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Effective hyperspectral unmixing (HU) is essential to the estimation of the underlying materials’ signatures (endmember signatures) and their spatial distributions (abundance maps) from a given image (data) of a hyperspectral scene. Recently, investigating HU under the non-negligible endmember variability (EV) and outlier effects (OE) has drawn extensive attention. Some state-of-the-art works either consider EV or consider OE, but none of them considers both EV and OE simultaneously. In this paper, we propose a novel HU algorithm, referred to as the variability/outlier-insensitive multi-convex unmixing (VOIMU) algorithm, which is robust against both EV and OE. Considering two suitable regularizers, a nonconvex minimization problem is formulated for which the perturbed linear mixing model proposed by Thouvenin et al., is used for modeling EV, while OE is implicitly handled by applying a  $p$  quasi-norm to the data fitting with  $0 < p < 1$ . Then, we reformulate it into a multi-convex problem which is then solved by the block coordinate descent method, with convergence guarantee by casting it into the block successive upper bound minimization framework. The proposed VOIMU algorithm can yield a stationary-point solution with convergence guarantee, together with some intriguing information of potential outlier pixels though outliers are neither physically modeled in the above problem nor detected in the algorithm operation. Finally, we provide some simulation results and experimental results using real data to demonstrate the efficacy and practical applicability of the proposed VOIMU algorithm.

An Outlier-Insensitive Unmixing Algorithm With Spatially Varying Hyperspectral Signatures