the RE associated with the o-LMM provides interesting information regarding the actual level of nonlinearities in the considered pixels. Note also that such oracle performance can not be computed for the other nonlinear models, since NM is based on a different abundance definition (e.g., they do not follow the constraints ) and GBM and PPNM require the prior knowledge of additional (unknown) parameters.

Moreover, to visualize the reconstruction error as a function of the wavelength, a signed error, defined as the mean reconstruction difference in the $\ell$th band, is also computed as $$\mathrm{RD}_{\ell} = \frac{1}{\nbpix} \sum_{\nopix=1}^{\nbpix}
 \left(\pix{\ell}{\nopix}-\hatpix{\ell}{\nopix}\right).$$ Finally, to measure the accuracy of the abundance estimation, the mean square errors (MSE) between the actual abundance vectors $\Vabond{\nopix}$ and the corresponding estimated $\hatVabond{\nopix}$ ($\nopix=1,\dots,\nbpix$) are computed as follows $$\mathrm{MSE} = \frac{1}{\nbmat\nbpix} \sum_{\nopix=1}^{\nbpix} \left\|\Vabond{\nopix}-\hatVabond{\nopix}\right\|^2.$$

\[sec:results\]

Simulated dataset
-----------------

### Virtual orchard {#subsubsec:results_orchard}

The unmixing results for the simulated orchard scenes are shown in Table \[tab:synth\_orchard\_RMSE\] in terms of MSE and RE. From these results, for both two- and three-endmembers, one can conclude that NM and LMM perform similarly in term of RE, while PPNM and FM provide the best results and, in particular, significantly better than LMM. It is interesting to note 