CN108122008B - SAR image recognition method based on sparse representation and multi-feature decision-level fusion - Google Patents

SAR image recognition method based on sparse representation and multi-feature decision-level fusion Download PDF

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CN108122008B
CN108122008B CN201711405236.3A CN201711405236A CN108122008B CN 108122008 B CN108122008 B CN 108122008B CN 201711405236 A CN201711405236 A CN 201711405236A CN 108122008 B CN108122008 B CN 108122008B
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谷雨
彭冬亮
冯秋晨
刘俊
陈华杰
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Hangzhou Dianzi University
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Abstract

The invention relates to an SAR image recognition method based on sparse representation and multi-feature decision-level fusion. In order to improve the recognition rate and the recognition speed of the SAR target recognition algorithm, the invention extracts gray features and dimension reduction random convolution feature vectors from an SAR slice image, then optimizes a dictionary formed by the feature vectors extracted from each class of training samples by adopting a dictionary learning algorithm to form the dictionary, and finally recovers sample sparse coefficients through the dictionary to obtain a classification result. The method provided by the invention greatly improves the identification speed, improves the identification precision and has better application prospect.

Description

SAR image recognition method based on sparse representation and multi-feature decision-level fusion
Technical Field
The invention belongs to the field of SAR (synthetic Aperture Radar) image automatic target identification, and relates to an SAR image identification method based on sparse representation and multi-feature decision-level fusion.
Background
The SAR image automatic target identification is one of core problems which need to be solved urgently in SAR image interpretation, and the working process of the SAR image automatic target identification is to find out an interested region in the SAR image and classify the interested region to determine a target category. SAR image target recognition has been widely used in national economy and national defense construction, including ocean monitoring systems, mineral exploration, and the like.
Feature extraction and classifier design are two key factors influencing SAR image target recognition accuracy. The features extracted from the SAR image mainly comprise features based on mathematical transformation, computer vision features, electromagnetic features and the like, wherein the computer vision features mainly comprise textures, attitude angles, shapes and the like. At present, the main SAR image target recognition algorithm comprises a template matching-based method, a support vector machine-based method, a Boosting-based method, a sparse representation-based method and the like. The target recognition algorithm based on sparse representation is firstly applied to face recognition, and has started to be widely applied to SAR image target recognition in recent years, and higher recognition accuracy is achieved. In order to improve the target recognition precision of the SAR image based on sparse representation, effective target features are extracted from the SAR image, and dictionary optimization is a commonly adopted means. The main features adopted at present comprise gray scale features, monogenic signal features, improved SIFT features and the like, and the main dictionary learning algorithm comprises KSVD, LCKSVD, OnlineLearning and the like.
The deep learning technology can be used for feature learning based on massive big data, the learned features are usually superior to manually designed features, particularly, the deep model based on the convolutional neural network can effectively extract multi-scale two-dimensional local features of a target by performing operations such as convolution and pooling on a two-dimensional image, and the classification performance in the aspect of face recognition is superior to that of HOG features. However, the following problems need to be solved when feature learning is performed based on the deep convolutional neural network: (1) lack of training samples; (2) the depth model needs to be optimally designed; (3) the training time is long. Literature studies have shown that even if images are filtered using a randomly generated convolution kernel, the extracted random convolution features can achieve excellent classification results by properly designing the classifier.
When multiple characteristics are adopted for SAR image target fusion recognition, how to effectively utilize complementary advantages of the characteristics and reasonably design a classifier and a fusion rule are key elements influencing SAR image target recognition accuracy. When the sparse representation method is adopted for target identification, in order to improve the target identification precision and identification speed of the SAR image, the invention respectively extracts the gray characteristic and the random convolution characteristic from the image, and adopts a decision level fusion strategy to carry out comprehensive judgment based on the classification results of the two characteristics. Because the calculated amount of the target recognition algorithm based on sparse representation is closely related to the feature dimension and the element number of the sparse dictionary, in order to improve the recognition speed of the SAR target recognition algorithm based on sparse representation, on one hand, a sparse random projection method is adopted to reduce the dimension of the extracted high-dimensional random convolution feature, on the other hand, an Online dictionary learning algorithm is utilized to optimize the dictionary for target classification, and under the condition of ensuring the target classification precision, fewer dictionary elements are used to form the dictionary, so that the calculated amount of the SAR target recognition algorithm based on sparse representation is reduced. When the recognition results of the two features are fused, the signal reconstruction error obtained after sparse coefficient optimization solution based on sparse representation is converted into the recognition probability of each class of targets, and then the classification results are fused based on Bayesian fusion rules. Experimental results show that the speed of target classification can be improved by adopting two means of sparse random projection mapping and dictionary optimization learning, the method designed by the invention can obtain recognition performance which is close to or even higher than that of the existing known documents under various operating conditions, and the algorithm applicability is strong.
