A Convex Low-Rank Regularization Method for Hyperspectral Super-Resolution

Hyperspectral super-resolution (HSR) is a technique of recovering a super-resolution image from a hyperspectral image (which has low spatial but high spectral resolutions) and a multispectral image (which has high spatial but low spectral resolutions). The problem is an ill-posed inverse problem in general, and thus judiciously designed formulations and algorithms are needed for good HSR performance. In this work, we employ the idea of low rank modeling, which was proven effective in helping enhance performance of HSR. Unlike the extensively employed nonconvex structured matrix factorization-based methods, we propose to use a convex regularizer for promoting low rank. Both unconstrained and constrained formulations are considered: the unconstrained case is tackled by the proximal gradient (PG) algorithm; while the more physically sound but challenging constrained case is solved by a custom-designed PG like algorithm, which uses the ideas of smoothing and majorization-minimization. Simulations are employed to showcase the effectiveness of the proposed methods.