Blind Hyperspectral Inpainting Via John Ellipsoid

Hyperspectral inpainting (HI) is a signal processing technique for recovering the complete hyperspectral imaging data cube from its incompletely acquired version. Some benchmark methods either rely on big data or the plug-and-play learning strategy. In this paper, we introduce John ellipsoid (JE), a key topology in functional analysis, to design a blind HI algorithm. JE criterion holds strong endmember identifiability like the well known (non-convex) minimum-volume simplex criterion in hyperspectral remote sensing, but just requires solving a convex optimization problem bringing it an advantage in computational aspect. As revealed in recent literature, comparing to widely adopted simplex topology, JE is robust against both low purity of hyperspectral data and ill-conditioned endmember matrix. Such robustness does bring us advantage in HI performance, as illustrated by experimental results on benchmark dataset.