Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A General Framework for Group Sparsity in Hyperspectral Unmixing Using Endmember Bundles

Gokul Bhusal, Yifei Lou, Cristina Garcia-Cardona, Ekaterina Merkurjev

TL;DR

The paper tackles hyperspectral unmixing under material spectral variability by introducing a bundle-based framework that enforces structured sparsity on an expanded abundance vector. It formalizes a general regularization $R_{\mathcal{G},p,f}$ and provides two concrete schemes: inter-group sparsity (Inter-Group) and sparsity within and across groups (SWAG), with transformed $\ell_1$ (TL1) as a novel, effective penalty. Through extensive experiments on synthetic and real datasets, the authors show that SWAG with TL1 (and TL1 variants) often yields the best abundance RMSE and competitive spectral performance, validating the framework's practicality. The approach offers a flexible, scalable HU method capable of integrating various sparsity-promoting penalties and endmember bundle constructions for robust material variability handling.

Abstract

Due to low spatial resolution, hyperspectral data often consists of mixtures of contributions from multiple materials. This limitation motivates the task of hyperspectral unmixing (HU), a fundamental problem in hyperspectral imaging. HU aims to identify the spectral signatures (\textit{endmembers}) of the materials present in an observed scene, along with their relative proportions (\textit{fractional abundance}) in each pixel. A major challenge lies in the class variability in materials, which hinders accurate representation by a single spectral signature, as assumed in the conventional linear mixing model. Moreover, To address this issue, we propose using group sparsity after representing each material with a set of spectral signatures, known as endmember bundles, where each group corresponds to a specific material. In particular, we develop a bundle-based framework that can enforce either inter-group sparsity or sparsity within and across groups (SWAG) on the abundance coefficients. Furthermore, our framework offers the flexibility to incorporate a variety of sparsity-promoting penalties, among which the transformed $\ell_1$ (TL1) penalty is a novel regularization in the HU literature. Extensive experiments conducted on both synthetic and real hyperspectral data demonstrate the effectiveness and superiority of the proposed approaches.

A General Framework for Group Sparsity in Hyperspectral Unmixing Using Endmember Bundles

TL;DR

The paper tackles hyperspectral unmixing under material spectral variability by introducing a bundle-based framework that enforces structured sparsity on an expanded abundance vector. It formalizes a general regularization and provides two concrete schemes: inter-group sparsity (Inter-Group) and sparsity within and across groups (SWAG), with transformed (TL1) as a novel, effective penalty. Through extensive experiments on synthetic and real datasets, the authors show that SWAG with TL1 (and TL1 variants) often yields the best abundance RMSE and competitive spectral performance, validating the framework's practicality. The approach offers a flexible, scalable HU method capable of integrating various sparsity-promoting penalties and endmember bundle constructions for robust material variability handling.

Abstract

Due to low spatial resolution, hyperspectral data often consists of mixtures of contributions from multiple materials. This limitation motivates the task of hyperspectral unmixing (HU), a fundamental problem in hyperspectral imaging. HU aims to identify the spectral signatures (\textit{endmembers}) of the materials present in an observed scene, along with their relative proportions (\textit{fractional abundance}) in each pixel. A major challenge lies in the class variability in materials, which hinders accurate representation by a single spectral signature, as assumed in the conventional linear mixing model. Moreover, To address this issue, we propose using group sparsity after representing each material with a set of spectral signatures, known as endmember bundles, where each group corresponds to a specific material. In particular, we develop a bundle-based framework that can enforce either inter-group sparsity or sparsity within and across groups (SWAG) on the abundance coefficients. Furthermore, our framework offers the flexibility to incorporate a variety of sparsity-promoting penalties, among which the transformed (TL1) penalty is a novel regularization in the HU literature. Extensive experiments conducted on both synthetic and real hyperspectral data demonstrate the effectiveness and superiority of the proposed approaches.

Paper Structure

This paper contains 19 sections, 45 equations, 4 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Bundle-Based Linear Mixing Model
  4. Group Sparsity
  5. Proposed Abundance Estimation Methods
  6. Inter-Group Sparsity for Endmember Bundles
  7. SWAG for Endmember Bundles
  8. EXPERIMENTS AND RESULTS
  9. Comparison and Proposed Methods
  10. Bundle Construction
  11. Synthetic Data
  12. Real Data
  13. Samson Data
  14. Jasper Ridge
  15. Houston Dataset
  16. ...and 4 more sections

Figures (4)

  • Figure 1: Abundance maps estimated by the competing methods on the synthetic data with the ground truth (top row).
  • Figure 2: Abundance maps estimated by the competing methods on the Samson dataset with the ground truth (top row).
  • Figure 3: Abundance maps estimated by the competing methods on the Jasper Ridge data with the ground truth (top row).
  • Figure 4: Abundance maps estimated by the competing methods on the Houston data.