Leuven, 3001 Leuven, Belgium\
    `ben.somers@ees.kuleuven.be` [^1]
bibliography:
- 'D:/Dropbox/strings\_all\_ref.bib'
- 'D:/Dropbox/all\_ref.bib'
title: A comparison of nonlinear mixing models for vegetated areas using simulated and real hyperspectral data
---

Introduction {#sec:introduction}
============

Spectral unmixing (SU) of hyperspectral images consists of extracting the spectral responses $\Vmat{1},\ldots,\Vmat{\nbmat}$ of the $\nbmat$ macroscopic materials (or *endmembers*) present in the imaged scene and, for each pixel $\Vpix{\nopix}$ of the image ($\nopix=1,\ldots,\nbpix$), estimating the corresponding proportions $\abond{1}{\nopix},\ldots,\abond{\nbmat}{\nopix}$ (or *abundances*) that represent the spatial distributions of these materials over the area of interest [@Bioucas2012jstars]. The first automated unmixing techniques have been proposed in the early 1990’s [@Keshava2002]. When no prior knowledge is available regarding the studied scene, SU can be usually decomposed into two successive steps. First, the endmembers are extracted from the image and, subsequently, the proportions of the materials are estimated in a so-called *inversion* step. A vast majority of the endmember extraction algorithms (EEA) and inversion techniques exploit some geometrical concepts that are intrinsically related to an assumption of a linear mixing process to explain the observed pixels. In other words, under this linear mixing model (LMM), each observed pixel of a given image is assumed to result from the linear combination of the $\nbmat$ 