Adaptive Variable Step Algorithm for Missing Samples Recovery in Sparse Signals

TL;DR

This paper introduces a simple, efficient adaptive variable step algorithm for recovering missing samples in sparse signals, applicable to both noiseless and noisy scenarios, without reformulating the problem as linear programming.

Contribution

It proposes a novel adaptive variable step algorithm that directly applies to concentration measures for missing sample recovery in sparse signals, avoiding standard linear programming reformulation.

Findings

Effective recovery in noiseless sparse signals

Robust performance with noisy sparse signals

Adaptive parameter adjustment improves convergence

Abstract

Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as compressive sensed signals by omitting the corrupted samples and considering them as unavailable during the recovery process. The reconstruction of missing samples is done by using one of the well known reconstruction algorithms. In this paper we will propose a very simple and efficient adaptive variable step algorithm, applied directly to the concentration measures, without reformulating the reconstruction problem within the standard linear programming form. Direct application of the gradient approach to the nondifferentiable forms of measures lead us to introduce a variable step size algorithm. A criterion for changing adaptive algorithm parameters is presented. The results are illustrated on the examples with sparse signals, including approximately sparse signals and noisy sparse signals.