Informed Spatial Regularizations For Fast Fusion Of Astronomical Images

This paper introduces two informed spatial regularizations dedicated to multiband image fusion. The fusion process combines a multispectral image with high spatial resolution and a hyperspectral image with high spectral resolution, with the aim of recovering a full resolution data-cube. In this work, we propose two spatial regularizations that exploit the spatial information of the multispectral image. A weighted Sobolev regularization identifies the sharp structures locations to locally mitigate a smoothness-promoting Sobolev regularization. A dictionary-based regularization takes advantage of spatial redundancy to recover spatial textures using a dictionary learned on the multispectral image. The proposed regularizations are evaluated on realistic simulations of James Webb Space Telescope (JWST) observations of the Orion Bar and show a better reconstruction of sharp structures compared to a non-informed regularization. Since JWST is now in orbit, we expect to use this method on real data in the near future.