Effective Spectral Unmixing via Robust Representation and Learning-based Sparsity

TL;DR

This paper introduces a robust spectral unmixing model that leverages learning-based sparsity and outlier-resistant representation to improve accuracy in hyperspectral image analysis.

Contribution

It proposes a novel hyperspectral unmixing approach combining $ ext{l}_{2,1}$-norm for outlier robustness and adaptive sparsity guided by learned mixed levels, with an efficient optimization algorithm.

Findings

Achieves more accurate unmixing results than state-of-the-art methods.

Provides effective guidance maps for hyperspectral unmixing.

Demonstrates robustness to outliers and varying mixed levels.

Abstract

Hyperspectral unmixing (HU) plays a fundamental role in a wide range of hyperspectral applications. It is still challenging due to the common presence of outlier channels and the large solution space. To address the above two issues, we propose a novel model by emphasizing both robust representation and learning-based sparsity. Specifically, we apply the $\ell_{2,1}$-norm to measure the representation error, preventing outlier channels from dominating our objective. In this way, the side effects of outlier channels are greatly relieved. Besides, we observe that the mixed level of each pixel varies over image grids. Based on this observation, we exploit a learning-based sparsity method to simultaneously learn the HU results and a sparse guidance map. Via this guidance map, the sparsity constraint in the $\ell_{p}\!\left(\!0\!<\! p\!\leq\!1\right)$-norm is adaptively imposed according to the learnt mixed level of each pixel. Compared with state-of-the-art methods, our model is better suited to the real situation, thus expected to achieve better HU results. The resulted objective is highly non-convex and non-smooth, and so it is hard to optimize. As a profound theoretical contribution, we propose an efficient algorithm to solve it. Meanwhile, the convergence proof and the computational complexity analysis are systematically provided. Extensive evaluations verify that our method is highly promising for the HU task---it achieves very accurate guidance maps and much better HU results compared with state-of-the-art methods.