Comparative Analysis of Sparse Signal Reconstruction Algorithms for Compressed Sensing

Compressed sensing (CS) is a rapidly growing field, attracting considerable attention in many areas from imaging to communication and control systems. This signal processing framework is based on the reconstruction of signals, which are sparse in some domain, from a very small data collection of linear projections of the signal. The solution to the underdetermined linear system, resulting from these data, allows us to estimate the original signal. Finding the solution is an optimization problem which is mainly based on the minimization of the l1-norm. For this purpose, fast algorithms have been developed, and the aim of this paper is to make a comparative analysis of some of these algorithms. Specifically, we study the performance of sparse reconstructions with five commonly used algorithms implemented in Matlab (CVX, L1magic, SPGL1, UnlocBoX and YALL1) in order to determine the viability of implementation of a large number of applications proposed in the last years using CS. The objective is to offer a reference analysis for algorithm selection in CS applications and also provide a methodology for algorithm analysis in sparse reconstruction. Consequently, in order to determine each algorithm’s effectiveness and being able to compare them in a standardized manner, three indicators are considered: execution time, percent error and CPU usage, being the first two indicators crucial to any application involving compressed sensing. In addition some general basic concepts on compressed sensing are included.