Disclosure of Invention
The SAR amplitude image directly reflects the back reflection coefficients of the target and the ground object, so that the gray scale characteristics of the SAR image can be directly utilized for target identification. Local features extracted based on each point of pixel field information generally have stronger feature description capability, but are greatly influenced by platform depression angle change, and compared with gray features, the influence of image noise can be weakened due to comprehensive utilization of local region information. The SAR image recognition method based on sparse representation and multi-feature decision-level fusion is designed in consideration of the fact that deep convolution features have strong target local information description capacity, in order to improve the recognition rate and the real-time performance of the SAR image target recognition algorithm based on sparse representation, the real-time performance of SAR image recognition based on sparse representation is improved by adopting two means of sparse random projection mapping and dictionary optimization learning, and the SAR image target recognition precision is improved by fusing the recognition results of gray features extracted from the SAR image and dimension reduction random convolution features.
In order to solve the problem of SAR image multi-feature decision-level fusion identification based on sparse representation and improve the identification precision and real-time performance of the algorithm, the technical scheme adopted by the invention comprises the following steps:
and (1) preprocessing the original SAR image to obtain a target slice image.
And (2) extracting a target gray level feature vector.
Randomly generating a plurality of convolution kernels with different sizes, carrying out convolution filtering on the target slice image, and extracting multi-scale random convolution characteristic vectors through mean square pooling operation; and reducing the dimension of the extracted random convolution feature vector by adopting sparse random projection mapping to obtain a dimension-reduced random convolution feature vector.
And (4) respectively optimizing dictionaries formed by two kinds of feature vectors extracted from each class of training samples by adopting a dictionary learning algorithm, and then combining the optimized dictionaries into a dictionary for target recognition.
And (5) when a sample is tested, performing sparse coefficient optimization solution based on the gray feature and the dimensionality reduction random convolution feature, converting the reconstruction error into a target classification probability and performing decision level fusion, thereby realizing target class judgment.
Compared with the prior art, the invention has the following remarkable advantages: (1) when the sparse representation frame is adopted for target recognition, the real-time performance of the target recognition is influenced by the excessively high feature dimension, the random projection dimension reduction is carried out on the extracted high-dimensional random convolution features, and a dictionary formed by the reduced-dimension convolution feature vectors is optimized by adopting a dictionary learning means, so that the real-time performance of the SAR target recognition performance is ensured, and meanwhile, the algorithm is improved. (2) Two characteristics with complementary advantages are fused, reconstruction errors obtained by sparse coefficient recovery based on sparse representation are converted into probabilities of targets belonging to each class, decision-level fusion is carried out by adopting a Bayes fusion rule, and the recognition rate of SAR image targets is improved. (3) A large number of experiments are carried out under standard test conditions and various extended test conditions, and the experimental results show that the method provided by the invention achieves higher classification precision and has strong algorithm applicability.
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FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in FIG. 1, the method comprises the following steps:
and (1) preprocessing the original SAR image to obtain a target slice image I. The specific operation is as follows:
and filtering the original SAR image by adopting a mean filtering algorithm, wherein the size of a filtering kernel is 3 multiplied by 3. And taking a two-dimensional central point of an image plane as a coordinate origin, extracting the SAR slice image I with the size of 64 multiplied by 64, and dividing by 255.0 to enable the gray level of the image to be positioned in an interval [0, 1 ].
