  When adopting a model-based formulation, solving inverse problems encountered
in multiband imaging requires to define spatial and spectral regularizations.
In most of the works of the literature, spectral information is extracted from
the observations directly to derive data-driven spectral priors. Conversely,
the choice of the spatial regularization often boils down to the use of
conventional penalizations (e.g., total variation) promoting expected features
of the reconstructed image (e.g., piecewise constant). In this work, we propose
a generic framework able to capitalize on an auxiliary acquisition of high
spatial resolution to derive tailored data-driven spatial regularizations. This
approach leverages on the ability of deep learning to extract high level
features. More precisely, the regularization is conceived as a deep generative
network able to encode spatial semantic features contained in this auxiliary
image of high spatial resolution. To illustrate the versatility of this
approach, it is instantiated to conduct two particular tasks, namely multiband
image fusion and multiband image inpainting. Experimental results obtained on
these two tasks demonstrate the benefit of this class of informed
regularizations when compared to more conventional ones.
