CN109344767B - SAR target identification method based on multi-azimuth multi-feature collaborative representation - Google Patents

SAR target identification method based on multi-azimuth multi-feature collaborative representation Download PDF

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CN109344767B
CN109344767B CN201811148970.0A CN201811148970A CN109344767B CN 109344767 B CN109344767 B CN 109344767B CN 201811148970 A CN201811148970 A CN 201811148970A CN 109344767 B CN109344767 B CN 109344767B
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张新征
刘苗苗
王娟
伍志林
刘书君
周喜川
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Abstract

The invention discloses a multi-azimuth multi-feature collaborative representation-based SAR target recognition method, which improves the traditional collaborative representation algorithm by mining the azimuth correlation of adjacent SAR images for the first time and provides a new multi-azimuth CRC algorithm. The method not only retains the advantage of simple operation of cooperative representation, but also improves the accuracy of SAR target classification, and has excellent anti-noise capability and robustness to various parameter changes.

Description

SAR target identification method based on multi-azimuth multi-feature collaborative representation
Technical Field
The invention relates to the technical field of radar target identification, in particular to an SAR target identification method based on multi-azimuth multi-feature collaborative representation.
Background
Synthetic Aperture Radars (SAR) are widely used in military and civilian applications due to their many advantages. The SAR target recognition technology is the technology for distinguishing and classifying specific targets by utilizing SAR, and is an important application of SAR.
SAR target identification methods can be mainly classified into three categories: (1) a template matching based approach. The good recognition performance of the method is required to be established on the basis of a template library which is as complete as possible, and if the template library is small, the recognition performance is greatly influenced. The large template library results in higher space complexity and lower efficiency of the template matching method. (2) A model-based approach. The model-based method has better clutter robustness, but the method has higher requirements on the quality of the SAR image, and higher theoretical level and computing power are required when the model is constructed, so that the current model-based SAR target identification method is not widely applied. (3) A machine learning based method. The sparse representation-based SAR target recognition is widely concerned by virtue of its good recognition performance. It should be noted that although SRC (sparse representation-based classification) has good classification performance, there are still disadvantages that the computation is complex, and it is difficult to obtain a global optimal solution. Therefore, as an alternative representation learning method, a collaborative representation algorithm is proposed. The results demonstrate that CRC (Collaborative reporting-Based classification) Based on the L2 norm constraint can achieve similar classification performance to SRC, but the computational complexity is much lower than SRC. However, to date, all CRC models do not take into account the dependence of SAR target scattering on azimuth angle and the complementarity between different features of the SAR target image. According to the SAR imaging mechanism, SAR target images of adjacent positions have similar scattering characteristics, so that the SAR target images have strong correlation in an image domain. And different features extracted from different aspects of the SAR image, each feature describes the SAR scene from a single angle, and the information provided by the features has strong complementarity.
Therefore, how to improve the classification performance of the high-cooperation representation on the SAR image target by a better method is an important issue of research in the field.
Disclosure of Invention
Aiming at the defects in the prior art, the application discloses an SAR target recognition method based on multi-azimuth multi-feature collaborative representation, the traditional CRC algorithm is improved by mining the azimuth correlation of adjacent SAR images, and a new multi-azimuth CRC algorithm is provided.
