On The Convergence of Linearized ADMM for Separable Reweighted Sparse Hyperspectral Unmixing

Keisuke Ozawa

Abstract: Reweighted sparse regularization is a popular technique in sparse hyperspectral unmixing (SHU). Alternating direction method of multipliers (ADMM) is used with local linearization to solve reweighted SHU models. Theoretical guarantee of its convergence is a fundamental issue, but is not clear owing to the nonconvex nature of reweighted sparsity. In this paper, the convergence of linearized ADMM for separable, reweighted SHU is analyzed. It is proved that the algorithm has a converging sequence toward a stationary point of SHU problems with separable concave penalties. Practical convergence behavior is also numerically examined and analytically characterized against two basic penalties: the log-sum penalty and the arctangent.