Hybrid vectorial and tensorial Compressive Sensing for hyperspectral imaging

Hyperspectral imaging has a wide range of applications; however, due to the high dimensionality of the data involved, the complexity and cost of hyperspectral imagers can be prohibitive. Exploiting redundancies along the spatial and spectral dimensions of a hyperspectral image of a scene has created new paradigms that do away with the limitations of traditional imaging systems. While Compressive Sensing (CS) approaches have been proposed and simulated with success on already acquired hyperspectral imagery, most of the existing work relies on the capability to simultaneously measure the spatial and spectral dimensions of the hyperspectral cube. Most real-life devices, however, are limited to sampling one or two dimensions at a time, which renders a significant portion of the existing work unfeasible. In this paper we propose a novel CS framework that is a hybrid between traditional vectorized approaches and recently proposed tensorial approaches, and that is compatible with real-life devices both in terms of the acquisition and reconstruction requirements.