And (2) extracting a target gray level feature vector. The specific operation is as follows:
arranging the target slice image I in columns and converting the target slice image I into a vector f1. Will vector f1Normalization is performed by first dividing by the vector f1Subtracting the mean value of the obtained vectors to obtain the gray level feature vector of the target
Figure GDA0002487688430000031
(i.e., an N-dimensional vector, adding N elements and dividing by N)
Randomly generating a plurality of convolution kernels with different sizes, carrying out convolution filtering on the target slice image, and extracting multi-scale random convolution characteristic vectors through mean square pooling operation; and reducing the dimension of the extracted random convolution eigenvector by adopting a sparse random projection matrix to obtain the dimension-reduced random convolution eigenvector. The specific operation is as follows:
in order to extract random convolution characteristics, firstly, scaling a target slice image I to ensure that the resolution ratio of the target slice image I is changed into 32 × 32, recording the obtained SAR target slice image as P, adopting a larger convolution Kernel to extract random convolution characteristics because the SAR image has stronger speckle noise, setting a width set of the adopted convolution Kernel as {5,7,9,11,13}, firstly sampling according to a certain probability, then determining the width of the convolution Kernel, and then generating a two-dimensional convolution Kernel based on a formula (1)mThe number of convolution kernels employed is N.
Kernelm(i, j) ═ 2 × rand () -1 formula (1)
Where i and j denote the row and column coordinates of the two-dimensional convolution kernel, respectively, m is 1, 2, …, and N denotes the index of the two-dimensional convolution kernel. And rand () generates random numbers that are uniformly distributed in the interval [ 01 ].
Because the widths of the adopted convolution kernels are inconsistent, in order to facilitate subsequent processing, when the two-dimensional convolution kernel is adopted to filter the target slice image, zero filling operation is carried out on the original image, so that the sizes of the characteristic images generated after the image filtering is checked by adopting different convolutions are kept consistent, and the specific formula is shown as (2).
Fm＝KernelmPadding (P) formula (2)
Wherein, FmRepresenting the computed two-dimensional convolution characteristic, representing the convolution operation, padding (P) representing the filling of the target slice image P edges with 0's according to the width of the convolution kernel, such that FmConsistent with the size of P.
In order to make the obtained two-dimensional random convolution characteristics have certain invariance to target translation, the mean square pooling operation is adopted to carry out characteristic transformation, as shown in formula (3).
Figure GDA0002487688430000041
Where i, j is 1, 2, …, 32+1-g, and g is the width of the region over which the pooling operation is performed.
After the SAR slice image is subjected to feature extraction through convolution and pooling operations based on N convolution kernels, a generated two-dimensional convolution feature map P is obtainedmStretched into a column of eigenvectors fmAnd will { fm}m＝1…NAre combined to form a feature vector f with a larger dimension2The dimension of which is [ N × (32+1-g)21]。
Due to the feature vector f2The dimensionality of the extracted features is large, when a classifier is designed by adopting a sparse representation method, it is time-consuming to recover sparse coefficients, and a random projection mapping method is generally adopted to reduce the dimensionality of the extracted features, for example, a random projection mapping matrix is generated by adopting Gaussian distribution. In order to make the features after dimensionality reduction more sparse, formula (4) is adopted to generate a sparse random projection mapping matrix Rab。
Figure GDA0002487688430000051
Wherein a is a sparse random projection mapping matrix RabDimension after dimensionality reduction, b ═ N × (32+1-g)2Is a feature vector f2Determines the matrix RabDegree of sparseness of. When ρ is b/c, the matrix R is ideallyabOnly c elements in each row of (a) are non-zero and c is a constant, experimental studies have shown that when c takes a very small value, the resulting mapping matrix R isabAre sparse.
Original feature vector f2After dimension reduction of the formula (5), obtaining a dimension reduction random convolution feature vector
Figure GDA0002487688430000052
Figure GDA0002487688430000053
And (4) respectively optimizing dictionaries formed by two kinds of feature vectors extracted from each class of training samples by adopting a dictionary learning algorithm, and then combining the optimized dictionaries into a dictionary for target recognition.
The specific operation is as follows:
the time consumption of the target recognition algorithm based on sparse representation is related to the adopted target feature dimension and the number of dictionary elements of each type of targets forming the dictionary, and generally, the real-time performance of the algorithm is improved by using less dictionary elements on the premise of ensuring the classification precision through a dictionary optimization means.
