data are reported in Section \[sec:results\]. A comprehensive discussion on these results is conducted in Section \[sec:discussion\]. Section \[sec:conclusion\] concludes the paper.

Nonlinear mixing models {#sec:models}
=======================

Bilinear models {#subsec:bilinear}
---------------

To take into account the scattering effects the photons are subjected to before reaching the sensor, a wide class of nonlinear models are derived by defining the nonlinear component $\boldsymbol{\mu}\left(\MATmat,\Vabond{\nopix},\Vnabond{\nopix}\right)$ in as a sum of bilinear terms [@Altmann2011whispers] $$\boldsymbol{\mu}\left(\MATmat,\Vabond{\nopix},\Vnabond{\nopix}\right)
  \triangleq \sum_{i=1}^{R-1}\sum_{j=i+1}^{R} \nabond{i,j}{\nopix} \Vmat{i}\odot \Vmat{j}$$ where the operator $\odot$ stands for a termwise product $$\label{eq:term_BLMM}
  \Vmat{i}\odot \Vmat{j} \triangleq \left(
                                      \begin{array}{c}
                                        \mat{1}{i}\mat{1}{j} \\
                                        \vdots \\
                                        \mat{\nbband}{i}\mat{\nbband}{j} \\
                                      \end{array}
                                    \right).$$ The set of nonlinearity coefficients $\left\{\nabond{i,j}{\nopix}\right\}_{i,j}$ allows the amount of nonlinearity in the $p$th pixel to be adjusted between each pair of materials $\Vmat{i}$ and $\Vmat{j}$. Most of the various bilinear models of the literature mainly differ by the definition of these coefficients $\nabond{i,j}{\nopix}$ and the associated constraints they are subject to. The most common models, that will be evaluated in Section \[sec:results\], are recalled below.

In [@Somers2009] and [@Nascimento2009spie], the authors propose to include the nonlinearity coefficients $\left\{\nabond{i,j}{\nopix}\right\}_{i,j}$ within the set of constraints defined by the LMM, leading to $$\label{eq:FM}
  \Vpix{\nopix}^{(\textrm{NM})} \triangleq \sum_{\nomat=1}^{\nbmat} \abond{\nomat}{\nopix}
  \Vmat{\nomat} + \sum_{i=1}^{R-1}\sum_{j=i+1}^{R} \nabond{i,j}{\nopix} \Vmat{i}\odot \Vmat{j} + 