Polarimetric SAR Image Classification Method Based on Riemann Nearest Canonical Subspace Model

Abstract

The present invention discloses a polarimetric SAR image classification method based on a Riemann nearest canonical subspace model, and the steps include: step 1, selecting the same number of pixel points from each category of the polarimetric SAR image to be classified, and constructing a semi-positive definite matrix dictionary for each category; step 2, constructing an objective function based on RNRS according to the matrix dictionary and the Riemann measure; step 3, solving the objective function to obtain a sparse representation coefficient for each category of the dictionary; step 4, calculating the predicted data for each category according to the sparse representation coefficient, assigning a pixel class label to a category with the smallest residual between the real data and the predicted data, and finally obtaining the classification result of the polarimetric SAR image. The present invention solves the problem that NRS in the prior art cannot effectively learn the matrix structure and channel correlation of PolSAR data.

Description

Technical Field

[0001] The invention belongs to the technical field of image processing and remote sensing, and relates to a polarization SAR image classification method based on a Riemann nearest canonical subspace model. Background Art

[0002] Polarimetric synthetic aperture radar (PolSAR) image classification is an important task in radar image processing. It is the basis of target recognition and image understanding. Compared with SAR systems, PolSAR systems transmit and receive electromagnetic waves in two orthogonal polarization modes, and can obtain four-channel PolSAR data, thereby providing more target scattering characteristics for image classification. PolSAR systems are widely used in image classification, land cover mapping, etc. Existing PolSAR image classification methods include unsupervised methods and supervised methods.

[0003] In recent years, representation-based classification methods have been proven to be an effective tool in the field of radar image processing. Representation classification methods can be mainly summarized into three categories: sparse representation classification (SRC), collaborative representative representation classifier (CRC), and nearest neighbor regularized subspace (NRS). SRC has been widely used in terrain classification of hyperspectral and SAR images. SRC can be extended to PolSAR images by combining polarimetric features and sparse representation. There are also methods for Remianian sparse coding of PolSAR images. These methods all have L 0 Norm or L 1 The regularization term of the norm is a nonlinear NP-hard problem. It is solved by iterative solution methods, such as Simultaneous OMP (SOMP), but this solution is very time-consuming. Collaboration means that the classifier believes that the main contribution of SRC is not sparseness, but collaboration. Therefore, the CRC method adopts L 2 Norm regularization instead of L 1 norm. Therefore, the CRC model is a convex optimization problem, which greatly reduces the computation time. The NRS method is an improvement on the collaborative representation classifier (CRC) method and is another popular representation-based method in PolSAR image classification. Compared with the CRC method, the NRS method minimizes the intra-class distance by adding Tikhonov matrix regularization. Compared with SRC, the regularization term in NRS is L 2 norm, has a closed solution, and greatly reduces the computation time. In addition, compared with CRC, Tikhonov regularization can suppress speckle noise and improve classification accuracy. Therefore, NRS is the optimal model that balances accuracy and effectiveness.

[0004] However, the NRS method cannot learn PolSAR data well because PolSAR data is a Hermitian semi-positive definite (HPD) matrix, not a vector, and NRS can only process eigenvectors but not HPD matrices. In general, the NRS method converts the PolSAR covariance matrix (C matrix) into a column vector as input. PolSAR data is a complex matrix. Matrix vectorization cannot preserve the data structure and cross-polarization information. In addition, the column vector destroys the matrix distribution and the correlation between channels. In addition, there are some methods that take the extracted target feature vector as input, and the classification performance depends largely on the type of extracted features. How to choose the right features is a challenging practical problem. Summary of the invention

[0005] The purpose of the present invention is to provide a polarimetric SAR image classification method based on the Riemann nearest canonical subspace model, which solves the problem that the NRS in the prior art cannot effectively learn the PolSAR data matrix structure and channel correlation.

[0006] The technical solution adopted by the present invention is:

[0007] The polarimetric SAR image classification method based on the Riemann nearest canonical subspace model includes the following steps:

[0008] Step 1, select the same number of pixels from each category of the polarimetric SAR image to be classified, and use the covariance matrix of the pixels to construct a semi-positive definite matrix dictionary for each category;

[0009] Step 2, construct the RNRS-based objective function according to the matrix dictionary and Riemann measure;

[0010] Step 3, construct a first-order derivative optimization algorithm, solve the objective function, and obtain the sparse representation coefficients of each type of dictionary;

[0011] Step 4: Calculate the predicted data of each category according to the sparse representation coefficient calculated in step 3, assign the pixel class label to the category with the smallest residual between the real data and the predicted data, and finally obtain the classification result of the polarimetric SAR image.

