  In this paper, we address the issue of hyperspectral pan-sharpening, which
consists in fusing a (low spatial resolution) hyperspectral image HX and a
(high spatial resolution) panchromatic image P to obtain a high spatial
resolution hyperspectral image. The problem is addressed under a variational
convex constrained formulation. The objective favors high resolution spectral
bands with level lines parallel to those of the panchromatic image. This term
is balanced with a total variation term as regularizer. Fit-to-P data and
fit-to-HX data constraints are effectively considered as mathematical
constraints, which depend on the statistics of the data noise measurements. The
developed Alternating Direction Method of Multipliers (ADMM) optimization
scheme enables us to solve this problem efficiently despite the non
differentiabilities and the huge number of unknowns.
