Minimum endmember-wise distance constrained Nonnegative Matrix Factorization for Spectral Mixture Analysis of hyperspectral images

Nonnegative Matrix Factorization (NMF) and its extensions have gained lots of attentions in Spectral Mixture Analysis (SMA) since they can handle highly mixed hyperspectral pixels in an unsupervised way. In order to overcome the non-uniqueness problem in NMF, a minimum endmember-wise distance constraint (MewDC), which optimizes endmember spectra as compact as possible, is imposed for satisfying unmixing results. The proposed constraint works similar to minimum volume constraint (MVC). However, the dimension reduction step and numerical instability problems in MVC can be avoided. As a result, a minimum endmember-wise distance constrained NMF (MewDC-NMF) algorithm is proposed to extract endmembers and estimate their corresponding fractional abundance simultaneously. Both synthetic and real hyperspectral data experiments have demonstrate the effectiveness of the proposed MewDC-NMF algorithm.