Robust endmember extraction using worst-case simplex volume maximization

Winter´s maximum-volume simplex approach is an efficient and representative endmember extraction approach, as evidenced by the fact that N-FINDR, one of the most widely used class of endmember extraction algorithms, employs simplex volume maximization as its criterion. In this work, we consider a robust generalization of Winter´s maximum-volume simplex criterion for the noisy scenario. Our development is based on an observation that the presence of noise would tend to expand the observed data cloud geometrically. The proposed robust Winter criterion is based on a max-min or worst-case approach, where we attempt to counteract the data cloud expansion effects by using a shrunk simplex volume as the metric to maximize. The proposed criterion is implemented by a combination of alternating optimization and projected subgradients. Some simulation results are presented to demonstrate the performance advantages of the proposed robust algorithm.