Hyperspectral Image Classification via Low-Rank and Sparse Representation with Spectral Consistency Constraint

In this letter, a low-rank and sparse representation classifier with a spectral consistency constraint (LRSRC-SCC) is proposed. Different from the SRC that represents samples individually, LRSRC-SCC reconstructs samples jointly and is able to capture the local and global structures simultaneously. In this proposed classifier, an adaptive spectral constraint is imposed on both the low-rank and sparse terms so as to better reveal the data structure and enhance its discriminative power. In addition, the alternating direction method is introduced to solve the underlying minimization problem, in which, more importantly, the subobjective function associated with the low-rank term is optimized based on the rank equivalence between a matrix and its Gram matrix, resulting in a closed-form solution. Finally, LRSRC-SCC is extended to LRSRC-SCCE for fully exploiting the spatial information. Experimental results on two hyperspectral data sets demonstrate that the proposed LRSRC-SCC and LRSRC-SCCE methods outperform some state-of-the-art methods.