Collaborative representation for hyperspectral anomaly detection

In this paper, collaborative representation is proposed for anomaly detection in hyperspectral imagery. The algorithm is directly based on the concept that each pixel in background can be approximately represented by its spatial neighborhoods, while anomalies cannot. The representation is assumed to be the linear combination of neighboring pixels, and the collaboration of representation is reinforced by ℓ₂-norm minimization of the representation weight vector. To adjust the contribution of each neighboring pixel, a distance-weighted regularization matrix is included in the optimization problem, which has a simple and closed-form solution. By imposing the sum-to-one constraint to the weight vector, the stability of the solution can be enhanced. The major advantage of the proposed algorithm is the capability of adaptively modeling the background even when anomalous pixels are involved. A kernel extension of the proposed approach is also studied. Experimental results indicate that our proposed detector may outperform the traditional detection methods such as the classic Reed-Xiaoli (RX) algorithm, the kernel RX algorithm, and the state-of-the-art robust principal component analysis based and sparse-representation-based anomaly detectors, with low computational cost.