algorithms, is evaluated with respect to i) their ability of accurately describing the physical processes yielding the considered mixtures and ii) their ability of providing meaningful estimations of the abundance coefficients, to properly account for the spatial distribution of the materials over each observed pixel. More precisely, let $\hatVabond{\nopix}$ and $\hatVnabond{\nopix}$ denote the abundance and nonlinearity coefficient vectors estimated by the algorithms introduced in paragraph \[subsec:algorithm\]. First, the average square reconstruction error (RE) is measured as $$\label{eq:RE}
 \mathrm{RE} = \frac{1}{\nbband\nbpix} \sum_{\nopix=1}^{\nbpix} \left\|\Vpix{\nopix}-\hatVpix{\nopix}\right\|^2$$ where $\left\|\cdot\right\|$ stands for the usual Euclidean norm ($\left\|\bfx\right\| = \sqrt{\bfx^T\bfx}$). In the right-hand side of , $\Vpix{\nopix}$ ($\nopix=1,\ldots,\nbpix$) are the observed pixels whereas $\hatVpix{\nopix}$ are the corresponding estimates given by $$\hatVpix{\nopix} = \MATmat\hatVabond{\nopix} + \boldsymbol{\mu}\left(\MATmat,\hatVabond{\nopix},\hatVnabond{\nopix}\right)$$ where $\boldsymbol{\mu}\left(\cdot\right)$ is equal to $0$ for the LMM or stands for the additional nonlinear contribution for the nonlinear models (see Section \[sec:models\]).

Since the actual endmember spectra and abundance coefficients (that satisfy the constraints in ) are perfectly known for each pixel of the considered scenes, these REs can also be computed from pixels reconstructed following the LMM and FM with the actual values of the abundances. These two “oracle” models are denoted o-LMM and o-FM in what follows. In particular, 