A Review on Fundamental Premises and Algorithmic Approaches in Compressive Sensing

Abstract

This paper addresses the classical approach of acquiring signals by following the well celebrated Shannon sampling theorem that underlies the majority devices of current technology, viz. analog-to-digital conversion, medical imaging, or audio and video electronics. In medical imaging, there are problems related to acquisition time and compression. Compressive sensing (CS) paradigm addresses the shortcomings of traditional data acquisition by sampling signals much more efficiently. CS is a novel kind of sampling theory, which suggests that the sparse signals can be reconstructed from what was formerly thought as insufficient information. CS has come into limelight in the near past years due to the fact that it utilizes the sparsity of signals; an inherent property of many natural signals. Sparsity enables us to store the signals in lesser samples and accurately recover it. This paper comprehensively discusses the mathematical and theoretical key concepts pertinent to the CS theory. At last the paper discusses the two distinct major algorithmic approaches for recovery in CS theory viz. the basis pursuit (BP) and the greedy algorithmic approach, each presenting different benefits and shortcomings.

Keywords: Compressive sensing (CS), sparsity, incoherence, restricted isometry property (RIP), â„“₁-minimization, basis pursuit (BP), greedy algorithms

Cite this Article

Mit Patel, Hardik Modi, Himanshu Patel. A Review on Fundamental Premises and Algorithmic Approaches in Compressive Sensing. Current Trends in Signal Processing. 2016; 6(1): 18–24p.