Compressively Sensed Hyperspectral Image Recovery using Total Variation Minimisation by Approximation

Abstract

Compressive sensing (CS) theory states that any signal that is sparse in a known basis may be recovered from a small set of linear combinations of the signal. Capturing data a fraction of the size of the original signal may be beneficial when applied to hyperspectral imaging (HSI), an imaging technique that introduces spectral content in order to classify materials in a scene. Recently, total variation (TV) minimisation algorithms have achieved success in recovering images captured using CS. In this paper we present a novel implementation of the TV minimisation algorithm that includes a differentiable approximation of the TV norm. This new method compares favourably with other TV minimisation algorithms, and we show how it can be extended from monochromatic to hyperspectral CS image recovery.