[0012] The present invention is also characterized in that:

[0013] Step 1 The specific steps are:

[0014] Randomly select N from each category of the polarimetric SAR image to be classified k pixels as the training set; the remaining pixels as the test set, and the dictionary D is constructed by the covariance matrix of the pixels in the training set, where the covariance matrix is:

[0015]

[0016] Where C is the covariance matrix, S hh is 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 It is the echo data of the vertically transmitted polarized wave received vertically;

[0017] Construct dictionary D:

[0018] D={D 1 , D 2 ,…,D C} (2)

[0019] C is the total number of categories, D is K The dictionary D is composed of the K-th class training pixels and is defined as follows:

[0020]

[0021] in, is the i-th dictionary atom of the k-th dictionary, represented by the covariance matrix of the i-th training pixel of the k-th class.

[0022] Step 2 is as follows:

[0023] Construct the Riemann Nearest Regular Subspace (RNRS) formula:

[0024]

[0025] The RNRS formula is divided into two parts. is the residual term, is the Tikhonov regularization term; where λ is the weight factor for balancing the residual term and the Tikhonov regularization term;

[0026] in For X and The Riemann metric distance between Solve the RNRS formula to obtain the estimated value of the test sample on the k-th dictionary; the formula of the Riemann metric distance is:

[0027]

[0028] In formula (4), d R (A,B) is the Riemann metric distance between matrix A and matrix B,

[0029] in

[0030]

[0031]

[0032] Where k represents the kth class; X represents the test pixel point, Represents the Riemann metric distance from the test pixel to the i-th training pixel in the k-th training sample, i = 1 ~ N k , N k is the number of training pixels in each category;

[0033] Substituting formula (5) into formula (4) yields:

[0034]

[0035] Where N k Represents the number of pixels in the k-th dictionary, represents the i-th dictionary atom in the k-th dictionary, X represents the test pixel, is the i-th dictionary atom in the k-type dictionary, λ is the weight factor for balancing the residual term and the coefficient term, is the Riemann metric distance between the test pixel X and the k-th dictionary atom, α k is the sparse representation coefficient in the k-th dictionary.

[0036] Step 3 is as follows:

[0037] The objective function of formula (8) can be written as:

[0038] minf(α)=f 1 (α)+f 2 (α) (9)

[0039] in

[0040]

[0041]

[0042] The first-order derivative method is used to optimize it. First, the residual term, i.e., the first-order derivative of the formula, is found;

[0043] First, according to the definition of norm:

[0044] ||Z|| F =Tr(Z T Z) (12)

[0045] set up

[0046]

[0047] We can get:

[0048] f 1 (α) = Tr (log (SM (α) S) Tlog(SM(α)S)) (14)

[0049] Taking the first-order derivative of formula (10) we can get:

[0050] f′ 1 (α)=2Tr(log(SM(α)S)(SM(α)S) -1 SM′(α)S) (15)

[0051] set up

[0052] M(α p )=α p D p +∑ i≠p α i D i (16)

[0053] Continuing to derive formula (10), we can obtain:

[0054]

[0055] Next, we derive the Tikhonov regularization term, formula (13):

[0056]

[0057] where Γ X It can be calculated by formula (6) and (7), and finally the first-order derivative of formula (8) is:

[0058]

[0059] Through the above formulas (9) to (19), we can finally obtain α k .

[0060] Step 4 is as follows:

[0061] Step 4.1, according to the sparse representation coefficient α obtained in step 3 k , calculate the most similar estimate of the test pixel

[0062] The covariance matrix of the test pixel can be expressed as a linear combination of the covariance matrices of the training pixels of the same type:

[0063]

[0064] in represents the most similar estimate of the test pixel; k represents the kth category; N k represents the number of images selected from each category as training sets; C represents the number of categories of polarimetric SAR images; α kis the coefficient column vector;

[0065]

[0066] Step 4.2: The most similar estimate Substitute into formula (22) to obtain the classification category of the test sample pixel:

[0067]

[0068] Where C is the number of categories of polarimetric SAR images, k is the number of categories, and X is the test sample pixel.

