Classification via Sparse Representation of Steerable Wavelet Frames on Grassmann Manifold: Application to Target Recognition in SAR Image

Automatic target recognition has been widely studied over the years, yet it is still an open problem. The main obstacle consists in extended operating conditions, e.g.., depression angle change, configuration variation, articulation, and occlusion. To deal with them, this paper proposes a new classification strategy. We develop a new representation model via the steerable wavelet frames. The proposed representation model is entirely viewed as an element on Grassmann manifolds. To achieve target classification, we embed Grassmann manifolds into an implicit reproducing Kernel Hilbert space (RKHS), where the kernel sparse learning can be applied. Specifically, the mappings of training sample in RKHS are concatenated to form an overcomplete dictionary. It is then used to encode the counterpart of query as a linear combination of its atoms. By designed Grassmann kernel function, it is capable to obtain the sparse representation, from which the inference can be reached. The novelty of this paper comes from: 1) the development of representation model by the set of directional components of Riesz transform; 2) the quantitative measure of similarity for proposed representation model by Grassmann metric; and 3) the generation of global kernel function by Grassmann kernel. Extensive comparative studies are performed to demonstrate the advantage of proposed strategy.