An NMF-Based Method For Hyperspectral Unmixing Using A Structured Additively-Tuned Linear Mixing Model To Address Spectral Variability

Remote sensing hyperspectral sensors are often limited in their spatial resolutions, which results in mixed pixels. The mixture is, usually, assumed to be linear and linear spectral unmixing techniques are employed to unmix observed pixel spectra. Most of these techniques consider that each endmember is represented by the same spectrum in the whole image. Nevertheless, in various situations, each endmember needs to be represented by slightly different spectra in all observed pixels. This spectral variability phenomenon must be tackled by introducing the concept of classes of endmembers. In this paper, a structured additively-tuned linear mixing model, without physical considerations, is first introduced to address this phenomenon. Then, an algorithm, based on nonnegative matrix factorization, is proposed for unmixing the considered data. This algorithm, which minimizes a cost function by using multiplicative update rules supplemented by additional constraints, derives, for each class of endmembers, slightly different estimated spectra in all pixels. The designed update rules are obtained by considering the structured variables introduced in the used mixing model. To assess the performance of the designed algorithm, experiments, based on realistic synthetic data, are conducted and obtained results are compared to those of approaches from the literature. This comparison shows that the proposed approach outperforms all other tested methods.

1. Introduction

Remote sensing hyperspectral sensors have a high spectral resolution, which allows an accurate classification of materials present in an imaged scene. However, their spatial resolutions are limited. This leads to the presence of mixed pixels. Usually, the mixture is assumed to be linear [1], and linear spectral unmixing (LSU) techniques (related to the blind source separation (BSS) problem [2], [3]) are used to estimate a collection of purematerial spectra (called endmembers) and their associated proportions (called abundance fractions).