Perturbed Orthogonal Matching Pursuit

Abstract

Abstract-Compressive Sensing theory details how a sparsely represented signal in a known basis can be reconstructed with an underdetermined linear measurement model. However, in reality there is a mismatch between the assumed and the actual bases due to factors such as discretization of the parameter space defining basis components, sampling jitter in A/D conversion, and model errors. Due to this mismatch, a signal may not be sparse in the assumed basis, which causes significant performance degradation in sparse reconstruction algorithms. To eliminate the mismatch problem, this paper presents a novel perturbed orthogonal matching pursuit (POMP) algorithm that performs controlled perturbation of selected support vectors to decrease the orthogonal residual at each iteration. Based on detailed mathematical analysis, conditions for successful reconstruction are derived. Simulations show that robust results with much smaller reconstruction errors in the case of perturbed bases can be obtained as compared to standard sparse reconstruction techniques.

Sparse delay-Doppler image reconstruction under off-grid problem

“…3(b). As it was reported in [6], use of finer grids in OMP does not provide comparable performance to the proposed PPOMP.…”

“…For a general non-parametric case, a reconstruction algorithm and some performance bounds are provided in [6].…”

Off-Grid Aware Channel and Covariance Estimation in mmWave Networks

“…This off-grid phenomena violates the sparsity assumption, resulting in a decrease in reconstruction performance. As a result, the estimation accuracy of the CS based methods is limited by the number of grid points [12], [13], [28], [29].…”

“…At any iteration k, the measurements y t,agg can be decomposed as [14], [28] y t,agg =ỹ t,agg ⊥ +ỹ t,agg , ∀t ∈ [T ],…”

A recursive way for sparse reconstruction of parametric spaces

“…Even though OMP with a fine grid has been reported with a limited performance gain [13], the results of OMP with a dense grid is also provided for the comparison purposes. Together with the standard deviations of the error in the estimated frequencies, the CRLB given in (22) is presented in Fig.…”