APPLICATION OF THE COMPRESSED SENSING FOR SPARSE SIGNAL RECOVERY

Compressed sensing is a signal processing technique for efficiently acquiring and reconstructing a signal, by nding solutions to underdetermined linear systems. This is based on the principle that, throughoptimization, the sparsity of a signal can be exploited to recover it from farfewer samples than required by the Shannon-Nyquist sampling theorem.In this paper, we want to investigate the ability of the OMP algorithm toreconstruct signals that are sparse. we consider the orthogonal matchingpursuit (OMP) algorithm for the recovery of a high-dimensional sparsesignal based on a small number of noisy linear measurements. OMP is aniterative greedy algorithm that selects at each step the column, which ismost correlated with the current residuals. It is shown that under con-ditions on the mutual incoherence and the minimum magnitude of thenonzero components of the signal, the support of the signal can be recov-ered exactly by the OMP algorithm with high probability. In this paper,we present the appropriate numerical examples of signals that show theadvantage and efficiency of this method in comparison with other methods.

APPLICATION OF THE COMPRESSED SENSING FOR SPARSE SIGNAL RECOVERY Keywords:

ℓ1minimization , compressed sensing , mutual incoherence , orthogonal matching pursuit (OMP) , sparse signal , signal reconstruction , support recovery