Mutual Incoherence and Relative Total Variation Regularizations for Blind Hyperspectral Unmixing

The unsupervised hyperspectral unmixing (HU) technique, also known as blind HU, directly decomposes the mixed pixels of a hyperspectral image (HSI) into a combination of endmembers weighted by their fractional abundances, without relying on a spectral library. To perform the blind HU, nonnegative matrix factorization (NMF) and its extensions have been widely used to improve the performance of the abundances, with sparse constraints and spatial information about the abundances. However, there are only a few works that exploit the prior information or constraints on the endmembers in the NMF-based methods for the blind HU. The linear mixing model (LMM) assumption assumes that the endmembers should be uncorrelated. Unfortunately, the spectra of HSI are highly correlated in practice, making it challenging to decompose the mixed spectra using only spatial information. Therefore, it is necessary to consider the proper constraints on the endmembers to obtain endmembers with higher accuracy from HSI. This article first introduces the mutual incoherence (MIC) regularization to promote incoherence between endmembers, that is, to minimize the correlation between the estimated endmembers. Then, the relative total variation (RTV) regularization is introduced on the abundances to exploit the spatial structure of the HSI. Finally, the MRNMF algorithm based on NMF is proposed for the HU task using multiplicative iteration rule. The experimental results on synthetic and real datasets show that the proposed MRNMF outperforms the state-of-the-art blind HU algorithms.