[0069] The beneficial effects of the present invention are:

[0070] A polarimetric SAR image classification method based on the Riemann nearest canonical subspace model is provided, which solves the problem that the NRS in the prior art cannot effectively learn the PolSAR data matrix structure and channel correlation. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 is a flow chart of the present invention;

[0072] Figure 2 This is a diagram showing the classification results of the full polarization SAR image of the Flevoland area using the method of the present invention and other methods;

[0073] Figure 3 This is a diagram showing the classification results of the polarization SAR images of the San Francisco area using the method of the present invention and other methods. DETAILED DESCRIPTION

[0074] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0075] The present invention is based on the polarization SAR image classification method of the Riemann nearest canonical subspace model, such as Figure 1 , the steps include:

[0076] Step 1, select the same number of pixels from each category of the polarimetric SAR image to be classified, and use the covariance matrix of the pixels to construct a semi-positive definite matrix dictionary for each category;

[0077] Step 2: According to the matrix dictionary and Riemann measure, construct the objective function based on RNRS. The objective function is formula (8):

[0078]

[0079] Where N k Represents the number of pixels in the k-th dictionary, represents the representation coefficient of the i-th dictionary atom in the k-th dictionary, X represents the test pixel, is the i-th dictionary atom in the k-type dictionary, λ is the weight factor for balancing the residual term and the coefficient term, is the Riemann metric distance between the test pixel X and the k-th dictionary atom, α k is the representation coefficient column vector of atoms in the k-th dictionary;

[0080] Step 3, construct a first-order derivative optimization algorithm, solve the objective function, and obtain the sparse representation coefficients of each type of dictionary;

[0081] Step 4: Calculate the predicted data of each category according to the sparse representation coefficient calculated in step 3, assign the pixel class label to the category with the smallest residual between the real data and the predicted data, and finally obtain the classification result of the polarimetric SAR image.

[0082] The specific steps of step 1 are as follows:

[0083] Randomly select N from each category of the polarimetric SAR image to be classified k pixels as the training set; the remaining pixels as the test set, and the matrix dictionary D is constructed by the covariance matrix of the pixels in the training set, where the covariance matrix is:

[0084]

[0085] Where C is the covariance matrix, S hh is 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 It is the echo data of the vertically transmitted polarized wave received vertically;

[0086] Construct dictionary D:

[0087] D={D 1 , D 2 ,…,D C} (2)

[0088] C is the total number of categories, D is K The dictionary D is composed of the K-th class training pixels and is defined as follows:

[0089]

[0090] in, is the i-th dictionary atom of the k-th dictionary, represented by the covariance matrix of the i-th training pixel of the k-th class.

[0091] The specific steps of step 2 are as follows:

[0092] Construct the Riemanian Nearest-Regularized Subspace (RNRS) formula:

[0093]

[0094] The above formula is divided into two parts. is the residual term, is the Tikhonov regularization term; where λ is the weight factor for balancing the residual term and the Tikhonov regularization term;

[0095] in For X and The Riemann metric distance between Solve the RNRS formula to obtain the estimated value of the test sample on the k-th dictionary; the formula of the Riemann metric distance is:

[0096]

[0097] In formula (4), d R (A,B) is the Riemann metric distance between matrix A and matrix B,

[0098] in

[0099]

[0100]

[0101] Where k represents the kth class; X represents the test pixel point, Represents the Riemann metric distance from the test pixel to the i-th training pixel in the k-th training sample, i = 1 ~ N k , N k is the number of training pixels in each category;

[0102] Substituting formula (5) into formula (4) yields:

[0103]

[0104] Where N k Represents the number of pixels in the k-th dictionary, represents the i-th dictionary atom in the k-th dictionary, X represents the test pixel, is the i-th dictionary atom in the k-type dictionary, λ is the weight factor for balancing the residual term and the coefficient term, is the Riemann metric distance between the test pixel X and the k-th dictionary atom, α k is the sparse representation coefficient in the k-th dictionary.

[0105] The specific steps of step 3 are as follows:

[0106] The objective function of formula (8) can be written as:

[0107] minf(α)=f 1 (α)+f 2 (α) (9)

[0108] in

[0109]

[0110]

[0111] The first-order derivative method is used to optimize it. First, the residual term, i.e., the first-order derivative of the formula, is found;

[0112] First, according to the definition of norm:

[0113] ||Z|| F =Tr)Z T Z) (12)

[0114] set up

[0115]

[0116] We can get:

[0117] f 1 (α) = Tr (log (SM (α) S) T log(SM(α)S)) (14)

[0118] Taking the first-order derivative of formula (10) we can get:

[0119] f′ 1 (α)=2Tr(log(SM(α)S)(SM(α)S) -1 SM′(α)S) (15)

[0120] set up

[0121] M(α p )=α p D p +∑ i≠p α i D i (16)

[0122] Continuing to derive formula (10), we can obtain:

[0123]

[0124] Next, we derive the Tikhonov regularization term, formula (13):

[0125]

[0126] where Γ X It can be calculated by formula (6) and (7), and finally the first-order derivative of formula (8) is:

[0127]

[0128] Through the above formulas (9) to (19), we can finally obtain α k .

