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Mathematical Problems in Engineering
Volume 2016, Article ID 7616393, 16 pages
http://dx.doi.org/10.1155/2016/7616393
Review Article

Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

1Faculty of Electrical Engineering, University of Montenegro, Džordža Vašingtona bb, 81000 Podgorica, Montenegro
2Faculty of Electrical Engineering, Mechanical Engineering & Naval Architecture, University of Split, Split, Croatia
3Grenoble Institute of Technology, GIPSA-Lab, Saint-Martin-d’Hères, France
4School of Information Science and Engineering, Hangzhou Normal University, Zhejiang, China

Received 26 March 2016; Revised 23 July 2016; Accepted 2 August 2016

Academic Editor: Francesco Franco

Copyright © 2016 Irena Orović et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Compressive sensing has emerged as an area that opens new perspectives in signal acquisition and processing. It appears as an alternative to the traditional sampling theory, endeavoring to reduce the required number of samples for successful signal reconstruction. In practice, compressive sensing aims to provide saving in sensing resources, transmission, and storage capacities and to facilitate signal processing in the circumstances when certain data are unavailable. To that end, compressive sensing relies on the mathematical algorithms solving the problem of data reconstruction from a greatly reduced number of measurements by exploring the properties of sparsity and incoherence. Therefore, this concept includes the optimization procedures aiming to provide the sparsest solution in a suitable representation domain. This work, therefore, offers a survey of the compressive sensing idea and prerequisites, together with the commonly used reconstruction methods. Moreover, the compressive sensing problem formulation is considered in signal processing applications assuming some of the commonly used transformation domains, namely, the Fourier transform domain, the polynomial Fourier transform domain, Hermite transform domain, and combined time-frequency domain.