A new convex model for linear hyperspectral unmixing

Abstract

Over the past two decades, Minimum Simplex Volume-based (MV) methods for linear hyperspectral unmixing have attracted considerable academic attention due to their robustness in the absence of pure pixels. Within this framework, certain prevalent MV models incorporate a Log-Absolute-Determinant Function (LADF) that operates on a matrix variable Q. In practical applications, the LADF inherently exhibits non-convex characteristics, thus limiting its applicability in real-world scenarios. To address this challenge, this paper employs Tikhonov regularization, combined with a series of equivalent transformations, to construct a positively definite matrix, thereby rendering the corresponding LADF convex. Theoretical foundations linking the newly convexified LADF and the original non-convex function are rigorously established. Experimental validation, conducted on standard hyperspectral benchmark datasets, confirms its efficiency and necessity. Notably, this paper introduces a unified strategy for ensuring convexity in MV models for linear hyperspectral unmixing.