In order to solve the technical problem, the following technical scheme is adopted in the application:
a SAR target recognition method based on multi-azimuth multi-feature collaborative representation comprises the following steps:
(1) aiming at different known radar targets of multiple types, SAR images of multiple directions of multiple known radar targets are respectively collected to serve as training samples, PCA (principal component analysis) features, wavelet features and 2DSZMS (two-dimensional space-time scaling) features of the training samples are respectively extracted, and therefore a training sample set X is formed by a set of the PCA features, the wavelet features and the 2DSZMS features of the training samples of the various typesu×vU represents the dimension of the sample, v represents the total number of training samples in the training sample set, and X is based on the training sample setu×vConstructing a feature dictionary { Dk}k＝1,2,3K is a feature type index;
(2) aiming at a radar target to be tested, SAR images of the radar target to be tested in multiple directions are collected to serve as test samples, PCA (principal component analysis) features, wavelet features and 2DSZMS (two-dimensional space-time scaling) features of the test samples are respectively extracted, and therefore a test sample set Y is formed by a set of the PCA features, the wavelet features and the 2DSZMS features of the test samplesu×wW represents the total number of test samples in the test sample set, and the test sample set Yu×wAny one of the test samples can be represented as yk}k＝1,2,3；
(3) Taking one test sample in the test sample set as a central test sample
Figure GDA0003180227410000021
m is the index number of the central test sample, the central test sample and the test samples in the azimuth neighborhood of the central test sample are used as a multi-azimuth neighborhood test sample set, the sector range of the adjacent eta degrees of the central test sample is the azimuth neighborhood of the central test sample, and the degrees are [ c-eta, c + eta ]]The test samples in the range are the test samples in the azimuth neighborhood of the central test sample, c is the angle of the central test sample, and the multi-azimuth neighborhood test sample set is expressed as
Figure GDA0003180227410000022
p is the number of test samples in the upper half azimuth sector of the central test sample, and q is the number of test samples in the lower half azimuth sector of the central test sample;
(4) linearly representing each multi-azimuth neighborhood test sample in the multi-azimuth neighborhood test sample set;
(5) establishing a multi-azimuth multi-feature collaborative representation classification model of the test sample set by utilizing each training sample in the training sample set and the multi-azimuth neighborhood test sample line represented linearly;
(6) respectively calculating temporary class labels of PCA (principal component analysis) features, wavelet features and 2DSZMS (two-dimensional singular value decomposition) features by utilizing a multi-azimuth multi-feature collaborative representation classification model;
(7) and performing multi-feature voting according to the PCA features, the wavelet features and the temporary class labels of the 2DSZMS features to obtain a final class label of the central test sample, thereby realizing the identification of the radar target to be detected.
Preferably, in step (4), the multi-azimuth neighborhood test samples in the multi-azimuth neighborhood test sample set may be linearly expressed as:
Figure GDA0003180227410000031
wherein,
Figure GDA0003180227410000032
denotes the τ -th class sub-dictionary under the feature k, N is the total number of classes,
Figure GDA0003180227410000033
indicating that the ith test sample is related to the sub-dictionary
Figure GDA0003180227410000034
Is used to represent a sub-vector of coefficients,
Figure GDA0003180227410000035
representing the random error at feature k.
Preferably, in step (5), the multi-azimuth multi-feature collaborative representation classification model is represented as:
Figure GDA0003180227410000036
wherein, BkIs a set of sub-vectors of coefficients,
Figure GDA0003180227410000037
and theta is a multi-azimuth multi-feature collaborative representation regularization parameter.
Preferably, the step (6) comprises the steps of:
1) solving an analytic solution of a multi-azimuth multi-feature collaborative representation classification model
Figure GDA0003180227410000038
Wherein
Figure GDA0003180227410000039
I represents an identity matrix;
2) solving a representation error set of the test samples in the azimuth neighborhood of the central test sample based on an analytic solution of a multi-azimuth multi-feature collaborative representation classification model
Figure GDA00031802274100000310
Wherein,
Figure GDA00031802274100000311
3) temporary class labels for computing center test specimens
Figure GDA00031802274100000312
Wherein,
Figure GDA00031802274100000313
Figure GDA00031802274100000314
Figure GDA00031802274100000322
that is to
Figure GDA00031802274100000315
Preferably, the step (7) comprises the steps of:
temporary class label
Figure GDA00031802274100000316
The possibility of belonging to the h-th class is
Figure GDA00031802274100000317
The multi-feature voting criteria is
Figure GDA00031802274100000318
Order to
Figure GDA00031802274100000319
The final class label of the center test specimen is
Figure GDA00031802274100000320
Figure GDA00031802274100000321
Representing results representing a multi-feature voting criterion.
