Robust minimum volume simplex analysis for hyperspectral unmixing

Most blind hyperspectral unmixing methods exploit convex geometry properties of hyperspectral data. The minimum volume simplex analysis (MVSA) is one of such methods which, as many others, estimates the minimum volume (MV) simplex where the measured vectors live. MVSA was conceived to circumvent the matrix factorization step often implemented by MV based algorithms and also to cope with outliers, which compromise the results produced by MV algorithms. Inspired by the recently proposed robust minimum volume estimation (RMVES) algorithm, we herein introduce the robust MVSA (RMVSA), which is a version of MVSA robust to noise. As in RMVES, the robustness is achieved by employing chance constraints, which control the volume of the resulting simplex. RMVSA differs, however, substantially from RMVES in the way optimization is carried out. The effectiveness of RVMSA is illustrated by comparing its performance in simulated data with the state-of-the-art.