Hyperspectral Super-Resolution: Exact Recovery In Polynomial Time

In hyperspectral remote sensing, the hyperspectral super-resolution (HSR) problem has recently received growing interest. Simply speaking, the problem is to recover a super-resolution image—which has high spectral and spatial resolutions—from some lower spectral and spatial resolution measurements. Many of the current HSR studies consider matrix factorization formulations, with an emphasis on algorithms and performance in practice. On the other hand, the question of whether a factorization model is equipped with provable recovery guarantees of the true super-resolution image is much less explored. In this paper we show that unique and exact recovery of the super-resolution image is not only possible, it can also be done in polynomial time. We employ the matrix factorization model commonly used in the context of hyperspectral unmixing, and show that if certain local sparsity conditions are satisfied then the matrix factors constituting the true super-resolution image can be recovered by a simple two-step procedure.