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Recovery of arbitrarily positioned samples that are missing in sparse signalsrecently attracted significant research interest. Sparse signals with heavilycorrupted arbitrary positioned samples could be analyzed in the same way ascompressive sensed signals by omitting the corrupted samples and consideringthem as unavailable during the recovery process. The reconstruction of missingsamples is done by using one of the well known reconstruction algorithms. Inthis paper we will propose a very simple and efficient adaptive variable stepalgorithm, applied directly to the concentration measures, withoutreformulating the reconstruction problem within the standard linear programmingform. Direct application of the gradient approach to the nondifferentiableforms of measures lead us to introduce a variable step size algorithm. Acriterion for changing adaptive algorithm parameters is presented. The resultsare illustrated on the examples with sparse signals, including approximatelysparse signals and noisy sparse signals.

Adaptive Variable Step Algorithm for Missing Samples Recovery in Sparse Signals