Adaptive variable step algorithm for missing samples recovery in sparse signals

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 analysed in the same way as compressive sensed signals by omitting the corrupted samples and con...

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Vydáno v:	IET signal processing Ročník 8; číslo 3; s. 246 - 256
Hlavní autoři:	Stankovic, Ljubisa, Dakovic, Milos, Vujovic, Stefan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Stevenage The Institution of Engineering and Technology 01.05.2014 John Wiley & Sons, Inc
Témata:	Adaptive algorithms adaptive variable step algorithm Algorithms approximately sparse signals arbitrarily positioned samples compressed sensing compressive sensed signals corrupted samples Criteria Linear programming missing samples recovery noisy sparse signals nondifferentiable forms Reconstruction reconstruction problem Recovery Signal processing signal reconstruction Special Issue on Compressive Sensing and Robust Transforms standard linear programming form compressed sensing compressive sensed signals adaptive variable step algorithm arbitrarily positioned samples standard linear programming form linear programming reconstruction problem corrupted samples nondifferentiable forms missing samples recovery approximately sparse signals noisy sparse signals signal reconstruction
ISSN:	1751-9675, 1751-9683, 1751-9683
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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 analysed 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 the missing samples is done by using one of the well-known reconstruction algorithms. In this study, the authors will propose a very simple and efficient 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 non-differentiable forms of measures lead us to introduce a variable step size algorithm. A criterion for changing the adaptive algorithm parameters is presented. The results are illustrated on the examples with sparse signals, including approximately sparse signals and noisy sparse signals.
AbstractList	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 analysed 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 the missing samples is done by using one of the well‐known reconstruction algorithms. In this study, the authors will propose a very simple and efficient 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 non‐differentiable forms of measures lead us to introduce a variable step size algorithm. A criterion for changing the adaptive algorithm parameters is presented. The results are illustrated on the examples with sparse signals, including approximately sparse signals and noisy sparse signals. 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 analysed 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 the missing samples is done, by using one of the well-known reconstruction algorithms. In this study, the authors will propose a very simple and efficient 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 non-differentiable forms of measures lead the authors to introduce a variable step size algorithm. A criterion for changing the adaptive algorithm parameters is presented. The results are illustrated on the examples with sparse signals, including approximately sparse signals and noisy sparse signals.
Author	Stanković, Ljubiša Vujović, Stefan Daković, Miloš
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Snippet	Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily...
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StartPage	246
SubjectTerms	Adaptive algorithms adaptive variable step algorithm Algorithms approximately sparse signals arbitrarily positioned samples compressed sensing compressive sensed signals corrupted samples Criteria Linear programming missing samples recovery noisy sparse signals nondifferentiable forms Reconstruction reconstruction problem Recovery Signal processing signal reconstruction Special Issue on Compressive Sensing and Robust Transforms standard linear programming form
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Title	Adaptive variable step algorithm for missing samples recovery in sparse signals
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