In summary, the invention discloses a multi-azimuth multi-feature collaborative representation-based SAR target recognition method, the method improves the traditional collaborative representation algorithm by mining the azimuth correlation of adjacent SAR images for the first time, and provides a new multi-azimuth CRC algorithm. The method not only retains the advantage of simple operation of cooperative representation, but also improves the accuracy of SAR target classification, and has excellent anti-noise capability and robustness to various parameter changes.
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For purposes of clarity, technical solutions and advantages, the present application will be described in further detail below with reference to the accompanying drawings, in which:
FIG. 1 is a near-azimuth SAR image of a target BMP 2;
FIG. 2 is a near-bearing SAR image of the target BTR 70;
FIG. 3 is a near-azimuth SAR image of the target T72;
FIG. 4 is a graph of classification effects (PCACRC, WCRC, 2 DSZCRC, MFCRC, MAMFCRC) of different methods under the same parameters;
FIG. 5 is a graph of classification effect of five methods (PCACRC, WCRC, 2 DSZCRC, MFCRC, MAMFCRC) as a function of feature dimension;
FIG. 6 is a graph of the variation of the classification effectiveness performance of the five methods (PCACRC, WCRC, 2 DSZCRC, MFCRC, MAMFCRC) with respect to the regularization parameter θ;
FIG. 7 is a graph of MAMFCRC average classification accuracy versus azimuth neighborhood angle;
FIG. 8 is a graph of MAMFCRC classification performance variation under different SNR noises;
FIG. 9 is a SAR image of BRDM 2;
fig. 10 is a SAR image of 2S 1;
FIG. 11 is a SAR image of ZSU 23/4;
fig. 12 is a flowchart of an SAR target identification method based on multi-azimuth multi-feature collaborative representation disclosed by the present invention.
Detailed Description
The present application will now be described in further detail with reference to the accompanying drawings.
As shown in fig. 12, the present invention discloses an SAR target identification method based on multi-azimuth multi-feature collaborative representation, which comprises the following steps:
(1) aiming at different known radar targets of multiple types, SAR images of multiple directions of multiple known radar targets are respectively collected to serve as training samples, PCA (principal component analysis) features, wavelet features and 2DSZMS (two-dimensional space-time scaling) features of the training samples are respectively extracted, and therefore a training sample set X is formed by a set of the PCA features, the wavelet features and the 2DSZMS features of the training samples of the various typesu×vU represents the dimension of the sample, v represents the total number of training samples in the training sample set, and X is based on the training sample setu×vConstructing a feature dictionary { Dk}k＝1,2,3K is a feature type index;
as shown in fig. 1 to 3 and 9 to 11, in the method of the present invention, various typical SAR target image features may be applied. These different features are extracted from different aspects of the SAR image, each describing the SAR scene from a single perspective. Because the information provided by the characteristics has strong complementarity, the accuracy and the robustness of SAR target identification can be improved by comprehensively utilizing the different characteristics.
PCA is a very common data compression and feature extraction technique. Firstly, the method centers data and then calculates the eigenvalue and eigenvector of the data covariance matrix. And then, arranging the eigenvalues from large to small, selecting the largest k eigenvalues, and forming an eigenvector matrix by the corresponding k eigenvectors. And finally, projecting the sample points to the selected feature vectors to obtain PCA feature data after dimension reduction.
The wavelet transformation can effectively extract the multi-scale characteristics of the two-dimensional image and can highlight singular points in the image. Two-dimensional discrete wavelet transform (2D-DWT) of an image is to decompose rows and columns by using low-pass and high-pass filters respectively to obtain a low-frequency approximate sub-image, a horizontal high-frequency sub-image, a vertical high-frequency sub-image and a diagonal high-frequency sub-image. In the invention, a low-frequency sub-image of two-dimensional discrete wavelet transform is used as a multi-scale wavelet feature.
The Zernike moments can easily construct arbitrarily high-order moments of an image and can reconstruct an image using fewer moments. In the present invention we use the 2DS-ZMs feature based on image domain. The method includes the steps that an SAR image is evenly cut into k pieces according to the amplitude direction, and multilayer 2D-Slice of the image is obtained. And then, the Zernike moments are used for describing each layer, so that each layer obtains a Zernike moment feature vector. And finally, stacking the feature vectors together, and describing the SAR image by using the column vector, wherein the column vector is called the 2D-Slice Zernike moments feature vector of the SAR image.
