Demystifying compressive sensing

Abstract

The conventional Nyquist-Shannon sampling theorem has been fundamental to the acquisition of signals for decades, relating a uniform sampling rate to the bandwidth of a signal. However, many signals can be compressed after sampling, implying a high level of redundancy. The theory of compressive sensing/sampling (CS) presents a sampling framework based on the ‘rate of information’ of a signal and not the bandwidth, thereby minimising redundancy during sampling. This means that a signal can be recovered from far fewer samples than conventionally required.