Unified Unsupervised Unmixing With Sparse Noise Estimation for Linear and Multilinear Models

Multimodal images (MIs) can capture different modalities of a scene with multiple applications in medicine, remote sensing, food inspection, among others. Over a 2D domain, these images acquire spectral/morphological/temporal information of each spatial point. Unmixing methodologies can decompose this spatial and spectral/morphological/temporal information. In this letter, a unified framework is proposed for unsupervised unmixing, explicitly accounting for Gaussian and sparse noise. Our approach is novel in three key aspects: (i) addresses the general case of multimodal images, (ii) unifies linear and multilinear mixing models, and (iii) incorporates noise effects into the synthesis schemes. The proposed methodology relies on cyclic coordinate descent optimization (CCDO), constrained quadratic estimation, and L1-regularization. For the validation stage, two types of synthetic MIs were used with additive Gaussian and sparse noise terms. Additionally, the Urban dataset was employed for further validation to consider a real-world scenario. The results show that the proposed methodologies provide accurate reconstructions of the datasets, as well as the ground-truth abundance maps and end-members with low computational time.