Technical Report: Band selection for nonlinear unmixing of hyperspectral images as a maximal clique problem

TL;DR

This paper introduces a novel band selection method for nonlinear hyperspectral unmixing in RKHS, formulated as a maximum clique problem, reducing computational complexity while maintaining accuracy.

Contribution

It presents a new centralized band selection approach based on the coherence criterion, linking it to the maximum clique problem for improved efficiency.

Findings

The method effectively reduces computational load in hyperspectral unmixing.

Simulation results demonstrate the approach's efficiency and accuracy.

The coherence threshold and kernel bandwidth are optimally selected using coherence bounds.

Abstract

Kernel-based nonlinear mixing models have been applied to unmix spectral information of hyperspectral images when the type of mixing occurring in the scene is too complex or unknown. Such methods, however, usually require the inversion of matrices of sizes equal to the number of spectral bands. Reducing the computational load of these methods remains a challenge in large scale applications. This paper proposes a centralized method for band selection (BS) in the reproducing kernel Hilbert space (RKHS). It is based upon the coherence criterion, which sets the largest value allowed for correlations between the basis kernel functions characterizing the unmixing model. We show that the proposed BS approach is equivalent to solving a maximum clique problem (MCP), that is, searching for the biggest complete subgraph in a graph. Furthermore, we devise a strategy for selecting the coherence threshold and the Gaussian kernel bandwidth using coherence bounds for linearly independent bases. Simulation results illustrate the efficiency of the proposed method.