processing technology, 20-dimensional feature vectors of polarimetric SAR images are extracted respectively; including: defining 4-dimensional texture features and 16-dimensional contour features based on gray-level co-occurrence matrix.

[0031] The Riemann distance in step 4 is obtained as follows:

[0032] Since the polarization covariance matrix is ​​an Emilian semi-positive matrix, it forms a Riemannian manifold instead of a Euclidean space. The similarity between two points on the Riemannian manifold is measured by the Riemannian metric. When extended to the polarimetric SAR data space, the affine invariant Riemannian metric is used to measure the distance in the Riemannian space. The Riemannian metric derives the Riemannian geometry. For two points in the polarimetric SAR image, the geometric distance between the two complex matrices X and Y is defined as:

[0033]

[0034] where d R (X, Y) is the Riemann distance between complex matrices X and Y. AIRM is an affine invariant in the geometric space of curves, which is defined for complex matrices, and their geometry naturally extends to complex matrices;

[0035] According to the Riemann distance, the Riemann nearest subspace model of the superpixel is constructed, which is defined as

[0036]

[0037] Where P is a superpixel, A is the coefficient vector set of adjacent pixels in S, and d(P, D k A) is the P matrix and D in the Riemann space k A is the distance of the matrix; D is the set of complex matrix dictionaries, Γ is the Riemann geodesic distance between the test sample X and the k-th dictionary atom, λ is the weight coefficient; the mathematical expressions are shown in formulas (6) to (8):

[0038]

[0039]

[0040]

[0041] For a superpixel P, the complex matrix set is X = {X 1 , X 2 , …, X m}, X i is the i-th covariance matrix in the superpixel, m is the number of pixels in the superpixel P, A={α 1 , α 2 , …, α m} is the coefficient vector set of m adjacent pixels in P, α i ={α i1 , α i2 , …, α im} is the coefficient vector of the i-th neighboring pixel;

[0042] Equation (5) can be rewritten as:

[0043]

[0044] After obtaining the coefficient matrix A, the joint error residual of the i-th class superpixel is calculated as follows:

[0045]

[0046] The final class labels are assigned as follows:

[0047]

[0048] Step 5 is to optimize formula (9) of the model in step 4. The specific steps are:

[0049] Step 5.1, write the objective function as:

[0050] minf(α)=f 1 (α)+f 2 (α) (12)

[0051] in

[0052]

[0053] f 2 (α)=λ||ΓA|| 2 (14)

[0054] We use the first-order derivative method to optimize it. First, we try to find the first-order derivative of the residual term; according to the definition of the F-norm, ||Z|| F =Tr(Z T Z), the first-order derivative derivation process is as follows:

[0055] set up Then we have:

[0056]

[0057]

[0058] The chain rule of calculus then immediately yields the derivation:

[0059]

[0060] Step 5.2, give the first-order derivative of the Tikhonov regularization term, for the objective function f 2 (α), we get

[0061]

[0062] In the formula, Γ X Calculated by equations (7) and (8); finally, the first-order derivative of the objective function in formula (9) is as follows:

[0063]

[0064] Based on the first-order derivative of equation (20), the approximate solution, i.e., the coefficient matrix A, is obtained by the spectral projection gradient method.

[0065] The specific steps of step 6 are:

[0066] The polarimetric SAR image classification model based on complex matrix and multi-feature collaborative learning is defined as:

[0067]

[0068] A, B are the coefficient vector sets of m adjacent pixels in P, A is the complex matrix coefficient, and B is the multi-feature coefficient;

[0069] For a superpixel P, the complex matrix set is X = {X 1 , X 2 , …, X m}, X i is the ith complex matrix in the superpixel, m is the number of pixels in the superpixel P, and the corresponding feature vector set is F = {f 1 , f 2 , …, f m}, f i is the feature vector of the i-th pixel in the superpixel, A={α 1 , α 2 , …, α m} is the coefficient vector set of m adjacent pixels in S, α i ={α i1 , α i2 , …, α im} is the coefficient vector of the i-th neighboring pixel; for the K-th feature dictionary F k , let B = {β 1 , β 2 , …, β m} is the coefficient vector set of m adjacent pixels in P, β i is the coefficient vector of the i-th neighboring pixel;

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] The coefficient A is estimated by equation (9) using the optimization method in step 5; the coefficient B is solved analytically by the formula in equation (26).