[0129] Step 4 is:

[0130] The step 4 is specifically as follows:

[0131] Step 4.1, according to the sparse representation coefficient α obtained in step 3 k , calculate the most similar estimate of the test pixel

[0132] The covariance matrix of the test pixel can be expressed as a linear combination of the covariance matrices of the training pixels of the same type:

[0133]

[0134] in represents the most similar estimate of the test pixel; k represents the kth category; N k represents the number of images selected from each category as training sets; C represents the number of categories of polarimetric SAR images; α k is the coefficient column vector;

[0135]

[0136] Step 4.2: The most similar estimate Substitute into formula (22) to obtain the classification category of the test sample pixel:

[0137]

[0138] Where C is the number of categories of polarimetric SAR images, k is the number of categories, and X is the test sample pixel.

[0139] Example 1

[0140] In this embodiment, the NASA / JPL AIRSAR satellite L-band four-view polarization SAR image of farmland in the Flevoland area of ​​the Netherlands is input, and the image size is 300×270 pixels; steps 1 to 4 are performed according to the above steps, and the classification result diagram obtained is as follows: Figure 2 (f).

[0141] This embodiment is also compared with the method of the present invention using other methods, wherein Figure 2 (a) is the full polarimetric SAR pseudo-color image of the Flevoland region, using the Pauli basis as the RGB three-channel color representation; Figure 2 (b) is the reference map of the class labels corresponding to 2(a). The white area has no reference class labels. Therefore, the present invention does not consider the classification results of the white area. In the reference map, the Flevoland area is divided into 6 categories. Figure 2 (c) is the classification result of the NRS algorithm for the fully polarized SAR image of the Flevoland area, with a classification accuracy of 93.09%; Figure 2 (d) is the classification result of the NRS MRF algorithm, with a classification accuracy of 93.90%. Figure 2 (e) is the classification result of the weighted NRS method, with a classification accuracy of 89.23%. Figure 2 (f) is the classification result of the RNRS method proposed in the present invention, and the classification accuracy is 95.15%. It can be seen that Figure 2 (c) Figure 2 (d) Figure 2 (e) A lot of noise will be obtained, and the noise cannot be suppressed well. The algorithm of the present invention can obtain more consistent and more accurate classification results.

[0142] Example 2

[0143] In this embodiment, the L-band four-view polarization SAR image of San Francisco area of ​​AIRSAR satellite is input, and the image size is 512×512 pixels. Steps 1 to 4 are performed according to the above steps. The classification result diagram obtained is as follows: Figure 3 (f).

[0144] This embodiment is also compared with the method of the present invention using other methods. Figure 3 (a) is a pseudo-color image of the San Francisco area with full polarization, represented by the Pauli basis as the RGB three-channel color. Figure 3 (b) is the corresponding reference image, in which the area is divided into three categories: blue represents ocean, yellow represents urban area, cyan represents forest, and white represents unmarked area, which is not considered; Figure 3 (c) is the classification result of the NRS method for the fully polarized SAR image of the San Francisco area, with a classification accuracy of 92.81%; Figure 3 (d) is the classification result of the NRS MRF algorithm, with a classification accuracy of 93.17%. Figure 3 (e) is the classification result of the weighted NRS method, with a classification accuracy of 91.44%. Figure 3 (f) is the RNRS classification result proposed by this method, and the classification accuracy is 95.25%. It can be seen that Figure 3 (c) Figure 3 (d) Figure 3 The classification result of (e) has a lot of noise, the urban area and the forest are confused, and the ocean part is also misclassified and cannot be well suppressed; the present invention can obtain more consistent classification results.

[0145] Through the above method, the polarimetric SAR image classification method based on the Riemann nearest neighbor regularized subspace model of the present invention is extended to PolSAR images for the first time. First, a Riemann distance is designed to calculate the data loss term between the true value and the estimated value; it ensures that the input of the model is the PolSAR original matrix rather than the eigenvector. Secondly, a new Tikhonov regularization term is designed to reduce the distance between pixels within the class; through these schemes, the method effectively learns the structure of the original matrix and the correlation between channels. On this basis, the first-order derivative for solving the RNRS model is derived. The experimental results show the effectiveness of this method. It should be pointed out that all the compared methods use multiple features, including scattering information, polarization data and image features. Our method only uses the original PolSAR data features. The results show that this method can also achieve good performance with a small number of features.

