A Dual Symmetric Gauss-Seidel Alternating Direction Method of Multipliers for Hyperspectral Sparse Unmixing

TL;DR

This paper introduces a novel dual symmetric Gauss-Seidel ADMM algorithm for hyperspectral sparse unmixing with TV regularization, improving efficiency and image quality while providing convergence analysis.

Contribution

The paper proposes a new convergent dual sGS-ADMM algorithm specifically designed for hyperspectral unmixing with TV regularization, with proven convergence and improved performance.

Findings

Enhanced unmixing efficiency compared to existing methods

Higher quality hyperspectral images obtained

Proven global convergence and local linear convergence rate

Abstract

Since sparse unmixing has emerged as a promising approach to hyperspectral unmixing, some spatial-contextual information in the hyperspectral images has been exploited to improve the performance of the unmixing recently. The total variation (TV) has been widely used to promote the spatial homogeneity as well as the smoothness between adjacent pixels. However, the computation task for hyperspectral sparse unmixing with a TV regularization term is heavy. Besides, the convergence of the primal alternating direction method of multipliers (ADMM) for the hyperspectral sparse unmixing with a TV regularization term has not been explained in details. In this paper, we design an efficient and convergent dual symmetric Gauss-Seidel ADMM (sGS-ADMM) for hyperspectral sparse unmixing with a TV regularization term. We also present the global convergence and local linear convergence rate analysis for this algorithm. As demonstrated in numerical experiments, our algorithm can obviously improve the efficiency of the unmixing compared with the state-of-the-art algorithm. More importantly, we can obtain images with higher quality.