[0076] Step 7 is as follows: After obtaining the coefficient matrices A and B, the residual errors of the k-type superpixels P are calculated as follows:

[0077]

[0078]

[0079] R k (P) A Measures the distance between two matrices, R k (P) B Measures the distance between two eigenvectors; since R k (P) A and R k (P) B The ranges of are very different, so they are standardized respectively to obtain the residual error after standardization:

[0080] U k (P) A =exp(-R k (P) A ) (28)

[0081] U k (P) B =exp(-R k (P) B ) (29)

[0082] The final class label is assigned as the maximum product of the two probabilities, i.e.

[0083]

[0084] The beneficial effects of the present invention are:

[0085] The present invention reduces speckle noise and computation time by introducing superpixels based on the Riemann NRS classification method, and integrates complex matrices and multiple features into the NRS classification framework through a collaborative learning method based on superpixels. The matrix information and polarization features can be fully utilized, and these complementary information can improve the classification accuracy, especially for heterogeneous terrain. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 is a flow chart of the present invention;

[0087] Figure 2This is the classification result of different algorithms for the four-view NASA / JPLAIRSAR satellite L-band dataset in the San Francisco area;

[0088] Figure 3 This is the classification result diagram of different algorithms for the RADARSAT-2 satellite C-band fully polarimetric SAR dataset in the Flevoland area of ​​the Netherlands. DETAILED DESCRIPTION

[0089] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0090] The remote sensing image classification method based on complex matrix and multi-feature collaborative learning is as follows: Figure 1 , the steps include:

[0091] Step 1, input the polarimetric SAR image to be classified, and perform refined Lee filtering preprocessing on the polarimetric SAR image;

[0092] Step 2, extracting the original complex matrix and multi-class features from the polarimetric SAR image, and constructing a polarimetric SAR complex matrix dictionary and a multi-feature dictionary respectively;

[0093] Step 3: Generate superpixels for polarimetric SAR images using a simple linear iterative clustering method. For each superpixel, extract a complex matrix and multiple features to represent the superpixel. The multiple features include original data features, target decomposition features, and context features.

[0094] Step 4, using the Riemann distance to measure the distance of the feature vectors in the polarimetric SAR complex matrix dictionary, constructing a superpixel-based Riemann nearest subspace model; using the Euclidean distance to measure the distance of the feature vectors in the multi-features;

[0095] Step 5, establish a first-order derivative optimization algorithm to solve the superpixel-based Riemann nearest subspace model in step 4 to obtain a coefficient matrix A;

[0096] Step 6, establishing a collaborative learning model through the complex matrix dictionary, the feature dictionary, the complex matrix of the superpixel obtained in step 3, and the multiple features, for jointly learning the complex matrix and the multiple features, and obtaining the representation coefficient B of the multiple features;

[0097] In step 7, based on coefficient A in step 5 and coefficient B in step 6, the residuals of the original data and feature vectors are calculated respectively. Then, their class probabilities are derived based on the residuals. Finally, the superpixels are assigned to the class with the largest product of the two probabilities, and the classification result of the polarimetric SAR image is finally obtained.

[0098] Step 2 is as follows:

[0099] Polarimetric SAR data contains more scattering information than conventional SAR data because its scattered echoes come from four channels according to different transmission and reception modes. Polarimetric data can be represented as an S matrix, i.e., a polarimetric scattering matrix. The polarimetric scattering matrix contains all polarization information of the target. Usually, it has a complex form. The polarimetric scattering matrix can be represented as:

[0100] S=[S hh , S hv , S vh , S vv ] (1)

[0101] Where h and v are horizontal and vertical transmission and reception modes respectively. Under the condition of reciprocity, S hv =S vh . S hh Indicates the echo data of the horizontally transmitted polarized wave received horizontally, S hv is the echo data of the horizontally transmitted polarized wave received vertically, S vv is the echo data of the vertically transmitted polarized wave received vertically. The S matrix can be expressed by the scattering vector K as

[0102]

[0103] Through multi-view processing, each pixel can be represented by the covariance matrix C. The polarization covariance matrix is ​​also called the complex Emilite matrix. The polarization covariance matrix C can be written as:

[0104]

[0105] The covariance matrix C is a complex matrix with real diagonal elements and complex off-diagonal elements. (.) * Refers to the conjugate transpose.

