Convex relaxation based sparse algorithm for hyperspectral target detection

Target detection in hyperspectral images is an important task. In this paper, we propose a sparsity based algorithm for target detection in hyperspectral images. In sparsity model, each hyperspectral pixel is represented by a linear combination of a few samples from an overcomplete dictionary, and the weighted vector for such reconstruction is sparse. This model has been applied in hyperspectral target detection and solved with several greedy algorithms. As conventional greedy algorithms may be trapped into a local optimum, we consider an alternative way to regularize the model and find a more accurate solution to the model. The proposed method is based on convex relaxation technique. The original sparse representation problem is regularized with a properly designed weighted ℓ₁ minimization and effectively solved with existing solver. The experiments on synthetic and real hyperspectral data suggest that the proposed algorithm outperforms the classical sparsity-based detection algorithms, such as Simultaneous Orthogonal Matching Pursuit (SOMP) and Simultaneous Subspace Pursuit (SSP) and conventional ℓ₁ minimization.