Hyperspectral unmixing with spectral variability using a perturbed linear mixing model

TL;DR

This paper presents a new linear mixing model for hyperspectral unmixing that explicitly accounts for spectral variability, improving estimation accuracy on synthetic and real datasets.

Contribution

Introduces a perturbed linear mixing model that explicitly models spectral variability and an optimization algorithm for parameter estimation.

Findings

Outperforms state-of-the-art algorithms in modeling endmember variability.

Effectively estimates endmembers and their variability on synthetic data.

Demonstrates improved unmixing accuracy on real hyperspectral images.

Abstract

Given a mixed hyperspectral data set, linear unmixing aims at estimating the reference spectral signatures composing the data - referred to as endmembers - their abundance fractions and their number. In practice, the identified endmembers can vary spectrally within a given image and can thus be construed as variable instances of reference endmembers. Ignoring this variability induces estimation errors that are propagated into the unmixing procedure. To address this issue, endmember variability estimation consists of estimating the reference spectral signatures from which the estimated endmembers have been derived as well as their variability with respect to these references. This paper introduces a new linear mixing model that explicitly accounts for spatial and spectral endmember variabilities. The parameters of this model can be estimated using an optimization algorithm based on the alternating direction method of multipliers. The performance of the proposed unmixing method is evaluated on synthetic and real data. A comparison with state-of-the-art algorithms designed to model and estimate endmember variability allows the interest of the proposed unmixing solution to be appreciated.