SAR target recognition based on improved joint sparse representation
© Cheng et al.; licensee Springer. 2014
Received: 26 February 2014
Accepted: 16 May 2014
Published: 9 June 2014
In this paper, a SAR target recognition method is proposed based on the improved joint sparse representation (IJSR) model. The IJSR model can effectively combine multiple-view SAR images from the same physical target to improve the recognition performance. The classification process contains two stages. Convex relaxation is used to obtain support sample candidates with the ℓ1-norm minimization in the first stage. The low-rank matrix recovery strategy is introduced to explore the final support samples and its corresponding sparse representation coefficient matrix in the second stage. Finally, with the minimal reconstruction residual strategy, we can make the SAR target classification. The experimental results on the MSTAR database show the recognition performance outperforms state-of-the-art methods, such as the joint sparse representation classification (JSRC) method and the sparse representation classification (SRC) method.
Synthetic aperture radar (SAR) is a high-resolution imaging radar. It can work regardless of climatic circumstances and time constraint. Thus, it is widely applied in kinds of military and civilian areas such as disaster assessment, resource exploration, and battlefield reconnaissance. SAR target recognition plays an important role in the automatic analysis and interpretation of the SAR image data. Over the past several decades, although lots of algorithms are exploited in SAR target recognition [1–3], it is a challenging issue due to the complexity of the measured information such as speckle noises, variation of azimuth, and poor visibility. Therefore, there is still no commonly agreed-upon system that settles SAR target recognition so far.
SAR target recognition includes two important parts, feature extraction and classifier construction. For feature extraction, classic methods, such as principal component analysis (PCA) , independent component analysis (ICA) , linear discriminant analysis (LDA) , nonnegative matrix factorization (NMF) [7, 8], and their improved algorithms , have been successfully used in SAR target recognition. Beyond those, in consideration of most features in nature distributing as a manifold structure, the manifold-based feature extraction algorithms become a new trend [10, 11]. Though kinds of feature extraction methods have their own advantages, no method extensively can be accepted. As for the classifier, support vector machine (SVM) and K-nearest neighbor (KNN) are the most common choices. To improve the performance of SAR target recognition, the classifying results under different features are fused to make the final classifier . In addition, sparse representation which closely bonds the feature extraction with the classifier has gradually aroused researchers' attention. Some advantages of sparse representation for recognition are mentioned in  such as its insensitivity to feature extraction method under certain conditions and the natural discriminative information in sparse representation coefficients, i.e., feature extraction is implicit in recognition and the classifier can be designed according to the sparse representation coefficients. The results for face recognition show the great competitiveness compared with other methods . Due to these advantages of sparse representation, Thiagarajan et al.  and Estabridis  both introduced sparse representation in target recognition. Thiagarajan et al. explained sparse representation from the point of manifold, which indicates the strength of sparse representation for SAR target recognition. They selected random projections as the feature extraction method and solved sparse representation using the greedy algorithm. Knee et al.  used image partitioning and sparse representation based feature to handle SAR target recognition.
The preceding methods only take one SAR image as the input signal to decide which class the target in the image belongs to. In practice, we can obtain multiple-view SAR images of the same physical target. Thus, some tried to make use of multiple-view SAR images under the theory framework of sparse representation. Exploring the sparse representation for the multiple input signals at the same time is a joint sparse representation problem [17, 18]. Therefore, Zhang et al.  used the joint sparse representation (JSR) model to seek common sparse patterns between multiple-view SAR images. In the JSR model, multiple-view SAR images are integrated in a matrix form. Under this context, the JSR model finally becomes a mixed-norm problem. An efficient and accurate greedy algorithm, CoSaMP [20, 21], is utilized to solve the model, and the classification algorithm is named as joint sparse representation classification (JSRC) which is similar with sparse representation classification (SRC).
