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In this paper, we study the regularization l p -norm minimization problem to recover the sparse signals. We first prove that every global optimal solution to the regularization l p -norm minimization problem also solves the l 0 -norm minimization problem if the certain conditions are satisfied, and then generate a truncated approximated difference algorithm to recover the sparse signals. At last, we provide some numerical simulations to test the performance of the truncated approximated difference algorithm, and the numerical results show that the proposed algorithm performs effectively in recovering the sparse signals compared with some state-of-art methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a novel algorithm is proposed to achieve robust high resolution detection in sparse multipath channels. Currently used sparse reconstruction techniques are not immediately applicable in multipath channel modeling. Performance of standard compressed sensing formulations based on discretization of the multipath channel parameter space degrade significantly when the actual channel parameters deviate from the assumed discrete set of values. To alleviate this off-grid problem, we make use of the particle swarm optimization (PSO) to perturb each grid point that reside in each multipath component cluster. Orthogonal matching pursuit (OMP) is used to reconstruct sparse multipath components in a greedy fashion. Extensive simulation results quantify the performance gain and robustness obtained by the proposed algorithm against the off-grid problem faced in sparse multipath channels. [Copyright &y& Elsevier]