(2) Aiming at a radar target to be tested, SAR images of the radar target to be tested in multiple directions are collected to serve as test samples, and PCA (principal component analysis) characteristics, wavelet characteristics and 2DSZMS (two-dimensional gradient magnetic field) characteristics of each test sample are respectively extractedWhereby a set of test samples Y is formed from a set of PCA features, wavelet features and 2DSZMS features of each test sampleu×wW represents the total number of test samples in the test sample set, and the test sample set Yu×wAny one of the test samples can be represented as yk}k＝1,2,3；
(3) Taking one test sample in the test sample set as a central test sample
Figure GDA0003180227410000051
m is the index number of the central test sample, the central test sample and the test samples in the azimuth neighborhood of the central test sample are used as a multi-azimuth neighborhood test sample set, the sector range of the adjacent eta degrees of the central test sample is the azimuth neighborhood of the central test sample, and the degrees are [ c-eta, c + eta ]]The test samples in the range are the test samples in the azimuth neighborhood of the central test sample, c is the angle of the central test sample, and the multi-azimuth neighborhood test sample set is expressed as
Figure GDA0003180227410000052
p is the number of test samples in the upper half azimuth sector of the central test sample, and q is the number of test samples in the lower half azimuth sector of the central test sample;
according to an imaging mechanism of the SAR sensor, SAR images with similar azimuth angles have strong correlation. That is, there is a high correlation and similarity between several SAR target image test samples within a small azimuthal neighborhood. We introduce this mechanism into the basic collaborative representation model. By taking the azimuth angle of a central test sample as a center, a plurality of test samples in a small azimuth angle sector are taken to form a multi-azimuth neighborhood sample set.
(4) Linearly representing each multi-azimuth neighborhood test sample in the multi-azimuth neighborhood test sample set;
(5) establishing a multi-azimuth multi-feature collaborative representation classification model of the test sample set by utilizing each training sample in the training sample set and the multi-azimuth neighborhood test sample line represented linearly;
(6) respectively calculating temporary class labels of PCA (principal component analysis) features, wavelet features and 2DSZMS (two-dimensional singular value decomposition) features by utilizing a multi-azimuth multi-feature collaborative representation classification model;
(7) and performing multi-feature voting according to the PCA features, the wavelet features and the temporary class labels of the 2DSZMS features to obtain a final class label of the central test sample, thereby realizing the identification of the radar target to be detected.
As shown in fig. 8, the classification performance change chart of the present invention under different SNR noises is obtained, the present invention improves the conventional collaborative representation algorithm by mining the azimuth correlation of adjacent SAR images for the first time, and provides a new multi-azimuth CRC algorithm. The method not only retains the advantage of simple operation of cooperative representation, but also improves the accuracy of SAR target classification, and has excellent anti-noise capability and robustness to various parameter changes.
In specific implementation, in step (4), the multi-directional neighborhood test samples in the multi-directional neighborhood test sample set can be linearly expressed as:
Figure GDA0003180227410000061
wherein,
Figure GDA0003180227410000062
denotes the τ -th class sub-dictionary under the feature k, N is the total number of classes,
Figure GDA0003180227410000063
indicating that the ith test sample is related to the sub-dictionary
Figure GDA0003180227410000064
Is used to represent a sub-vector of coefficients,
Figure GDA0003180227410000065
representing the random error at feature k.
In the specific implementation, in the step (5), the multi-azimuth multi-feature collaborative representation classification model is represented as:
Figure GDA0003180227410000071
wherein, BkIs a set of sub-vectors of coefficients,
Figure GDA0003180227410000072
and theta is a multi-azimuth multi-feature collaborative representation regularization parameter.
