A Novel Sharpening Approach for Superresolving Multiresolution Optical Images

This paper aims to provide a compact superresolution formulation specific for multispectral (MS) multiresolution optical data, i.e., images characterized by different scales across different spectral bands. The proposed method, named multiresolution sharpening approach (MuSA), relies on the solution of an optimization problem tailored to the properties of those images. The superresolution problem is formulated as the minimization of an objective function containing a data-fitting term that models the blurs and downsamplings of the different bands and a patch-based regularizer that promotes image self-similarity guided by the geometric details provided by the high-resolution bands. By exploiting the approximately low-rank property of the MS data, the ill-posedness of the inverse problem in hand is strongly reduced, thus sharply improving its conditioning. The state-of-the-art color block-matching and 3D filtering (C-BM3D) image denoiser is used as a patch-based regularizer by leveraging the “plug-and-play” framework: the denoiser is plugged into the iterations of the alternating direction method of multipliers. The main novelties of the proposed method are: 1) the introduction of an observation model tailored to the specific properties of (MS) multiresolution images and 2) the exploitation of the high-spatial-resolution bands to guide the grouping step in the color block-matching and 3D filtering (C-BM3D) denoiser, which constitutes a form of regularization learned from the high-resolution channels. The results obtained on the real and synthetic Sentinel 2 data sets give an evidence of the effectiveness of the proposed approach.