Random Acquisition in Compressive Sensing: A Comprehensive Overview

Introduction

Compressive sensing (Candès et al. 2006) is a highly efficient paradigm of signal sampling with a maximum volume of data rate by minimum sensory records. It is realized by using the sparse nature of the information contained signals wherein the fact that the informative events are not distributed uniformly but sparsely has been effectively used to sense the signal not based on the uniform pattern assumed in Nyquist sampling theorem but in a compressive manner that the signal is compressed at the level of sensing, and the sensors put out a minimum number of samples which are compressive measures of the signal given by few sensors instead of a big number of sensory data in uniform patter. Compressive sensing deploys the sparsity nature of information in sensing and reconstruction of the data from the compressively sensed ones. Different signals have different levels of sparsity as it is measurable (Khosravy et al. 2020a), and as the signal moves toward informative rather than having a random nature its sparsity increases. (Khosravy et al. 2020b) gives a simplified review to fundamental theory of compressive sensing and (Khosravy et al. 2020c) simply explains the recovery process of signal/image in compressive sensing. Besides the deterministic techniques in compressive sensing (Ramalho et al. 2020), a common approach to compressive sensing is random acquisition. To have a good comprehension of deterministic compressive sensing, we invite the reader to read the compressive sensing by chirp codes (Applebaum et al. 2009) from the tutorial presented by (Khosravy et al. 2020d) and its corresponding MATLAB tutorial in (Khosravy et al. 2020e). This article presents a comprehensive review of random acquisition techniques in compressive sensing.

Compressive sensing is already deployed in a broad range of applications ranging from power line communication (Picorone et al, 2020) to healthcare (Khosravy et al. 2020f, Cabral et al. 2019). Just in the case of health care, it has been applied to the electrocardiogram (Dias et al. 2020), neural signals (Resende et al. 2020), electroencephalogram (de Oliveira et al. 2020), etc. As well it has a great potential to be used for hydraulic data acquisition on IoT sensors (Gupta et al. 2019a, Gupta et al. 2019b), telecommunications (Asharif et al. 2013, Khosravy et al. 2010, 2020g), electrocardiogram processing (Dey et al. 2015a, Sedaaghi et al. 2003, Khosravi et al. 2004, Khosravy et al. 2020h), internet of things (IoT) (Dey et al. 2017), robotics (Li et al. 2018), acoustic OFDM (Khosravy et al. 2014), power quality analysis (Santos et al. 2019, Santos et al. 2020), image enhancement (Dey et al. 2015b, Khosravy et al. 2017a), data mining (Lan et al. 2018, Gutierrez et al. 2013, Gutierrez et al. 2014a,b), image adaptation (Khosravy et al. 2017b), agriculture vehicle health monitoring (Gupta et al. 2020a,b,c), communication in smart grids (Gupta D. et al, 2020a, Gupta D. et al, 2020b), etc.