Journal of Pattern Recognition Research

This paper describes a new application of kernel sparse detection technique for hyperspectral imagery (HSI) in conjunction with a sequential forward feature selection (SFFS) scheme that reduces the dimensionality to a tractable volume. The proposed approach, kernel sparse representation-based detection (KSD) algorithm, is essentially an extension of the sparsity-based detection (SD) algorithm to a high dimensional (possibly infinite) feature space via a certain nonlinear mapping function of the input data. The SD algorithm in this high dimensional feature space is easily formulated in terms of kernels that implicitly compute dot products in the feature space. The proposed algorithm relies on the observation that a hyperspectral signature can be sparsely represented by a nonlinear combination of a few training samples from a structured dictionary and a sparse vector whose nonzero entries corresponds to the weights of the selected training samples. The sparse vector is recovered by solving a sparsity constrained optimization problem, and can directly determine the class label of the sample. The proposed algorithm is applicable to both spectrally pure as well as mixed pixels. Experimental results show that the proposed algorithm outperforms the standard sparsity-based and other baseline HSI detection algorithms.