Joint sparsity for target detection

Abstract

In this paper, we propose a joint sparsity model for target detection in hyperspectral imagery. The key innovative idea here is that hyperspectral pixels within a small neighborhood in the test image can be simultaneously represented by a linear combination of a few common training samples, but weighted with a different set of coefficients for each pixel. The joint sparsity model automatically incorporates the inter-pixel correlation within the hyperspectral imagery by assuming that neighboring spectral pixels usually consists of similar materials. The sparse representations of the neighboring pixels are obtained by simultaneously decomposing the pixels over a given dictionary consisting of training samples of both the target and background classes. The recovered sparse coefficient vectors are then directly used for determining the label of the test pixels. Simulation results on several real hyperspectral images show that the proposed algorithm based on the joint sparsity model outperforms the classical hyperspectral target detection algorithms, such as the popular spectral matched filters, matched subspace detectors, adaptive subspace detectors, as well as binary classifiers such as support vector machines.