© 1980-2012 IEEE. Recently, the Sentinel-2 (S2) satellite constellation was deployed for mapping and monitoring the Earth environment. Images acquired by the sensors mounted on the S2 platforms have three levels of spatial resolution: 10, 20, and 60 m. In many remote sensing applications, the availability of images at the highest spatial resolution (i.e., 10 m for S2) is often desirable. This can be achieved by generating a synthetic high-resolution image through data fusion. To this end, researchers have proposed techniques exploiting the spectral/spatial correlation inherent in multispectral data to sharpen the lower resolution S2 bands to 10 m. In this paper, we propose a novel method that formulates the sharpening process as a solution to an inverse problem. We develop a cyclic descent algorithm called S2Sharp and an associated tuning parameter selection algorithm based on generalized cross validation and Bayesian optimization. The tuning parameter selection method is evaluated on a simulated data set. The effectiveness of S2Sharp is assessed experimentally by comparisons to state-of-the-art methods using both simulated and real data sets.