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A Generalized Multiscale Bundle-Based Hyperspectral Sparse Unmixing Algorithm

Luciano Carvalho Ayres, Ricardo Augusto Borsoi, José Carlos Moreira Bermudez, Sérgio José Melo de Almeida

TL;DR

The paper tackles hyperspectral sparse unmixing under endmember variability by leveraging structured spectral bundles and a generalized multiscale spatial regularization framework that supports mixed-norm penalties to enforce inter- and intra-class sparsity. It introduces GMBUA, which combines a multiscale (superpixel) transform with a reformulated objective that enables efficient optimization for arbitrary sparsity penalties, and a graph-based centrality method to select a representative abundance map across multiple library extractions, improving reproducibility. Empirical results on synthetic data and the Cuprite dataset show that GMBUA achieves higher robustness and more reproducible abundance estimates than state-of-the-art methods, with competitive reconstruction quality and reasonable computational cost. The approach advances practical sparse unmixing by (i) handling spectral variability through structured libraries, (ii) enabling flexible regularization with mixed norms, and (iii) ensuring reproducibility via a centrality-based selection of the most representative solution.

Abstract

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational complexity, and the solutions are very noise-sensitive. We generalize a multiscale spatial regularization approach to solve the unmixing problem by incorporating group sparsity-inducing mixed norms. Then, we propose a noise-robust method that can take advantage of the bundle structure to deal with endmember variability while ensuring inter- and intra-class sparsity in abundance estimation with reasonable computational cost. We also present a general heuristic to select the \emph{most representative} abundance estimation over multiple runs of the unmixing process, yielding a solution that is robust and highly reproducible. Experiments illustrate the robustness and consistency of the results when compared to related methods.

A Generalized Multiscale Bundle-Based Hyperspectral Sparse Unmixing Algorithm

TL;DR

The paper tackles hyperspectral sparse unmixing under endmember variability by leveraging structured spectral bundles and a generalized multiscale spatial regularization framework that supports mixed-norm penalties to enforce inter- and intra-class sparsity. It introduces GMBUA, which combines a multiscale (superpixel) transform with a reformulated objective that enables efficient optimization for arbitrary sparsity penalties, and a graph-based centrality method to select a representative abundance map across multiple library extractions, improving reproducibility. Empirical results on synthetic data and the Cuprite dataset show that GMBUA achieves higher robustness and more reproducible abundance estimates than state-of-the-art methods, with competitive reconstruction quality and reasonable computational cost. The approach advances practical sparse unmixing by (i) handling spectral variability through structured libraries, (ii) enabling flexible regularization with mixed norms, and (iii) ensuring reproducibility via a centrality-based selection of the most representative solution.

Abstract

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational complexity, and the solutions are very noise-sensitive. We generalize a multiscale spatial regularization approach to solve the unmixing problem by incorporating group sparsity-inducing mixed norms. Then, we propose a noise-robust method that can take advantage of the bundle structure to deal with endmember variability while ensuring inter- and intra-class sparsity in abundance estimation with reasonable computational cost. We also present a general heuristic to select the \emph{most representative} abundance estimation over multiple runs of the unmixing process, yielding a solution that is robust and highly reproducible. Experiments illustrate the robustness and consistency of the results when compared to related methods.
Paper Structure (9 sections, 11 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 9 sections, 11 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Structured sparse spectral unmixing
  3. SU with structured EM libraries
  4. Mixed sparsity-promoting norms (penalties)
  5. Proposed method
  6. Multiscale approach for sparse and structured SU
  7. Selecting a consistent abundance estimate
  8. Experimental Results and Discussion
  9. Conclusions

Figures (3)

  • Figure 1: SRE($\,\hat{\!\mathbf{Z}}$) distribution for the synthetic data and all algorithms.
  • Figure 2: Estimated abundance maps for the synthetic dataset with an SNR of 20 dB. The sampled abundance maps are the ones corresponding to the median SRE($\,\hat{\!\mathbf{Z}}$) results for each algorithm.
  • Figure 3: Estimated abundance maps for a random execution of the SU algorithms on the Cuprite HSI (a reference map is shown on the left).