## 4 Discussion  
From the results presented in Section 3, we can identify several limitations of this work.  
First, analysis of the errors based on type of surface (material, land cover, vegetation status, etc.) should be carried out in order to assess the impact on different applications. Although the spatial sampling of the data for this study contained enough variability for the results to be general, particular surfaces with specificities may need special attention. Furthermore, selecting the appropriate samples in the areas of most interest for particular applications can allow fine-tuning of the regression algorithm and improve the performance of the estimations.  
Figure 13: Scatterplots for the double-band regression of the SWIR bands in L1C (**top**) and L2A (**bottom**). The colors indicate the increasing density of points.  
A second limitation is related to the choice of regression algorithm for the study. The goal of the work was not to propose an optimal regression algorithm, but rather to show that band reconstruction is possible using regression. The choice of the neural network with a negative log-likelihood as a loss function was made for simplicity of implementation, the possibility of performing multi-target regression, and the generation of uncertainties associated with the estimations. Other approaches could yield better results and even produce a different set of bands candidate for removal.  
All of the above suggests that replication of the study by other teams would be useful. For this purpose, the dataset has been published [25], and the source code is available for inspection and download ([[https://src.koda.cnrs.fr/mmdc/mmdc-legacy/-/blob/master/mmdc/spectral_regression.py](https://src.koda.cnrs.fr/mmdc/mmdc-legacy/-/blob/master/mmdc/spectral_regression.py)]([https://src.koda.cnrs.fr/mmdc/mmdc-legacy/-/blob/master/mmdc/spectral_regression.py](https://src.koda.cnrs.fr/mmdc/mmdc-legacy/-/blob/master/mmdc/spectral_regression.py)), accessed on 10 May 2022).  
A third limitation is the pixel-based approach taken here. Reconstructing a missing band from the reflectances of the other bands of the same pixel assumes unicity of the solution: one combination of observed bands can only correspond to one value of the missing band. Although the results of this study tend to show that this is the case, there are pixels for which the error is high. In the current setting, the regression algorithm is able to flag these pixels by reporting high uncertainty, but this is not fully satisfactory. One way of lifting the ambiguity would be to add some spatial context for the regression, so that the observations of neighboring pixels, and therefore the local texture, helps the prediction. This could be implemented with spatial convolutional layers in the regression algorithm.  
In the same way, a multi-temporal extension of the algorithm could improve the estimations. However, this extension is less straightforward than adding spatial context, since clouds and cloud shadows introduce irregular temporal sampling that should be taken into account. Further, the relative geometric accuracy of multi-temporal series should be taken into account in this case.