Designing targets with T categories in total, and when performing dictionary optimization, designing feature vectors extracted from all training samples belonging to the same category T
Figure GDA0002487688430000054
Forming a dictionary in a column arrangement
Figure GDA0002487688430000055
Wherein n istRepresenting a category tNumber of all training samples, i ═ 1, …, nt. Obtaining optimized dictionary by using Online dictionary learning method
Figure GDA0002487688430000056
1 denotes a dictionary of gray features and 2 denotes a random convolution feature.
An objective function optimized by the Online dictionary learning method is shown in formula (6). Wherein, XtFor the input classification dictionary to be optimized, the sparse coding sparse coefficient matrix is set to
Figure GDA0002487688430000057
Sparse coding and dictionary learning processes are carried out through interaction, and a sparse coding sparse coefficient matrix A and an optimized dictionary are obtained through iterative optimization
Figure GDA0002487688430000058
Finally, the dictionaries belonging to all categories are combined to obtain the dictionary for target classification
Figure GDA0002487688430000059
Figure GDA00024876884300000510
Wherein l is the dimension of the input feature vector, d is the number of dictionary elements of the optimized category t, and λ is a regularization coefficient.
Dictionary formed by gray level feature vector extracted from training sample and dimension reduction random convolution feature
Figure GDA0002487688430000061
Respectively optimizing and combining based on the formula (6) to obtain an optimized dictionary D1And D2。
And (5) when a sample is tested, performing sparse coefficient optimization solution based on the gray feature and the dimensionality reduction random convolution feature, converting the reconstruction error into a target classification probability and performing decision level fusion, thereby realizing target class judgment. The specific operation is as follows:
respectively extracting gray characteristic vectors from samples x to be detected
Figure GDA0002487688430000062
Sum dimension reduction random convolution feature vector
Figure GDA0002487688430000063
Based on l1The norm is respectively solved for the convex optimization problem shown in the formula (7), and corresponding sparse coefficients α are obtained1And α2. The symbol index is marked as p; wherein, the value is a threshold value, and is generally 0.01.
Figure GDA0002487688430000064
Obtaining sparse coefficient α according to solution1And α2The object type can be discriminated. Since the SAR image has strong speckle noise, a method based on a minimum reconstruction error is usually adopted to discriminate the target class. For the kth class target, the function is defined:
Figure GDA0002487688430000065
for the
Figure GDA0002487688430000066
Is a coefficient vector in which α only the value at the index corresponding to the kth class target remains unchanged and the values at the remaining indices are set to zero.
Defining a residual error rk(x) Is composed of
Figure GDA0002487688430000067
Figure GDA0002487688430000068
N is the minimum residual error, obtained from equation (9)1，n2The values respectively correspond to the recognition results of the test sample x based on the gray scale features and the dimensionality reduction random convolution features. To facilitate recognition based on two characteristicsThe other results are fused to obtain a reconstruction error according to the formula (8)
Figure GDA0002487688430000069
And then, converting the reconstruction error based on the sparse coefficient obtained by recovery into the identification probability belonging to each class of targets based on the SoftMax idea, as shown in the formula (10) and the formula (11).
Figure GDA00024876884300000610
Figure GDA00024876884300000611
And (3) fusing the two feature recognition results by adopting a Bayesian fusion rule, wherein the two feature recognition results are shown as a formula (12). The class of the target is represented by formula (13).
Figure GDA00024876884300000612
Figure GDA00024876884300000613
In order to verify the effectiveness of the present invention, the performance of the algorithm is tested by using the MSTAR database, the SAR images in the MSTAR database are acquired by HH polarization, 0.3 × 0.3m resolution, and X band SAR sensors, the total of 10 types of targets including mixed targets, the number of training samples and the number of test samples are shown in table 1, a64 × 64 slice is extracted with the center of the image as the origin, the directly extracted grayscale feature dimension is 4096 × 1, the extracted SAR target slice image is scaled to 32 × 32 for extracting the two-dimensional random convolution features, the part of parameters in the experiment are as follows, N-48, g-3, λ -0.01, c-4, and the number of each type of target dictionary element is set as d-75, at this time, b-N × (32+1-g)243200, and 4000 is set as the dimension a of the random convolution characteristic after dimensionality reduction.
