A new convex model for linear hyperspectral unmixing
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 Funct...
Saved in:
Published in | Journal of computational and applied mathematics Vol. 441; p. 115708 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
15.05.2024
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | 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. |
---|---|
ISSN: | 0377-0427 1879-1778 |
DOI: | 10.1016/j.cam.2023.115708 |