With the inspiration from the JSR model, we propose an improved joint sparse representation (IJSR) model for SAR target recognition with multiple-view images. Compared with the original JSR model, there are two improvements in the IJSR model. The first is that sparse representation for the single-view image is described by a ℓ1-norm minimization model. The second is that common patterns in sparse representation coefficients of multiple-view images are sought by low-rank matrix recovery. The ℓ1-norm minimization model has two benefits for SAR target recognition. One benefit is that the proper sparse level parameter which is hard to choose in the original JSR model is not needed anymore. Another benefit is that sparse representation coefficients of the ℓ1-norm minimization are more concentrated in one class, which enhances the discrimination of sparse representation coefficients. Different from the greedy algorithm in the original JSR model, the ℓ1-norm minimization usually produces more nonzero entries in sparse representation coefficients of SAR target images. With the excessive nonzero entries, it becomes difficult to seek support samples which refer to the samples in the dictionary that associate with the nonzero entries in sparse representation coefficients. To tackle this problem, we further make some hypotheses that the matrix of joint sparse representation coefficients associating with support samples is low rank, and the rest that excludes the joint sparse representation coefficients associating with support samples is a sparse matrix. These hypotheses are based on the following reasons. According to the common sparse pattern assumption in the JSR model, these images with close views share the same support sample set. The common sparse pattern means important sparse representation coefficients which correspond to the support sample set have the same indexes in the dictionary and occupy the most nonzero entries in sparse representation coefficients. The problem of seeking the support samples converts to a low-rank matrix recovery problem; meanwhile, the low-rank matrix recovery algorithm could directly obtain the proper sparse representation coefficients on support samples.
The paper is organized as follows: In Section 2, we review the joint sparse representation model and describe the classification strategy. Section 3 analyzes the disadvantages of joint sparse representation and proposes the improved joint sparse representation model along with the classification strategy. In Section 4, we verify the proposed method with experiments on publicly available MSTAR database and compare with the classical SRC method and the original JSRC method.
2 Joint sparse representation for SAR target recognition
In the real scenario, the multiple-view SAR images from one same target can be captured, and those images are highly correlated. When a uniform dictionary is used for these multiple-view images' sparse representation, an implicit correlation in the sparse representation coefficients can emerge. The correlation is defined as the common patterns which specifically mean the same positions of the nonzero entries in the sparse representation coefficients in the work of Zhang et al. . The JSR model, which can combine the sparse representation coefficients of multiple-view images to extract the common patterns, is introduced in SAR target recognition.
2.1 Joint sparse representation model
where the is the mixed-norm of the matrix X which is defined by two computing processes. Firstly, the ℓ2-norm is applied on each row of the matrix, and then the ℓ0-norm of the resulting vector is computed as the result of the mixed-norm. The K training samples corresponding to the nonzero entries in the resulting vector are the support samples whose class labels reflect the label of the testing SAR target in some sense. The number of support samples is usually far less than the total number of samples.
2.2 Joint sparse representation classification
where c and are the class labels, is the recovery for Y with only the c th training samples involve in the reconstruction, and the operation δ c (∙) is redefined as preserving the rows corresponding to class c in the matrix X and setting all others to be zeroes. The Frobenius norm indicates that the decision is based on the total reconstruction error of multiple views. This whole classification algorithm is named as JSRC, and greedy algorithm can solve this problem in an approximate sense. Since greedy algorithm is one way to solve sparse representation without any transformation for the original sparse representation model, we call it ℓ0-norm model/minimization in this paper.
3 Improved joint sparse representation
In the JSR model, the common pattern is sought on the ℓ0-norm minimization model whose performance depends on a proper choice of parameter K. According to the ℓ0-norm minimization, the mixed-norm strategy is used to explore the common patterns in sparse representation coefficients of multiple SAR images. However, the proper K is hard to determine. Therefore, in this section, we propose an improved joint sparse representation model which firstly replaces ℓ0-norm minimization with ℓ1-norm minimization to avoid the parameter K selection problem and then adopts the low-rank matrix recovery strategy to seek the common patterns based on the characteristics of the ℓ1-norm minimization solutions.
3.1 Improved joint sparse representation model
As Section 2.2 says, greedy algorithm is one way to solve sparse representation in the approximate sense. Another way, which has strong theoretical foundations, is convex relaxation. Under the theoretical framework of convex relaxation, the ℓ0-norm in the original sparse representation model is replaced with the ℓ1-norm, and then the original model is converted as a convex quadratic programming problem. This solving strategy is called the ℓ1-norm minimization in this paper. Zhang et al. did not discuss the possibility to use convex relaxation in the JSR model . So, we firstly explore the potentiality of the ℓ1-norm minimization through an elaborate experiment.
This model can be solved by computing the sparse representation coefficient vectors one by one as well. However, there are another two problems for the ℓ1-norm minimization model. First, the solution using (5) usually contains more nonzero items. In ideal case, we expect a few nonzero items in because this can give us a clear position indication of support samples. Second, the sparse representation coefficients of each inputting image with close azimuth are obtained independently. Therefore, the combination between multiple-view images is lacking, which makes the solution lost the jointing meaning.
