An active-set algorithm for spectral unmixing

TL;DR

This paper introduces a specialized active-set algorithm for spectral unmixing that improves computational efficiency by leveraging problem-specific features and extends constraints to include minimum abundance levels.

Contribution

A novel active-set algorithm tailored for spectral unmixing that enhances performance and incorporates broader minimum abundance constraints.

Findings

Improved computational efficiency over generic solvers.

Effectiveness demonstrated on spectral unmixing problems.

Extended constraints to include minimum abundance levels.

Abstract

Linear spectral unmixing under nonnegativity and sum-to-one constraints is a convex optimization problem for which many algorithms were proposed. In practice, especially for supervised unmixing (i.e., with a large dictionary), solutions tend to be sparse due to the nonnegativity of the abundances, thereby motivating the use of an active-set solver. Given the problem specific features, it seems advantageous to design a dedicated algorithm in order to gain computational performance compared to generic solvers. In this paper, we propose to derive such a specific algorithm, while extending the nonnegativity constraints to broader minimum abundance constraints.