Robust Blind Linear Unmixing for Correlated Multimodal Images in Medical Applications

In this work, we introduce a new algorithm for robust blind linear unmixing focused in correlated multimodal images (CMI) with emphasis on medical applications. Our proposal is based on a linear model between end-members and abundances, and additive Gaussian and sparse noise components. The end-members represent spectral, time or morphological information, and their abundances denote their spatial contributions in the CMIs. Our formulation for blind linear umixing presents an iterative optimization scheme that uses a convex cost function, and jointly estimates end-members and their abundances, and a sparse noise component. The iterative methodology relies on cyclic coordinate descent optimization, constrained quadratic estimation and L1-regularization. In our evaluation, we consider synthetic datasets of biological tissue absorbance by hyperspectral imaging, and multi-spectral fluorescence life-time imaging. Our proposal was compared with five algorithms from the literature in linear unmixing, and it was able to provide the best compromise between estimation performance and complexity.