Nonnegative matrix factorization with collaborativity for hyperspectral unmixing

Spectral unmixing is an important task for remotely sensed hyperspectral data exploitation. It expresses each (possibly mixed) pixel of the hyperspectral image as a combination of spectrally pure substances (called endmembers) weighted by their corresponding abundances. The spectral unmixing chain usually consists of three main steps: 1) estimation of the number of endmembers in a scene; 2) automatic identification of the spectral signatures of these endmembers; and 3) estimation of the endmember abundances in each pixel of the scene. Over the last years, several algorithms have been developed for each part of the chain. In this paper, we develop a new algorithm which can perform the three steps of the unmixing chain (at once) for hyperspectral images with significant amount of noise. The proposed algorithm, which does not require a previous subspace identification step to estimate the number of endmembers, starts with an overestimated number of endmember and then iteratively removes the less relevant endmember detected by a collaborative regularization prior. Our experimental results demonstrate that the proposed method exhibits very good performance when the number of endmember is not available a priori, a situation that is very common in practice.