Simulation and analysis of compressed sensing technique as sampling and data compression and reconstruction of signals using convex programming

Abstract

The information management has been treated primarily under the Nyquist sampling theory, but it is important to introduce new theories that replace deficiencies of what we know as the classical theory of sampling. These deficiencies create difficulties in data acquisition; this is a problem when large volumes of information are handled, in addition to the higher costs in storage and processing. This article presents the results obtained from the compressed sensing simulation technique applied to two types of signals. The aim of this paper was to simulate a communication system involving the data recovery applying the compressed sensing technique, analyzing sampling rates reduction, measuring the efficiency of the process and the behavior of the technique. The recovery of the signal is made using convex programming and using l1 norm minimization for recover the signals in the time domain. We used the L1Magic toolbox, which is a set of Matlab® functions used to solve optimization problems in this case with the l1eqpd function. As a summary of the obtained results, we checked the efficiency of the compressed sensing technique, minimum average rates for sampling the constructed signals, and the best performance of the technique to recover soft signals compared to non-differentiable signals. Additionally, the recovery results of an audio signal with the compressed sensing technique, by varying the sampling rate and checking the audibility of the signal, are presented. This allowed the testing of this technique in a real scenario, finding a good opportunity for the transmission of audio signals in a more efficient way.