Successive Nonnegative Projection Algorithm for Linear Quadratic Mixtures

TL;DR

This paper introduces SNPALQ, an algorithm extending SNPA to handle Linear-Quadratic hyperspectral unmixing by explicitly modeling nonlinear interactions, leading to improved separation quality in realistic experiments.

Contribution

It develops a novel extension of SNPA for LQ models, explicitly modeling nonlinear terms to enhance unmixing accuracy.

Findings

Improved unmixing performance in LQ hyperspectral models

Explicit modeling of nonlinear terms enhances separation quality

Validated effectiveness through realistic numerical experiments

Abstract

In this work, we tackle the problem of hyperspectral (HS) unmixing by departing from the usual linear model and focusing on a Linear-Quadratic (LQ) one. The proposed algorithm, referred to as Successive Nonnegative Projection Algorithm for Linear Quadratic mixtures (SNPALQ), extends the Successive Nonnegative Projection Algorithm (SNPA), designed to address the unmixing problem under a linear model. By explicitly modeling the product terms inherent to the LQ model along the iterations of the SNPA scheme, the nonlinear contributions in the mixing are mitigated, thus improving the separation quality. The approach is shown to be relevant in a realistic numerical experiment.