A Variable Splitting Augmented Lagrangian Approach to Linear Spectral Unmixing

TL;DR

This paper introduces SISAL, a fast and effective linear hyperspectral unmixing method based on a variable splitting augmented Lagrangian approach, solving a nonconvex minimum volume simplex problem with soft constraints.

Contribution

The paper proposes a novel unmixing algorithm that replaces positivity constraints with soft constraints and employs augmented Lagrangian optimization for improved speed and scalability.

Findings

SISAL outperforms existing algorithms on simulated data.

The method efficiently handles large-scale hyperspectral unmixing problems.

SISAL achieves faster convergence with comparable or better accuracy.

Abstract

This paper presents a new linear hyperspectral unmixing method of the minimum volume class, termed \emph{simplex identification via split augmented Lagrangian} (SISAL). Following Craig's seminal ideas, hyperspectral linear unmixing amounts to finding the minimum volume simplex containing the hyperspectral vectors. This is a nonconvex optimization problem with convex constraints. In the proposed approach, the positivity constraints, forcing the spectral vectors to belong to the convex hull of the endmember signatures, are replaced by soft constraints. The obtained problem is solved by a sequence of augmented Lagrangian optimizations. The resulting algorithm is very fast and able so solve problems far beyond the reach of the current state-of-the art algorithms. The effectiveness of SISAL is illustrated with simulated data.