Hyperspectral Target Detection Based on a Spatially Regularized Sparse Representation

Sparse representation (SR) is an effective method for target detection in hyperspectral imagery (HSI). The structured dictionary is arranged according to the target class and the background class, the sparse coefficients associated with each dictionary element of a given test sample can be recovered by solving an $\ell_{1}$-norm minimization problem. It is possible to introduce further regularization to improve the detection performance. The classical SR detection algorithms does not consider the spatial information of the detected pixels. It can be expected that sparse coefficients of adjacent pixels are similar due to the spatial correlation. This paper proposes a novel SR model which takes into account a spatial regularization term to promote the piecewise continuity of the sparse vectors. The formulated problem is solved via alternating direction method of multipliers (ADMM). We illustrate the enhanced performance of the proposed algorithm via both synthetic and real hyperspectral data.