# Sparse Representation-Based SAR Image Target Classification on the 10-Class MSTAR Data Set
## 1 Introduction  
Synthetic Aperture Radar (SAR), an active sensor, has been widely applied in many areas such as disaster assessment and military defense, due to its ability to work against 24 h a day and severe weather. With the high-resolution SAR coming to work, it is hard to carry on manual interpretation, thus making the Automatic Target Recognition (ATR) popular. ATR uses the signal processing techniques to recognize the unknown targets. Moreover, a typical ATR in SAR has three separate stages: detection, discrimination and classification [1]. Detection focuses on finding local Regions of Interest (ROI) which include targets and numerous false alarms. Then the following stage, discrimination, is to filter natural clutter out. Finally, the identities of targets are predicted and the man-made clutter is be rejected. The classification of unknown targets is discussed in this article. The SAR images contain coherent speckle noise, which lowers the images quality significantly, so it is very difficult to interpret them. Despite that, many works have been done in research SAR. Firstly, template matching-based algorithms are utilized to achieve classification [2]. The methodology usually defines \"distances\" between the test sample and the templates generated by the training set. Then the identity of the test sample will be assigned to the class to which the matched template selected by the \"distances\" belongs. So the addition of an object requires creating an additional set of templates, thus causing burdensome calculation. To improve the performance, a number of methods called correlation pattern recognition have been presented [3], and they accomplish the training of thefilter through minimizing the correlation between the filter and the spectral envelope of the training set in the frequency domain. Beyond that, a Learning Vector Quantization (LVQ) has been used for learning the templates for classification in [4]. Then, the nonlinear classifier is used for the SAR ATR, e.g., [5], and its performance is better than the conventional template-based approaches. All these algorithms reduce their complexity by applying a set of classifiers trained by the training samples over a given range of aspect angles, so the performances of the algorithms are limited by the accuracy of aspect angle estimate. Recently, a considerable resurgence of interest in the sparse representation of signals has been witnessed [6; 7; 8; 9; 10]. Much of its effectiveness is caused by the fact that signals can be well represented by a set of basis vectors in most cases. Given the basis vectors, finding the sparse representation of a signal is processed as an optimal problem. The optimal problem, called \(l_{0}\)-norm minimization, is known to be a NP-hard problem, which can be solved by the Greedy algorithm [11; 12] or the convex relaxation algorithm [13]. The Sparse Representation-based Classifications (SRC) are recommended firstly in [14], and then the framework is extensively utilized in many classifications [6; 7]. The framework is re-explained from the perspective of class manifolds in [1]; meanwhile, it is applied in the classification on three-class MSTAR targets. Then SRC on three-class MSTAR targets (BMP2, BTR70 and T72) is further studied in [8; 9; 10], which focuses on extracting effective features to improve the classification performance. Simultaneously, a better classification performance of SRC over SVM has been verified. It is noticeable that the MINACE filter and SVM are used in recognition of the three-class targets, respectively [3; 5]. Then, the two methods are extended to the recognition of the 10-class targets [15; 16]. Therefore, in this paper, SRC is extended to classify the 10 targets, which really is more challenging than three-class targets.