Blind non-linear spectral unmixing with spatial coherence for hyper and multispectral images

Multi and hyperspectral images have become invaluable sources of information, revolutionizing various fields such as remote sensing, environmental monitoring, agriculture and medicine. In this expansive domain, the multi-linear mixing model (MMM) is a versatile tool to analyze spatial and spectral domains by effectively bridging the gap between linear and non-linear interactions of light and matter. This paper introduces an upgraded methodology that integrates the versatility of MMM in non-linear spectral unmixing, while leveraging spatial coherence (SC) enhancement through total variation theory to mitigate noise effects in the abundance maps. Referred to as non-linear extended blind end-member and abundance extraction with SC (NEBEAE-SC), the proposed methodology relies on constrained quadratic optimization, cyclic coordinate descent algorithm, and the split Bregman formulation. The validation of NEBEAE-SC involved rigorous testing on various hyperspectral datasets, including a synthetic image, remote sensing scenarios, and two biomedical applications. Specifically, our biomedical applications are focused on classification tasks, the first addressing hyperspectral images of in-vivo brain tissue, and the second involving multispectral images of ex-vivo human placenta. Our results demonstrate an improvement in the abundance estimation by NEBEAE-SC compared to similar algorithms in the state-of-the-art by offering a robust tool for non-linear spectral unmixing in diverse application domains.