[0106] Construct a complex matrix dictionary: In polarimetric SAR images, randomly select N from each category of polarimetric SAR data k pixels; each pixel is represented by a covariance matrix C through multi-view processing, where C is a complex matrix, and each selected complex matrix is ​​placed in a dictionary set D to form a complex matrix dictionary, which is represented by D = {D 1 , D 2 , …D c}, where c is the number of classes;

[0107] Extract polarimetric SAR multi-class features to build a multi-feature dictionary: The multi-feature dictionary includes the following vectors:

[0108] ① Based on the polarization data representation, the 16-dimensional feature vectors of the polarization SAR image are extracted respectively, including the 6-dimensional features of the polarization scattering matrix S, the 9-dimensional features of the coherence matrix T, and the 1-dimensional features of the SPAN map;

[0109] ② Based on polarization target decomposition, 17-dimensional feature vectors of polarimetric SAR images are extracted respectively; including 3-dimensional features obtained by Cloude-Pottier decomposition, 3-dimensional features obtained by Freeman decomposition, and 9-dimensional features obtained by Huynen decomposition {A 0 , B 0 , C 0 , D 0 , E 0 , F 0 , G 0 , H 0 , I 0} and 2D characteristics of polarization parameters;

[0110] Among them A 0 Indicates the target symmetry, B 0 -C 0 Indicates the target asymmetry, B 0 +C 0 Indicates the irregularity of the target, D 0 represents the target linear characteristic, E 0 represents the local curvature difference, F 0 Indicates the surface torsion, G 0 represents the target helicity, H 0 Represents the symmetric and asymmetric adhesion, I 0 Indicates the target direction;

[0111] ③ Based on image processing technology, 20-dimensional feature vectors of polarization SAR images are extracted respectively; including: defining 4-dimensional texture features and 16-dimensional contour features based on gray-level co-occurrence matrix.

[0112] According to the multi-feature case, we assume that c different features can be extracted from each pixel. For each pixel, the feature vector is defined as y = {y 1 ,y 2 , …, y c},y c is the c-th type of feature vector, and the c types of features are put into the dictionary to form a multi-feature dictionary G = {G 1 , G 2 , …, G C}, c is the number of classes.

[0113] In step 4, the Riemann distance is used to measure the distance between the eigenvectors in the complex matrix, using

[0114] The Riemann distance is obtained as follows:

[0115] Since the polarization covariance matrix is ​​an Emilian semi-positive matrix, it forms a Riemannian manifold instead of a Euclidean space. The similarity between two points on the Riemannian manifold is measured by the Riemannian metric. Extended to the polarimetric SAR data space, the affine invariant Riemannian metric (AIRM) is used to measure the distance in the Riemannian space. The Riemannian metric derives the Riemannian geometry. For two points in the polarimetric SAR image, the geometric distance between the two complex matrices X and Y can be defined as:

[0116]

[0117] where d R (X, Y) is the Riemann distance between complex matrices X and Y. AIRM is an affine invariant in the geometric space of curves, which is defined for complex matrices, and their geometry naturally extends to complex matrices;

[0118] According to the Riemann distance, the Riemann nearest subspace model of superpixel is constructed, which can be defined as

[0119]

[0120] Where P is a superpixel, A is the coefficient vector set of adjacent pixels in P, and d(P, D k A) is the P matrix and D in the Riemann space k A is the distance of the matrix. D is the set of complex matrix dictionaries, Γ is the Riemann geodesic distance between the test sample X and the k-th dictionary atom, and λ is the weight coefficient. The mathematical expressions are shown in formulas (6) to (8):

[0121]

[0122]

[0123]

[0124] For a superpixel P, the complex matrix set is X = {X 1 , X 2 , …, X m}, X i is the i-th covariance matrix in the superpixel, m is the number of pixels in the superpixel P, A={α 1 , α 2 , …, α m} is the coefficient vector set of m adjacent pixels in P, α i ={α i1 , α i2 , …, α im} is the coefficient vector of the i-th neighboring pixel.