According to the target multi-azimuth strong correlation characteristic, the representation coefficient
Figure GDA0003180227410000073
Should be similar in nature. If strict requirements are made on this similarity, let each
Figure GDA0003180227410000074
All are equal, the above problem can be expressed as:
Figure GDA0003180227410000075
here, ,
Figure GDA0003180227410000076
according to the principle of the collaborative representation classifier, a multi-azimuth multi-feature collaborative representation classification model in the form of a matrix can be obtained as follows:
Figure GDA0003180227410000077
in specific implementation, the step (6) comprises the following steps:
1) solving an analytic solution of a multi-azimuth multi-feature collaborative representation classification model
Figure GDA0003180227410000078
Wherein
Figure GDA0003180227410000079
I represents an identity matrix;
in the above multi-azimuth multi-feature collaborative representation classification model, the Frobenius norm of the matrix can be written as l of each column vector2The sum of the norms, i.e. the formula:
Figure GDA00031802274100000710
and
Figure GDA00031802274100000711
therefore, the multi-azimuth neighborhood collaborative representation model becomes the following solution problem:
Figure GDA00031802274100000712
on the other hand, due to noise and the like, there is a difference between the test samples at different azimuth angles, and the representation coefficients should also have a difference to ensure that sufficient complementary information is provided, which makes the representation more flexible. Thus, we will still each
Figure GDA00031802274100000713
Considered different, the representation coefficients of the multi-azimuth neighborhood co-representation can thus be solved by the following optimization problem:
Figure GDA00031802274100000714
the above-mentioned multidirectional neighborhood collaborative representation model optimization problem has an analytic solution as follows:
Figure GDA00031802274100000715
2) solving a representation error set of the test samples in the azimuth neighborhood of the central test sample based on an analytic solution of a multi-azimuth multi-feature collaborative representation classification model
Figure GDA0003180227410000081
Wherein,
Figure GDA0003180227410000082
according to
Figure GDA0003180227410000083
We can find the co-expression coefficients of the test samples in the azimuthal neighborhood. Further, the representation error of each orientation neighborhood test sample can be found as follows:
Figure GDA0003180227410000084
3) temporary class labels for computing center test specimens
Figure GDA0003180227410000085
Wherein,
Figure GDA0003180227410000086
Figure GDA0003180227410000087
Figure GDA0003180227410000088
that is to
Figure GDA0003180227410000089
Temporary class labels for current test samples
Figure GDA00031802274100000810
The method can be obtained according to the principle that the representation error sum of all the test samples in the azimuth neighborhood is minimum.
In specific implementation, the step (7) comprises the following steps:
temporary class label
Figure GDA00031802274100000811
The possibility of belonging to the h-th class is
Figure GDA00031802274100000812
The multi-feature voting criteria is
Figure GDA00031802274100000813
When in use
Figure GDA00031802274100000814
When the final class label of the central test specimen is
Figure GDA00031802274100000815
Figure GDA00031802274100000816
Representing results representing a multi-feature voting criterion.
In order to fully utilize discrimination information of different features of an SAR target, a multi-azimuth multi-feature collaborative representation classification model classification result under three features (PCA, wavelet and 2DSZMs) of a current test sample is fused. That is, y for the current unclassified samplemObtaining three temporary labels under each feature through a multi-azimuth multi-feature collaborative representation classification model
Figure GDA00031802274100000817
Assume temporary class labels
Figure GDA00031802274100000818
The possibility of belonging to the h-th class is
Figure GDA00031802274100000819
The multi-feature voting criteria are:
Figure GDA00031802274100000820
the technical solution of the present invention will be further described below by way of examples.
Example (b):
in the experiment, five methods of PCACRC, WCRC, 2 DSZCRC, MFCRC and MAMFCRC are subjected to experimental comparison under the same parameters and the same conditions. Here, the regularization parameter for each method is 0.1, each feature dimension is 200 dimensions, and the azimuth neighborhood angle in mamcrc is 5 °. The five methods are respectively realized as follows:
(1) PCACRC: and extracting PCA characteristic data of the SAR training sample and the test sample, and inputting the PCA characteristic data into a basic CRC frame to obtain a recognition result.
(2) WCRC: extracting wavelet feature data of the SAR training sample and the test sample, and inputting the wavelet feature data into a basic CRC framework to obtain a recognition result.
