Adaptive variable step algorithm for missing samples recovery in sparse signals

Stanković, Ljubiša; Daković, Miloš; Vujovic, Stefan

doi:10.1049/iet-spr.2013.0385

Cited by 74 publications

(57 citation statements)

References 22 publications

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“…For a reconstruction of unavailable/corrupted samples in the time domain, we will use a very simple and efficient algorithm, based on the gradient of a sparsity measure [25,28,29]. This algorithm is inspired by the adaptive signal processing methods with an adaptive step size.…”

Section: Definitions and Reconstruction Algorithmmentioning

confidence: 99%

“…The stopping criterion for this loop can be based on the minimal value of Δ or on the sparsity measure of the reconstructed signal. The rate of algorithm convergence is considered in detail in [28,29].…”

Section: Algorithm 1 Reconstruction Procedures Gradrecmentioning

confidence: 99%

“…Small step value influences only the rate of the algorithm convergence [28,29]. In order to examine the algorithm behavior for a large Δ, note that…”

Section: Algorithm 1 Reconstruction Procedures Gradrecmentioning

confidence: 99%

“…By increasing the number of iterations, with a sufficient number of available samples ( Fig. 1), the value of SRR could be of the computer precision order, [28].…”

Section: Example 1 Consider a Signalmentioning

confidence: 99%

“…A gradient-based algorithm for reconstruction of sparse signal with missing samples has been proposed in [28]. In this paper, the idea of gradient calculation is reviewed in Sect.…”

Section: Introductionmentioning

confidence: 99%

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Reconstruction of Sparse Signals in Impulsive Disturbance Environments

Stanković

Daković

Vujovic

2016

Circuits Syst Signal Process

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Sparse signals corrupted by impulsive disturbances are considered. The assumption about disturbances is that they degrade the original signal sparsity. No assumption about their statistical behavior or range of values is made. In the first part of the paper, it is assumed that some uncorrupted signal samples exist. A criterion for selection of corrupted signal samples is proposed. It is based on the analysis of the first step of a gradient-based iterative algorithm used in the signal reconstruction. An iterative extension of the original criterion is introduced to enhance its selection property. Based on this criterion, the corrupted signal samples are efficiently removed. Then, the compressive sensing theory-based reconstruction methods are used for signal recovery, along with an appropriately defined criterion to detect a full recovery event among different realizations. In the second part of the paper, a case when all signal samples are corrupted by an impulsive disturbance is considered as well. Based on the defined criterion, the most heavily corrupted samples are removed. The presented criterion and the reconstruction algorithm are applied on the signal with a Gaussian noise.

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Section: Definitions and Reconstruction Algorithmmentioning

confidence: 99%

Section: Algorithm 1 Reconstruction Procedures Gradrecmentioning

confidence: 99%

“…Small step value influences only the rate of the algorithm convergence [28,29]. In order to examine the algorithm behavior for a large Δ, note that…”

Section: Algorithm 1 Reconstruction Procedures Gradrecmentioning

confidence: 99%

“…By increasing the number of iterations, with a sufficient number of available samples ( Fig. 1), the value of SRR could be of the computer precision order, [28].…”

Section: Example 1 Consider a Signalmentioning

confidence: 99%

“…A gradient-based algorithm for reconstruction of sparse signal with missing samples has been proposed in [28]. In this paper, the idea of gradient calculation is reviewed in Sect.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Reconstruction of Sparse Signals in Impulsive Disturbance Environments

Stanković

Daković

Vujovic

2016

Circuits Syst Signal Process

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Sparse Signal Reconstruction–Introduction

Stanković

Daković

Stanković

et al. 2017

Wiley Encyclopedia of Electrical and Electronics Engineering

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Sparse signals are characterized by a few nonzero values in one of their representation domains. The reconstruction of such signals is possible with a reduced set of measurements. The description and basic definitions of sparse signals, along with the conditions for their reconstruction, are discussed in the first part of this article. Among numerous reconstruction algorithms developed for the sparse signals reconstruction, three classes are reviewed. The first one is based on the principle of matching components. Analysis of noise and nonsparsity influence to the reconstruction is done. The second class of reconstruction algorithms is based on the problem reformulation into a constrained convex form when the linear programming optimization and regression methods can be used. The third class of algorithms to obtain the solution is based on the Bayesian approach. The examples of reconstruction using all of the considered approaches are presented, for a common transformation and observation matrices. Pseudo‐codes are provided for all considered reconstruction algorithms.

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