## Reconstruction of signals by compressed sensing methods

Paula Cerejeiras1, Narciso Gomes1,2
1University of Aveiro, Portugal; 2University of Cabo-Verde, Cabo-Verde

Abstract

Compressed sensing is a new concept in signal processing where one aims to reconstruct a signal from a small number of measurements. In particular, we study the problem of reconstructing a multivariate trigonometric polynomial having only few non-zero coefficients from few random samples. The main idea behind this approach is that for a matrix satisfying the restrictive isometry property (RIP) the sparse decomposition can be performed by an $\ell_1$-minimization procedure. In this talk we prove that sampling matrices coming from quaternionic and bicomplex signals can have the restrictive isometry property (RIP) with high probability. Based on this property, we can establish a fast reconstruction scheme of a sparse signal from a few random samples based on compressive sensing principles.

ISSN 1611 - 4086 | © IKM 2015