(3)2 DSZMRCC: and extracting 2DSZMs characteristic data of the SAR training sample and the testing sample, and inputting the 2DSZMs characteristic data into a basic CRC frame to obtain a recognition result.
(4) MFCRC: first, PCA, wavelet and 2DSZMs features are extracted from the SAR image. Then, the training sample and the current test sample under each feature are input to the basic CRC model, thereby obtaining a temporary output label. And finally, voting decision is carried out on the three temporary labels to obtain a classification result of the current test sample.
(5) MAMFCRC: firstly, three typical characteristics of PCA, wavelet and 2DSZMS are extracted from the SAR image. And then, according to the principle that the adjacent directions of the SAR target image are strongly correlated, expanding the basic collaborative representation model into a multi-direction neighborhood collaborative representation model. And for each feature, respectively inputting the multi-azimuth neighborhood test sample of the current test sample into the model to obtain a temporary output label corresponding to each feature. And finally, voting decision is carried out on the multidirectional neighborhood temporary output labels with the three types of characteristics to obtain a final identification result of the current test sample.
The results of this experiment are shown in table 2 and fig. 4. Fig. 4 compares the five methods against the average classification effect of the same SAR target image, and table 2 shows specific data. From table 2, it can be seen that under the condition that the parameters are the same, the recognition rate of the multi-feature based collaborative representation algorithm (MFCRC) is improved to 96.36% compared with the single-feature CRC algorithm. Nevertheless, as is apparent from table 2 and fig. 4, the accuracy of the mamcrc algorithm proposed by the present invention is greatly improved, which can reach 99.32%, compared with the other 4 methods, and at this time, the accuracy of the classification of the BTR70 class data and the T72 class data reaches even 100%, which sufficiently illustrates the superiority of mamcrc. In addition, as shown in fig. 5 and 6, the classification effect of the method of the present invention is not obvious along with the change of the feature dimension and the regularization parameter, so that the method of the present invention has better stability compared with other existing methods.
TABLE 1 type and number of training and test samples
Figure GDA0003180227410000091
TABLE 2 Performance comparison of Single feature CRC (PCACRC, WCRC, 2 DSZCRC), MFCRC and MAMFCRC algorithms
Figure GDA0003180227410000101
TABLE 3 Classification accuracy of MAMFCRC algorithm under different azimuth neighborhood angles
Figure GDA0003180227410000102
As can be seen from table 3 and fig. 7, when the neighborhood angles of different azimuths are set, the accuracy of the mamcrc algorithm is high, and the classification accuracy gradually increases with the increase of the domain angle, so that the optimal neighborhood angle is 10 °.
Table 4: data set for pitch angle experiment
Figure GDA0003180227410000103
TABLE 5 MAMFCRC algorithm Classification accuracy at different pitch angles
Figure GDA0003180227410000104
The data in table 4 are used as a test set, and the obtained results are shown in table 5, and the accuracy of the algorithm adopting the method of the invention is reduced with the increase of the depression angle, so that the method of the invention is suitable for being used in scenes with smaller depression angles.
Finally, it is noted that the above-mentioned embodiments illustrate rather than limit the invention, and that, while the application has been described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the application as defined by the appended claims.