[0125] Equation (5) can be rewritten as:

[0126]

[0127] After obtaining the coefficient matrix A, the joint error residual of the i-th superpixel P can be calculated as follows:

[0128]

[0129] The final class labels can be specified as follows:

[0130]

[0131] Step 5, optimizing formula (9) of the model in step 4;

[0132] Step 5.1, we divide it into two parts. The first part is the residual term, and the second part is the Tikhonov regularization term. Therefore, the objective function can be written as:

[0133] min f(α)=f 1 (α)+f 2 (α) (12)

[0134] in

[0135]

[0136] f 2 (α)=λ||ΓA|| 2 (14)

[0137] We use the first-order derivative method to optimize it. First, we try to find the first-order derivative of the residual term. According to the definition of the F-norm, ||Z|| F =Tr(Z T Z), the first-order derivative derivation process is as follows:

[0138] set up Then we have:

[0139]

[0140]

[0141] The chain rule of calculus then immediately yields the derivation:

[0142]

[0143] Step 5.2, simplify as needed. Next, we give the first-order derivative of the Tikhonov regularization term. For the objective function f 2 (α), we can directly get

[0144]

[0145] In the formula, Γ X It can be calculated by equations (7) and (8). Finally, the first-order derivative of the objective function in equation (9) is as follows:

[0146]

[0147] Based on the first-order derivative of equation (20), the approximate solution can be obtained by the spectral projection gradient method, that is, the coefficient matrix A;

[0148] The specific steps of step 6 are:

[0149] The polarimetric SAR image classification model based on complex matrix and multi-feature collaborative learning (CM_SJNRS) is defined as:

[0150]

[0151] A and B are coefficient vector sets of m adjacent pixels in P, A is the complex matrix coefficient, and B is the multi-feature coefficient.

[0152] For a superpixel P, the complex matrix set is X = {X 1 , X 2 , …, X m}, X i is the ith complex matrix in the superpixel, m is the number of pixels in the superpixel P, and the corresponding feature vector set is F = {f 1 , f 2 , …, f m}, f i is the feature vector of the i-th pixel in the superpixel, A={α 1 , α 2 , …, α m} is the coefficient vector set of m adjacent pixels in P, α i ={α i1 , α i2 , …, α im} is the coefficient vector of the i-th neighboring pixel. For the K-th feature dictionary F k , let B = {β 1 , β 2 , …, β m} is the coefficient vector set of m adjacent pixels in P, β i is the coefficient vector of the i-th neighboring pixel.

[0153]

[0154]

[0155]

[0156]

[0157]

[0158] The coefficient A can be estimated by equation (9) through the optimization method in step 5. The coefficient B can be solved analytically by the formula in equation (26).

[0159] Step 7, after obtaining the coefficient matrices A and B, the residual errors of the k-type superpixels P can be calculated as follows:

[0160]

[0161]

[0162] R k (P) A Measures the distance between two matrices, R k (P) B Measures the distance between two eigenvectors. Since R k (S) A and R k (S) B The ranges of are very different, so they are standardized respectively to obtain the residual error after standardization:

[0163] U k (P) A =exp(-R k (P) A ) (28)

[0164] U k (P) B =exp(-R k (P) B ) (29)

[0165] The final class label can be specified as the maximum product of the two probabilities, i.e.

[0166]

[0167] Example 1

[0168] like Figure 2 (a) The input polarimetric SAR image to be classified is a four-view polarimetric SAR image of the San Francisco area acquired by NASA / JPL AIRSAR satellite in the L band, with an image size of 900 × 700 pixels. Execute steps 1 to 7 above and the result is Figure 2 (g).

