Hyperspectral Pan-sharpening: a Convex Formulation to Impose Parallel Level Lines

In this paper, we address the issue of hyperspectral pansharpening, 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 convex variational constrained formulation. The fit-to-P data term favors high resolution hyperspectral images with level lines parallel to those of the panchromatic image. This term is balanced with a total variation term as regularizer. The fit-to-HX data is a constraint such that depends on the statistics of the data noise measurements. The developed Alternate Direction Method of Multipliers (ADMM) optimization scheme enables us to solve this problem efficiently despite the non differentiabilities and the huge number of unknowns.