Hybrid tenso-vectorial compressive sensing for hyperspectral imaging

Abstract

Hyperspectral imaging has a wide range of applications relying on remote material identification, including astronomy, mineralogy, and agriculture; however, due to the large volume of data involved, the complexity and cost of hyperspectral imagers can be prohibitive. The exploitation of redundancies along the spatial and spectral dimensions of a hyperspectral image of a scene has created new paradigms that overcome 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. We propose a new variant of the recently proposed serial hybrid vectorial and tensorial compressive sensing (HCS-S) algorithm that, like its predecessor, is compatible with reallife devices both in terms of the acquisition and reconstruction requirements. The newly introduced approach is parallelizable, and we abbreviate it as HCS-P. Together, HCS-S and HCS-P comprise a generalized framework for hybrid tenso-vectorial compressive sensing, or HCS for short. We perform a detailed analysis that demonstrates the uniqueness of the signal reconstructed by both the original HCS-S and the proposed HCS-P algorithms. Last, we analyze the behavior of the HCS reconstruction algorithms in the presence of measurement noise, both theoretically and experimentally. IntroductionHyperspectral imaging refers to the process of using specialized sensors to collect image information across the electromagnetic (EM) spectrum, often beyond the visible wavelength range. As commonly understood, hyperspectral sensors sample the portion of the EM spectrum that extends from the visible part of the spectrum to near-infrared and beyond, in multiple narrow and continuous bands. A hyperspectral image (see Fig. 1) can be represented as a third-order or three-dimensional data cube, the face of which is a function of the spatial coordinates and the depth of which is a function of spectral bands. 1 The hyperspectral cube from Fig. 1 was acquired by JPL's Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) on August 20, 1992, when it was flown on a NASA ER-2 plane at an altitude of 20,000 m (65,000 feet) over Moffett Field, California. 2 Hyperspectral data provide a wealth of information about the scene being imaged; consequently, there is a wide range of remote sensing problems that rely on extracting the spectral signature of objects in the scene. These applications include environmental mapping, 3 global change research, 4 assessment of trafficability, 5 plant and material identification, 6 crop analysis, 7 astronomy and space surveillance, 8 mineralogy, 9 agriculture, 10 healthcare 11 and surveillance, 12 among others.The significant amount of data (three tensorial...