[0169] This example also compares the method of the present invention with other methods, wherein Figure 2(a) is a grayscale pseudo-color image of the full polarimetric SAR in the San Francisco area. The original image is represented by the Pauli basis as the RGB three-channel color. Figure 2 (b) is the corresponding class label reference map, in which the San Francisco area is divided into four categories: red represents mountainous areas, yellow represents oceans, cyan represents vegetation, and blue represents urban areas. Figure 2 (c) is the classification map obtained by using the NRS method, with a classification accuracy of 80.23%; Figure 2 (d) is the classification map obtained by the NRSMRF method, with a classification accuracy of 83.48%; Figure 2 (e) is the classification map obtained by using the RNRS method, with a classification accuracy of 84.13%; Figure 2 (f) is the classification map obtained by the SRNRS method, with a classification accuracy of 85.29%; Figure 2 (g) is the classification diagram obtained using the CM-SJNRS method, with a classification accuracy of 92.39%. It can be seen that Figure 2 The classification effect of (g) is significantly better than other algorithms, the noise suppression effect is more obvious, and it also has better classification results in heterogeneous areas.

[0170] Example 2

[0171] like Figure 3 (a) The input polarimetric SAR image to be classified is a fully polarimetric SAR image of Flevoland in the C band of the RADARSAT 2 satellite, with an image size of 1400 × 1200 pixels. After executing steps 1 to 7 above, the result is Figure 3 (g).

[0172] This example also compares the method of the present invention with other methods, wherein Figure 3 (a) is a grayscale pseudo-color image of the Flevoland region. The original image is represented by the Pauli basis as the RGB three-channel color. Figure 3 (b) is the corresponding class label reference map, in which the area is divided into four categories: red represents farmland, yellow represents vegetation, cyan represents ocean, and blue represents urban area. Figure 3 (c) is the classification map obtained by the NRS method, with a classification accuracy of 77.84%; Figure 3 (d) is the classification map obtained by the NRSMRF method, with a classification accuracy of 80.96%; Figure 3 (e) is the classification map obtained by using the RNRS method, with a classification accuracy of 81.75%; Figure 3 (f) is the classification map obtained by the SRNRS method, with a classification accuracy of 83.02%; Figure 3(g) is the classification diagram obtained using the CM-SJNRS method, with a classification accuracy of 92.79%. It can be seen that Figure 3 (c) Figure 3 The classification method of (d) can classify urban areas well, but it will lead to some over-classification. In addition, it cannot classify forests well. Figure 3 (e) It can obtain fine classification, especially in forests and agricultural lands, however, it can lead to misclassification in urban areas; Figure 3 (f) can greatly improve regional uniformity, but will cause misclassification in heterogeneous regions; Figure 3 (g) Cities and forests can be classified well and more accurately than other classification methods; the present invention can obtain excellent classification results.

[0173] Through the above-mentioned method, the present invention proposes a method for simultaneously jointly learning the labels of adjacent pixels. The pixels in the superpixel are regarded as a neighborhood set, and their representation coefficients are jointly learned through the SRNRS method. The introduction of superpixels reduces noise interference and also shortens the calculation time. Secondly, we first proposed to collaboratively learn the original C matrix and polarization features under the NRS classification framework. In this way, the matrix information and polarization features can be fully utilized. These complementary information can improve the classification accuracy, especially for heterogeneous terrain types. The results show that the above-mentioned method can obtain very excellent classification results.

Claims

1. A remote sensing image classification method based on complex matrix and multi-feature collaborative learning, characterized in that the steps include: Step 1, input the polarimetric SAR image to be classified, and perform refined Lee filtering preprocessing on the polarimetric SAR image; Step 2, extracting the original complex matrix and multi-class features from the polarimetric SAR image, and constructing a polarimetric SAR complex matrix dictionary and a multi-feature dictionary respectively; Step 3: Generate superpixels using a simple linear iterative clustering method for the polarimetric SAR image. For each superpixel, extract a complex matrix and multiple features to represent the superpixel. Step 4, using the Riemann distance to measure the distance of the feature vectors in the polarimetric SAR complex matrix dictionary, constructing a superpixel-based Riemann nearest subspace model; using the Euclidean distance to measure the distance of the feature vectors in the multi-features; Step 5, establish a first-order derivative optimization algorithm to solve the superpixel-based Riemann nearest subspace model in step 4 to obtain a coefficient matrix A; Step 6, establishing a collaborative learning model through the complex matrix dictionary, the feature dictionary, the complex matrix of the superpixel obtained in step 3, and the multiple features, for jointly learning the complex matrix and the multiple features, and obtaining the representation coefficient B of the multiple features; Step 7: Based on the coefficient A in step 5 and the coefficient B in step 6, a classification result of the polarimetric SAR image is obtained.