Table 1MSTAR database object description
Figure GDA0002487688430000071
The classification test using the 10 classes of deformation targets in Table 1 is denoted SOC1, and the classification test using three classes of targets, BMP2, BTR70 and T72, is denoted SOC 2. Firstly, two configurations of SOC1 and SOC2 are adopted, the discrimination capability of gray level feature vectors and dimension reduction random convolution features extracted from SAR images is compared, and meanwhile the influence of dictionary learning on classification accuracy and algorithm instantaneity is analyzed. Because the random convolution feature extraction and dimension reduction in the designed method have certain randomness, 5 Monte Carlo simulation experiments are carried out, and the experimental results are shown in a table 2. As can be seen from the convolution feature extraction formula, as shown in formula (2), the neighborhood information of each pixel is utilized to generate enhanced features, so that under the condition that the depression angles are close (the training sample is 17 degrees, and the test sample is 15 degrees), the backscattering distribution of the target is close, the recognition accuracy based on the random convolution features is higher, and the discrimination capability of the extracted random convolution features is not significantly reduced even if a sparse random projection method is adopted for feature dimension reduction.
TABLE 2 comparison of different feature classification performance based on sparse representation (5 Monte Carlo simulations)
Figure GDA0002487688430000072
As can be seen from table 2, when 10 classes of deformed objects are classified (SOC1), the classification accuracy is improved from 94.75% to 96.05% by using the reduced-dimension random convolution features slightly higher than the classification result directly using the gray feature vectors, and when the dictionary optimization algorithm is used, the recognition accuracy based on the reduced-dimension random convolution features is improved from 94.18% to 96.05%. When 3 types of deformation targets are classified (SOC2), the classification result of the dimensionality reduction random convolution characteristics is superior to that of the gray level characteristics, the classification performance is improved to 95.62% from 92.16%, and if dictionary optimization is not adopted, the classification result based on the dimensionality reduction random convolution characteristics reaches 96.35%. Comparing the configurations of SOC1 and SOC2 can find that the deformation condition is mainly reflected in the two types of targets of BMP2 and T72, so when the target types are increased but the deformation condition is not increased, the identification result based on the gray scale feature is close to the identification result based on the dimensionality reduction random convolution feature.
Comparing the real-time performance of several algorithms, it can be seen that the real-time performance of the algorithm is improved because the number of dictionary elements forming the target recognition method based on sparse representation is reduced based on the dictionary optimization learning method. The dictionary optimization method has different influences on the recognition performance of the target, when the dimension reduction random convolution characteristic is adopted, the target recognition accuracy is improved for the SOC1 scene, and the target recognition accuracy is reduced for the SOC2 scene. When a grayscale feature is employed, the situation is just the opposite.
In order to further verify the effectiveness of the adopted sparse random projection mapping and dictionary optimization learning method, the dimension a of the dimensionality-reduced random convolution features is set to be 1000, and as can be seen from the results in table 2, the real-time performance of the classification algorithm is obviously improved under the condition that the overall classification accuracy is slightly reduced, and at the moment, under the condition of the same SOC2 scene and the dictionary learning, the overall classification accuracy of the adopted dimensionality-reduced random convolution features is still higher than the classification accuracy based on the gray features. This illustrates the effectiveness of the random convolution feature employed.
