Inverse Problem Transform: Solving Hyperspectral Inpainting Via Deterministic Compressed Sensing

摘要

Hyperspectral inpainting (HI) is a challenging inverse problem for reconstructing the image from its incomplete acquisition. Unlike existing methods that solve HI directly, this paper explores a different line of attack by transforming HI into another inverse problem, i.e., decoding in hyperspectral compressed sensing (DHCS). Since HI and DHCS both aim to output the complete hyperspectral data, we can solve HI via DHCS, if we are given an effective DHCS method, and if the required input of such DHCS method can be computed from the observable but incomplete image (OII). Computing the required inputs of most DHCS methods is in general very difficult due to the involved randomness of spectrum projection, so the DHCS method considered here is a deterministic one recently developed for satellite remote sensing. The motivation is that though it is hard to recover the complete image from OII, we found that the input of this deterministic DHCS method can be easily computed from OII. This simple idea of inverse problem transform surprisingly yields completive HI performance.