Apparently, the rank of the signal matrix rank(S) in the JSR matrix, the number of view J, and the proper sparse level K have close relations, which affects the recognition performance in some sense. With consideration of the computation cost, the number of views should be limited in a proper range. Generally, J is far less than the dimensionality of the inputting sparse representation coefficient vector. Therefore, the maximal rank of the signal matrix is definitely no more than the number of views. When rank(S) < K, the nonzero entries with the same indexes are not enough to reveal real support samples. The support samples in this case tend to be the linear combinations of K real support samples, which also can make the right recognition. When rank(S) = K, the low-rank matrix S is very likely to attain the K real support samples which contains explicit classification information. This is the best situation for recognition. When rank(S) > K, the low-rank matrix S fails to find the support samples. As a result, small coefficients tend to appear on nonsupport sample to meet the low-rank condition, while most sparse representation coefficients solved by (5) will remain in the signal matrix S. The reconstruction to the multiple-view SAR images may become worse than the reconstruction by ℓ1-norm solutions in (5) as small coefficients' influence. However, the recognition is still right for most cases due to the sparse representation coefficients via (5) almost concentrating on one class.
According to the above analysis, the IJSR model can be described as two stages. The first stage is seeking the ℓ1-norm solutions for multiple-view SAR images via (5). The second stage is combining the ℓ1-norm solutions from the first stage to recover a low-rank matrix which can indicate the common patterns through (7). Different from the JSR model, in the first stage, the ℓ1-norm minimization in the IJSR model avoids choosing a proper sparse level which is hard to predict. In addition, the solution for the ℓ1-norm minimization contains more discriminative information. In the second stage, discarding the mixed-norm strategy in JSR, the problem of finding the support samples is converted into a low-rank matrix recovery problem.
3.2 Improved joint sparse representation classification
Experimental database information
Depression angle (deg)
The database is firstly preprocessed as follows: The logarithm transformation is made to turn the multiplicative speckle to the additive noise. To reduce the disturbance from the background of SAR image, a 50 × 50 sub-image which mainly contains the SAR target is extracted in the center of the original SAR image. Then, PCA is used as the feature extraction algorithm for its convenience and effectiveness.
4.1 One important precondition
The support sample indexes of five samples with greatly different azimuths
Testing sample number
Support sample set indexes
50, 51, 53, 103, 166
59, 60, 114, 176, 177
28, 171, 198, 199, 200
38, 40, 87, 88, 150
44, 96, 158, 159, 160
The support sample indexes of five samples with close azimuths
Testing sample number
Support sample set indexes
28, 171, 198, 199, 200
27, 28, 139, 198, 199
29, 140, 142, 199, 200
29, 30, 140, 199, 201
30, 140, 199, 200, 201
The testing samples have greatly different azimuths in Table 2 and have close azimuths in Table 3. As shown in Table 3, five samples with close azimuths apparently have a more similar support sample set. For the samples with greatly different azimuths, the common support samples cannot be found as example in Table 2. It is obvious that the right recognition cannot be made if we adopt testing samples in Table 2. Therefore, we expect more samples with a closer azimuth interval in practice. Fortunately, in real case, one can capture more SAR images of one physical target in a much smaller azimuth interval. In this paper, all experiments are performed under the condition that multiple-view images have close azimuths.
4.2 Experimental results and discussions
An IJSR model for SAR target recognition under multiple views is proposed in this paper. In the IJSR model, the ℓ0-norm minimization is replaced by the ℓ1-norm minimization to solve the sparse representation of single-view SAR image, which can overcome the problem of choosing the proper sparse level and concentrates sparse representation coefficients in one class. Moreover, the low-rank matrix recovery strategy is proposed to seek the common support samples for SAR target recognition under multiple views. Experiments on the MSTAR database show that our algorithm outperforms JSRC and SRC in a low-dimensional feature space. With the increase of the number of view, the recognition rates of IJSRC increase faster and reach a higher point than those of JSRC and SRC. In conclusion, IJSRC generally outperforms JSRC and SRC.
This research was supported by the National Natural Science Foundation of China (61201271, 61301269), the Fundamental Research Funds for the Central Universities (ZYGX2013J019, ZYGX2013J017), and the Sichuan Science and Technology Support Program (cooperated with the Chinese Academy of Sciences) (2012JZ001).
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