Claims (2)

1. A SAR target recognition method based on multi-azimuth multi-feature collaborative representation is characterized by comprising the following steps:
(1) aiming at different known radar targets of multiple types, SAR images of multiple directions of multiple known radar targets are respectively collected to serve as training samples, PCA (principal component analysis) features, wavelet features and 2DSZMS (two-dimensional space-time scaling) features of the training samples are respectively extracted, and therefore a training sample set X is formed by a set of the PCA features, the wavelet features and the 2DSZMS features of the training samples of the various typesu×vU represents the dimension of the sample, v represents the total number of training samples in the training sample set, and X is based on the training sample setu×vConstructing a feature dictionary { Dk}k＝1,2,3K is a feature type index; the 2DSZMs of the SAR image refer to 2D-Slice Zernike moments feature vectors of the SAR image;
(2) aiming at a radar target to be tested, SAR images of the radar target to be tested in multiple directions are collected to serve as test samples, PCA (principal component analysis) features, wavelet features and 2DSZMS (two-dimensional space-time scaling) features of the test samples are respectively extracted, and therefore a test sample set Y is formed by a set of the PCA features, the wavelet features and the 2DSZMS features of the test samplesu×wW represents the total number of test samples in the test sample set, and the test sample set Yu×wAny one of the test samples can be represented as yk}k＝1,2,3；
(3) Taking one test sample in the test sample set as a central test sample
Figure FDA0003180227400000011
m is the index number of the central test sample, the central test sample and the test samples in the azimuth neighborhood of the central test sample are used as a multi-azimuth neighborhood test sample set, the sector range of the adjacent eta degrees of the central test sample is the azimuth neighborhood of the central test sample, and the degrees are [ c-eta, c + eta ]]The test samples in the range are the test samples in the azimuth neighborhood of the central test sample, c is the angle of the central test sample, and the multi-azimuth neighborhood test sample set is expressed as
Figure FDA0003180227400000012
p is the number of test samples in the upper half azimuth sector of the central test sample, and q is the number of test samples in the lower half azimuth sector of the central test sample;
(4) linearly representing each multi-azimuth neighborhood test sample in the multi-azimuth neighborhood test sample set; wherein the multi-azimuth neighborhood test samples in the multi-azimuth neighborhood test sample set can be linearly represented as:
Figure FDA0003180227400000013
wherein,
Figure FDA0003180227400000021
denotes the τ -th class sub-dictionary under the feature k, N is the total number of classes,
Figure FDA0003180227400000022
indicating that the ith test sample is related to the sub-dictionary
Figure FDA0003180227400000023
Is used to represent a sub-vector of coefficients,
Figure FDA0003180227400000024
representing the random error under the characteristic k;
(5) establishing a multi-azimuth multi-feature collaborative representation classification model of the test sample set by utilizing each training sample in the training sample set and the multi-azimuth neighborhood test sample line represented linearly; wherein, the multi-azimuth multi-feature collaborative representation classification model is expressed as:
Figure FDA0003180227400000025
wherein, BkIs a set of sub-vectors of coefficients,
Figure FDA0003180227400000026
Figure FDA00031802274000000222
the regularization parameters are represented in a multi-azimuth and multi-feature collaborative mode;
(6) respectively calculating temporary class labels of PCA (principal component analysis) features, wavelet features and 2DSZMS (two-dimensional singular value decomposition) features by utilizing a multi-azimuth multi-feature collaborative representation classification model; the method specifically comprises the following steps:
1) solving an analytic solution of a multi-azimuth multi-feature collaborative representation classification model
Figure FDA0003180227400000027
Wherein
Figure FDA0003180227400000028
I represents an identity matrix;
2) solving a representation error set of the test samples in the azimuth neighborhood of the central test sample based on an analytic solution of a multi-azimuth multi-feature collaborative representation classification model
Figure FDA0003180227400000029
Wherein,
Figure FDA00031802274000000210
3) temporary class labels for computing center test specimens
Figure FDA00031802274000000211
Wherein,
Figure FDA00031802274000000212
Figure FDA00031802274000000213
Figure FDA00031802274000000214
that is to
Figure FDA00031802274000000215
(7) And performing multi-feature voting according to the PCA features, the wavelet features and the temporary class labels of the 2DSZMS features to obtain a final class label of the central test sample, thereby realizing the identification of the radar target to be detected.
2. The SAR target recognition method based on multi-azimuth multi-feature collaborative representation according to claim 1, wherein the step (7) comprises the steps of:
temporary class label
Figure FDA00031802274000000216
The possibility of belonging to the h-th class is
Figure FDA00031802274000000217
The multi-feature voting criteria is
Figure FDA00031802274000000218
Order to
Figure FDA00031802274000000219
The final class label of the center test specimen is
Figure FDA00031802274000000220
Figure FDA00031802274000000221
Representing results representing a multi-feature voting criterion.
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