For the SAR image recognition in the MSTAR database, besides the two standard operating conditions, another four extended operating conditions are adopted to perform SAR target recognition experiments, which are respectively marked as EOC1, EOC2, EOC3 and EOC 4. Under the condition of EOC1, training four types of training samples of targets of BMP2, BTR70, BRDM2 and T72 in Table 1 to obtain a classifier, classifying 5 different types of test samples of T72, and mainly testing the classification capability of the classifier on deformed targets in an EOC1 classification experiment. Under the condition of EOC2, training classifiers are trained by using training samples of targets of four types of 2S1, BRDM2, T72 and ZSU234 in Table 1, a test sample is a target sample image obtained when the depression angle is 30 degrees, and T72 adopts a model of A64. The EOC2 classification experiment mainly tested the classification ability of the classifier for objects with large depression difference. Unlike EOC2, EOC3 only used the three targets 2S1, BRDM2 and ZSU234, and not T72, the training samples used the data in table 1, and the test samples used target sample images at 30 ° and 45 ° depression, respectively, where target distortion was present in BRMD2 and ZSU 234. Under the condition of EOC4, four targets of BMP2, T72, BTR60 and T62 in Table 1 are used for classification, wherein BMP2 and T72 have deformation target conditions, SN9563 and SN132 models are used for training, and the models of test samples are SN9566, SNC21, SN812, SNS7 and EOC4 respectively and mainly test the classification capability of the classifier on the deformation target.
Table 3 lists the characteristics of several typical SAR image target recognition algorithms involved in comparison, including the features used, the classifier method, and whether pose estimation and dictionary learning are required. Table 4 shows the target classification results under 6 operating conditions, SOC1, SOC2, EOC1, etc. The results of the experiments, except for the designed method, are directly from the corresponding literature. As can be seen from table 4, the algorithm of the present invention is comparable to the optimal classification accuracy achieved in each case, except for the EOC1 case. In the case of EOC1, the classifier based on sparse representation is the same as the K-nearest neighbor classifier in mechanism, and when the target deformation is large and has a large difference from the target in the training sample, the target is affected by speckle noise, so that the recognition accuracy may be reduced. The EOC4 scene also examines the recognition capability of the deformed object, and the method designed by the invention has the highest recognition accuracy. Therefore, although a randomization method is adopted for feature extraction and dimension reduction, a dictionary optimization means is combined, two features with complementary characteristics are fused, and the classification algorithm based on sparse representation can still better judge the target class, so that excellent classification results can be obtained under various conditions.
It can be seen from the results of the experiments in tables 2 and 4 that, after the grayscale feature and the dimensionality reduction random convolution feature are fused, although the recognition accuracy of the SOC2 scene is slightly reduced, under the extended operating condition, because the two adopted features have complementarity, the adaptability of the design method is improved and higher classification accuracy is obtained by reasonably selecting the classifier and the design fusion rule.
TABLE 3 characteristic analysis of typical SAR image target recognition algorithm
Figure GDA0002487688430000091
Figure GDA0002487688430000101
TABLE 4 Classification Performance comparison with typical Algorithm under multiple scenarios (5 Monte Carlo simulations)
Figure GDA0002487688430000102

Claims (2)

1. The SAR image recognition method based on sparse representation and multi-feature decision-level fusion is characterized by comprising the following steps of:
the method comprises the following steps of (1) preprocessing an original SAR image to obtain a target slice image I;
step (2) extracting target gray level feature vectors of target slice images
Figure FDA0002487688420000011
Step (3) randomly generating a plurality of convolution kernels with different sizes, carrying out convolution filtering on the target slice image, and extracting a multi-scale random convolution feature vector f through mean square pooling2(ii) a Reducing the dimension of the extracted random convolution feature vector by adopting sparse random projection mapping to obtain a dimension-reduced random convolution feature vector
Figure FDA0002487688420000012
Respectively optimizing dictionaries formed by two feature vectors extracted from each class of training samples by adopting a dictionary learning algorithm, and then combining the optimized dictionaries into a dictionary for target recognition;
step (5), when a sample is tested, sparse coefficient optimization solving is carried out based on the gray feature and the dimensionality reduction random convolution feature, the reconstruction error is converted into a target classification probability, and decision level fusion is carried out, so that target class discrimination is realized;
the step (3) is specifically as follows:
