A hierarchical approach to superresolution of multispectral images with different spatial resolutions

In this paper, we focus the attention on the superresolution of multispectral (MS) multiresolution images (e.g., Sentinel 2, Aster, MODIS). By taking advantage of the high spatial resolution bands, we minimize an objective function containing a quadratic data fitting term, an edge preserving regularizer, and a patch-based plug-and play prior promoting self-similar images. To cope with the ill-posedness of the problem we i) exploit the fact that the images are approximately low-rank, and ii) propose a hierarchical method which sharpens in the first place the medium resolution bands and then the coarse resolution ones. The optimization is solved with the alternating direction method of multipliers (ADMM), yielding a fast, flexible, and effective solver, named Superresolution MUltiband multireSolution Hierarchical approach (SMUSH). Quantitative and qualitative results obtained on simulated and real Sentinel 2 (S2) images show the SMUSH effectiveness.