A graph Laplacian regularization for hyperspectral data unmixing

TL;DR

This paper presents a novel graph Laplacian regularization method for hyperspectral unmixing that leverages spectral and spatial similarities between pixels to improve abundance estimation, solved efficiently with ADMM and graph-cut techniques.

Contribution

Introduces a graph Laplacian regularization framework for hyperspectral unmixing that enhances smoothness and collaboration in abundance maps, with computational efficiency improvements.

Findings

Outperforms classical regularizations in synthetic data experiments

Effective in promoting smoothness and collaboration in abundance maps

Reduces computational complexity with graph-cut methods

Abstract

This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph represents a pixel's spectrum, and edges connect spectrally and spatially similar pixels. The proposed graph framework promotes smoothness in the estimated abundance maps and collaborative estimation between homogeneous areas of the image. The resulting convex optimization problem is solved using the Alternating Direction Method of Multipliers (ADMM). A special attention is given to the computational complexity of the algorithm, and Graph-cut methods are proposed in order to reduce the computational burden. Finally, simulations conducted on synthetic data illustrate the effectiveness of the graph Laplacian regularization with respect to other classical regularizations for hyperspectral unmixing.