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

2025-05-20

AI Summary

Hyperspectral images suffer from low spatial resolution, leading to mixed pixels and significant intra-class spectral variability—challenging conventional single-endmember linear unmixing models. To address this, we propose a bundle-based unmixing framework incorporating endmember bundles and introducing the first group-wise sparse (within-group and across-group, SWAG) regularization for hyperspectral unmixing. We design a novel truncated ℓ₁ (TL1) norm as a regularizer to jointly model endmember bundle representation and group sparsity. The resulting optimization problem is efficiently solved via the alternating direction method of multipliers (ADMM). Extensive experiments on synthetic and real-world datasets demonstrate that our method significantly outperforms state-of-the-art linear and nonlinear unmixing approaches in both endmember identification and abundance estimation accuracy, while exhibiting strong robustness to spectral variability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Mixture of Experts (MoE)
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

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 ( extit{endmembers}) of the materials present in an observed scene, along with their relative proportions ( extit{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.

Problem

• Addressing material variability in hyperspectral unmixing
• Proposing group sparsity with endmember bundles for HU
• Enhancing accuracy using flexible sparsity-promoting penalties

Innovation

• Uses endmember bundles for material representation
• Enforces group sparsity on abundance coefficients
• Incorporates transformed L1 penalty for regularization