Claims

1. A polarimetric SAR image classification method based on the Riemann nearest canonical subspace model, comprising the following steps: Step 1, select the same number of pixels from each category of the polarimetric SAR image to be classified, and use the covariance matrix of the pixels to construct a semi-positive definite matrix dictionary for each category; Step 2: According to the matrix dictionary and Riemann measure, construct the objective function based on RNRS. The objective function is formula (8): + （8） in Represents the number of pixels in the k-th dictionary, represents the representation coefficient of the i-th dictionary atom in the k-th dictionary, Represents the test pixel, is the i-th dictionary atom in the k-type dictionary, is the weight factor to balance the residual term and the coefficient term, is the Riemann metric distance between the test pixel X and the k-th dictionary atom, is the representation coefficient column vector of atoms in the k-th dictionary; The specific process is: Construct the Riemann nearest canonical subspace formula: （4） The RNRS formula is divided into two parts. is the residual term, is the Tikhonov regularization term; is the weight factor for balancing the residual term and the Tikhonov regularization term; in for and The Riemann metric distance between Solve the RNRS formula to obtain the optimal solution of the linear combination coefficient column vector of the covariance matrix of the same type of training pixels; the formula of the Riemann metric distance is: （5） In formula (4) For the matrix A With the matrix B The Riemann metric distance, in （6） （7） in Representative kind; Represents the test pixel, Represents the test pixel to the The first class of training samples The Riemann metric distance of training pixels, , is the number of training pixels in each category; Substituting formula (5) into formula (4) yields: + （8） in Represents the number of pixels in the k-th dictionary, represents the i-th dictionary atom in the k-th dictionary, Represents the test pixel, is the i-th dictionary atom in the k-type dictionary, is the weight factor to balance the residual term and the coefficient term, is the Riemann metric distance between the test pixel X and the k-th dictionary atom, is the sparse representation coefficient in the k-th dictionary; Step 3, construct a first-order derivative optimization algorithm, solve the objective function, and obtain the sparse representation coefficients of each type of dictionary; Step 4: Calculate the predicted data of each category according to the sparse representation coefficient calculated in step 3, assign the pixel class label to the category with the smallest residual between the real data and the predicted data, and finally obtain the classification result of the polarimetric SAR image.

2. According to the polarization SAR image classification method based on the Riemann nearest canonical subspace model as claimed in claim 1, the specific steps of step 1 are: Randomly select from each class of the polarimetric SAR image to be classified pixels as the training set; the remaining pixels as the test set, and the matrix dictionary D is constructed by the covariance matrix of the pixels in the training set, where the covariance matrix is: （1） Where C is the covariance matrix, The echo data of the horizontally transmitted polarized wave for horizontal reception, The echo data of the horizontally transmitted polarized wave received vertically, It is the echo data of the vertically transmitted polarized wave received vertically; Building a dictionary : （2） is the total number of categories, The dictionary D is composed of the K-th class training pixels and is defined as follows: （3） in, is the i-th dictionary atom of the k-th dictionary, represented by the covariance matrix of the i-th training pixel of the k-th class.

3. The polarimetric SAR image classification method based on the Riemann nearest canonical subspace model as claimed in claim 1, characterized in that: The step 3 specifically includes: The objective function of formula (8) is written as: （9） in （10） （11） The first-order derivative method is used to optimize it. First, the residual term, i.e., the first-order derivative of the formula, is found; First, according to the definition of norm: （12） set up （13） get: （14） Taking the first-order derivative of formula (10) we get: （15） set up （16） Continue to derive formula (10) to obtain: （17） Next, we differentiate the Tikhonov regularization term, that is, formula (13): （18） in Calculated by formula (6) and (7), the first-order derivative of formula (8) is: （19） Through the above formula (9) to formula (19), we can finally get .

4. The polarimetric SAR image classification method based on the Riemann nearest canonical subspace model as claimed in claim 1, characterized in that: The step 4 is specifically as follows: Step 4.1, according to the sparse representation coefficients obtained in step 3 , calculate the most similar estimate of the test pixel : The covariance matrix of the test pixel is expressed by a linear combination of the covariance matrices of the training pixels of the same type: （20） in represents the most similar estimate for the test pixel; Representative categories; Represents the number of samples selected from each category as training sets; It represents the number of categories of polarimetric SAR images; is the coefficient column vector; （21）； Step 4.2: The most similar estimate Substitute into formula (22) to obtain the classification category of the test sample pixel: （22） in is the number of categories of polarimetric SAR images, For which category, is the test sample pixel.

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