in order to extract random convolution characteristics, firstly, scaling a target slice image I to ensure that the resolution ratio of the target slice image I is changed to 32 × 32, recording the obtained target slice image as P, setting a width set of adopted convolution kernels as {5,7,9,11 and 13}, firstly sampling according to a certain probability, then determining the width of the convolution kernels, and then generating a two-dimensional random convolution Kernel based on an equation (1)mThe number of convolution kernels adopted is N;
Kernelm(i, j) ═ 2 × rand () -1 formula (1)
Wherein i and j respectively represent row and column coordinates of the two-dimensional random convolution kernel, m is 1, 2 and …, and N represents an index of the two-dimensional random convolution kernel; rand () generates random numbers that are uniformly distributed in the interval [0, 1 ];
when filtering is carried out on a target slice image by adopting two-dimensional random convolution kernel, zero padding operation is carried out on an original image, so that sizes of characteristic images generated after filtering of the image by adopting different convolution kernels are kept consistent, and the specific formula is shown in (2);
Fm＝Kernelmpadding (P) formula (2)
Wherein, FmRepresenting the computed two-dimensional random convolution characteristic representing the convolution operation, padding (P) representing the filling of the target slice image P edges with 0's according to the width of the convolution kernel, such that FmKeeping the same as the size of P;
in order to enable the obtained two-dimensional random convolution characteristics to have certain invariance to target translation, feature transformation is carried out by adopting mean square pooling operation, as shown in a formula (3);
Figure FDA0002487688420000021
wherein i, j is 1, 2, …, 32+1-g, g is the width of the region in which the pooling operation is performed;
after the target slice image is subjected to feature extraction through convolution and pooling operations based on N convolution kernels, a generated two-dimensional random convolution feature map P is obtainedmDraw into a characteristic direction of columnQuantity fmAnd will { fm}m＝1…NAre combined to form a feature vector f with a larger dimension2The dimension of which is [ N × (32+1-g)21]；
Reducing the dimension of the extracted features by adopting a random projection mapping method; in order to make the features after dimensionality reduction more sparse, formula (4) is adopted to generate a sparse random projection mapping matrix Rab；
Figure FDA0002487688420000022
Wherein a is a sparse random projection mapping matrix RabDimension after dimensionality reduction, b ═ N × (32+1-g)2As feature vector f2Of (d), rho determines the matrix RabDegree of sparsity of; when ρ is b/c, the matrix R is ideallyabOnly c elements in each row of (a) are non-zero, indicating that when c takes a very small value, the resulting mapping matrix R isabIs sparse;
original feature vector f2After dimension reduction is carried out by the formula (5), the dimension reduction random convolution feature vector is obtained
Figure FDA0002487688420000023
Figure FDA0002487688420000024
2. The SAR image recognition method based on sparse representation and multi-feature decision-level fusion as claimed in claim 1, wherein the step (5) is specifically:
respectively extracting gray characteristic vectors from samples x to be detected
Figure FDA0002487688420000025
Sum dimension reduction random convolution feature vector
Figure FDA0002487688420000026
Based on l1The norm is respectively solved for the convex optimization problem shown in the formula (7), and corresponding sparse coefficients α are obtained1And α2(ii) a The symbol index is marked as p; wherein is a threshold value;
Figure FDA0002487688420000027
obtaining sparse coefficient α according to solution1And α2The object type can be judged; because the SAR image has strong speckle noise, a method based on minimum reconstruction error is adopted to judge the target category; for the kth class target, the function is defined:
Figure FDA0002487688420000028
for the
Figure FDA0002487688420000029
Is a coefficient vector in which α only the value at the index corresponding to the kth class target remains unchanged and the values at the remaining indices are set to zero, defines the reconstruction error
Figure FDA0002487688420000031
Is composed of
Figure FDA0002487688420000032
Figure FDA0002487688420000033
N is the minimum residual error, obtained from equation (9)1，n2The values respectively correspond to the recognition results of the test sample x based on the gray feature and the dimensionality reduction random convolution feature; in order to facilitate the fusion of the recognition results based on the two features, the reconstruction error is obtained according to the formula (8)
Figure FDA0002487688420000034
Then, reconstructing the sparse coefficient obtained by solving the formula (8) based on the SoftMax ideaThe difference is converted into the recognition probability belonging to each class of targets, as shown in formulas (10) and (11);
Figure FDA0002487688420000035
Figure FDA0002487688420000036
fusing two feature recognition results by adopting a Bayesian fusion rule, as shown in a formula (12); the class of the target is represented by formula (13);
Figure FDA0002487688420000037
Figure FDA0002487688420000038
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