A sparse reduced-rank regression approach for hyperspectral image unmixing

In this paper we propose a semi-supervised method for hyperspectral image unmixing. Given a set of endmembers present in the image, we assume that (a) each pixel is composed of a subset of the available endmembers and (b) adjacent pixels are, in all possibility, correlated. Then, we define an inverse problem, where the abundance matrix to be estimated is assumed to be simultaneously sparse and low-rank. These assumptions give rise to a regularized linear regression problem, where a mixed penalty is enforced, comprising the weighted ℓ₁ norm and an upper bound of the nuclear matrix norm. The resulting optimization problem is efficiently solved using a novel coordinate descend type unmixing algorithm. The estimation performance of the proposed scheme is illustrated in experiments conducted on both simulated and real data.