Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization

Endmember extraction is a process to identify the hidden pure source signals from the mixture. In the past decade, numerous algorithms have been proposed to perform this estimation. One commonly used assumption is the presence of pure pixels in the given image scene, which are detected to serve as endmembers. When such pixels are absent, the image is referred to as the highly mixed data, for which these algorithms at best can only return certain data points that are close to the real endmembers. To overcome this problem, we present a novel method without the pure-pixel assumption, referred to as the minimum volume constrained nonnegative matrix factorization (MVC-NMF), for unsupervised endmember extraction from highly mixed image lata. Two important facts are exploited: First, the spectral data are nonnegative; second, the simplex volume determined by the endmembers is the minimum among all possible simplexes that circumscribe the data scatter space. The proposed method takes advantage of the fast convergence of NMF schemes, and at the same time eliminates the pure-pixel assumption. The experimental results based on a set of synthetic mixtures and a real image scene demonstrate that the proposed method outperforms several other advanced endmember detection approaches.