2. The remote sensing image classification method based on complex matrix and multi-feature collaborative learning as claimed in claim 1, characterized in that: The step 2 is specifically as follows: Polarimetric SAR data contains more scattering information than conventional SAR data because its scattered echoes come from four channels according to different transmission and reception modes. Polarimetric data is represented as an S matrix, i.e., a polarimetric scattering matrix. The polarimetric scattering matrix contains all polarization information of the target. Usually, it has a complex form. The polarimetric scattering matrix is ​​represented as: S=[S hh ,S hv ,S vh ,S vv ] (1) Where h and v are horizontal and vertical transmission and reception modes respectively. Under the condition of reciprocity, S hv =S vh ; S hh Indicates the echo data of the horizontally transmitted polarized wave received horizontally, S hv is the echo data of the horizontally transmitted polarized wave received vertically, S vv is the echo data of the vertically transmitted polarized wave received vertically; the S matrix is ​​expressed by the scattering vector K as follows: Through multi-view processing, each pixel is represented by a covariance matrix C. The polarization covariance matrix is ​​also called a complex Emilite matrix. The polarization covariance matrix C is written as: The covariance matrix C is a complex matrix with real diagonal elements and complex non-diagonal elements; (.) * Refers to the conjugate transpose.

3. The remote sensing image classification method based on complex matrix and multi-feature collaborative learning as claimed in claim 1, characterized in that: The method of the complex matrix dictionary in step 3 is: randomly select N from each category of polarization SAR data k pixels; each pixel is represented by a covariance matrix C through multi-view processing, where C is a complex matrix, and each selected complex matrix is ​​placed in a dictionary set D to form a complex matrix dictionary, which is represented by D = {D 1 ,D 2 ,…D c }, where c is the number of classes.

4. The remote sensing image classification method based on complex matrix and multi-feature collaborative learning as claimed in claim 1, characterized in that: The multiple features in step 3 include the following feature vectors: Based on the polarization data representation, 16-dimensional feature vectors of polarization SAR images are extracted respectively; including 6-dimensional features of polarization scattering matrix S, 9-dimensional features of coherence matrix T, and 1-dimensional features of SPAN map; Based on polarization target decomposition, 17-dimensional feature vectors of polarimetric SAR images are extracted respectively, including 3-dimensional features obtained by Cloude-Pottier decomposition, 3-dimensional features obtained by Freeman decomposition, 9-dimensional features {A0, B0, C0, D0, E0, F0, G0, H0, I0} obtained by Huynen decomposition, and 2-dimensional features of polarization parameters; in A0 represents the target symmetry, B0-C0 represents the target asymmetry, B0+C0 represents the target irregularity, D0 represents the target linear property, E0 represents the local curvature difference, F0 represents the surface twist, G0 represents the target helicity, H0 represents the symmetric and asymmetric adhesion, and I0 represents the target direction; Based on image processing technology, 20-dimensional feature vectors of polarimetric SAR images are extracted respectively; including: defining 4-dimensional texture features and 16-dimensional contour features based on gray-level co-occurrence matrix.

