Hyperspectral Image Unmixing with Endmember Bundles and Group Sparsity Inducing Mixed Norms

TL;DR

This paper introduces a novel group sparsity-based method using mixed norms for hyperspectral image unmixing, effectively handling spectral variability and improving material identification accuracy.

Contribution

It proposes a new nonconvex penalty that enforces group and within-group sparsity in abundance estimation, compatible with sum-to-one constraints, enhancing unmixing performance.

Findings

Improved unmixing accuracy on simulated datasets

Enhanced material identification in real hyperspectral images

Significant performance gains over traditional bundle methods

Abstract

Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the observations are usually mixtures of the contributions of several materials. The spectral unmixing problem aims at recovering the spectra of the pure materials of the scene (endmembers), along with their proportions (abundances) in each pixel. In order to deal with the intra-class variability of the materials and the induced spectral variability of the endmembers, several spectra per material, constituting endmember bundles, can be considered. However, the usual abundance estimation techniques do not take advantage of the particular structure of these bundles, organized into groups of spectra. In this paper, we propose to use group sparsity by introducing mixed norms in the abundance estimation optimization problem. In particular, we propose a new penalty which simultaneously enforces group and within group sparsity, to the cost of being nonconvex. All the proposed penalties are compatible with the abundance sum-to-one constraint, which is not the case with traditional sparse regression. We show on simulated and real datasets that well chosen penalties can significantly improve the unmixing performance compared to the naive bundle approach.