5. The remote sensing image classification method based on complex matrix and multi-feature collaborative learning as claimed in claim 1, characterized in that: The method for obtaining the Riemann distance in step 4 is: Since the polarization covariance matrix is ​​an Emilian semi-positive matrix, it forms a Riemannian manifold instead of a Euclidean space. The similarity between two points on the Riemannian manifold is measured by the Riemannian metric. When extended to the polarimetric SAR data space, the affine invariant Riemannian metric is used to measure the distance in the Riemannian space. The Riemannian metric derives the Riemannian geometry. For two points in the polarimetric SAR image, the geometric distance between the two complex matrices X and Y is defined as: where d R (X,Y) is the Riemann distance between complex matrices X and Y. AIRM is an affine invariant in the geometric space of curves. It is defined for complex matrices, and their geometry naturally extends to complex matrices. According to the Riemann distance, the Riemann nearest subspace model of the superpixel is constructed, which is defined as Where P is a superpixel, A is the coefficient vector set of adjacent pixels in P, and d(P,D k A) is the P matrix and D in the Riemann space k A is the distance of the matrix; D is the set of complex matrix dictionaries, Γ is the Riemann geodesic distance between the test sample X and the k-th dictionary atom, λ is the weight coefficient; the mathematical expressions are shown in formulas (6) to (8): For a superpixel P, the complex matrix set is X = {X1, X2, ..., X m }, X i is the i-th covariance matrix in the superpixel, m is the number of pixels in the superpixel P, A={α1,α2,…,α m } is the coefficient vector set of m adjacent pixels in P, α i ={α i1 ,α i2 ,…,α im } is the coefficient vector of the i-th neighboring pixel; Equation (5) can be rewritten as: After obtaining the coefficient matrix A, the joint error residual of the i-th class superpixel is calculated as follows: The final class labels are assigned as follows:

6. The remote sensing image classification method based on complex matrix and multi-feature collaborative learning as claimed in claim 5, characterized in that: The step 5 is to optimize the formula (9) of the model in step 4, and the specific steps are: Step 5.1, write the objective function as: min f(α)=f1(α)+f2(α) (12) in f2(a)=λ||ΓA|| 2 (14) We use the first-order derivative method to optimize it. First, we try to find the first-order derivative of the residual term; according to the definition of the F-norm, ||Z|| F =Tr(Z T Z), the first-order derivative derivation process is as follows: set up Then we have: The chain rule of calculus then immediately yields the derivation: Step 5.2, give the first-order derivative of the Tikhonov regularization term, for the objective function f2(α), we get In the formula, Γ X Calculated by equations (7) and (8); finally, the first-order derivative of the objective function in formula (9) is as follows: Based on the first-order derivative of equation (20), the approximate solution, i.e., the coefficient matrix A, is obtained by the spectral projection gradient method.

7. The remote sensing image classification method based on complex matrix and multi-feature collaborative learning as claimed in claim 5, characterized in that: The specific steps of step 6 are: The polarimetric SAR image classification model based on complex matrix and multi-feature collaborative learning is defined as: A, B are the coefficient vectors of m adjacent pixels in the superpixel P, A is the complex matrix coefficient, and B is the multi-feature coefficient; For a superpixel P, the set of complex matrices is X = {X1, X2, ..., X m }, X i is the ith complex matrix in the superpixel, m is the number of pixels in the superpixel P, and the corresponding feature vector set is F = {f1,f2,…,f m },f i is the feature vector of the i-th pixel in the superpixel, A={α1,α2,…,α m } is the coefficient vector set of m adjacent pixels in P, α i ={α i1 ,α i2 ,…,α im } is the coefficient vector of the i-th neighboring pixel; for the K-th feature dictionary F k , let B = {β1,β2,…,β m } is the coefficient vector set of m adjacent pixels in P, β i is the coefficient vector of the i-th neighboring pixel; The coefficient A is estimated by equation (9) through the optimization method in step 5; the coefficient B is solved analytically by the formula in equation (26).

8. The remote sensing image classification method based on complex matrix and multi-feature collaborative learning as claimed in claim 5, characterized in that: Step 7 is as follows: After obtaining the coefficient matrices A and B, the residual errors of the k-type superpixels P are calculated as follows: R k (P) A Measures the distance between two matrices, R k (P) B Measures the distance between two eigenvectors; since R k (P) A and R k (P) B The ranges of are very different, so they are standardized respectively to obtain the residual error after standardization: U k (P) A =exp(-R k (P) A ) (28) U k (P) B =exp(-R k (P) B ) (29) The final class label P is specified as the maximum product of the two probabilities, that is,

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