Adaptive Variable Step Algorithm for Missing Samples Recovery in Sparse Signals

Stanković, Ljubiša; Daković, Miloš; Vujovic, Stefan

doi:10.48550/arxiv.1309.5749

Cited by 2 publications

(8 citation statements)

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“…This minimization problem, under the conditions defined within the restricted isometry property (RIP), [3], [4], can produce the same result as (2). Note that other norms ℓ p between the ℓ 0 -norm and the ℓ 1 -norm, with values 0 < p < 1, are also used in the minimization in attempts to combine good properties of these two norms [1,26,35].…”

Section: Gradient-based Reconstructionmentioning

confidence: 99%

“…Some signals that cover whole considered interval in one domain could be sparse in a transformation domain. Compressive sensing theory, in general, deals with a lower dimensional set of linear observations of a sparse signal, in order to recover all signal values [1]- [26]. This area intensively develops in the last decade.…”

Section: Introductionmentioning

confidence: 99%

“…Recently a method for the reconstruction of a sparse signal with disturbed/missing samples has been proposed [26]. In contrast to the common reconstruction methods that recover the signal in their sparsity domain the proposed method reconstructs missing samples/measurements to make the set of samples/measurements complete.…”

Section: Introductionmentioning

confidence: 99%

“…A new criterion for the parameter adaptation of this simple algorithm, based on the gradient directions, is proposed in this paper. Computational time to achieve the target reconstruction accuracy is significantly reduced with respect to the original criterion in [26]. The Fourier transform domain is used as a case study, although the algorithm application is not restricted to this transform [27].…”

Section: Introductionmentioning

confidence: 99%

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Reconstruction of Randomly Sampled Sparse Signals Using an Adaptive Gradient Algorithm

Stankovic,

Dakovic

2014

Preprint

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Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the remaining missing samples/measurements is recently proposed. The available samples are fixed, while the missing samples are considered as minimization variables. Recovery of missing samples/measurements is done using an adaptive gradient-based algorithm in the time domain. A new criterion for the parameter adaptation in this algorithm, based on the gradient direction angles, is proposed. It improves the algorithm computational efficiency. A theorem for the uniqueness of the recovered signal for given set of missing samples (reconstruction variables) is presented. The case when available samples are a random subset of a uniformly or nonuniformly sampled signal is considered in this paper. A recalculation procedure is used to reconstruct the nonuniformly sampled signal. The methods are illustrated on statistical examples.

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Section: Gradient-based Reconstructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reconstruction of Randomly Sampled Sparse Signals Using an Adaptive Gradient Algorithm

Stankovic,

Dakovic

2014

Preprint

Self Cite

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“…A large number of algorithms is based on approximate solutions based on thresholding or greedy methods [8]- [14]. In this paper, we have analyzed the performance of the iterative algorithm for reconstruction of sparse signals, based on gradient calculation and signal concentration as a measure of sparsity [6], [7]. When the iterations approach the optimal point, gradient value oscillates around the true value.…”

Section: Introductionmentioning

confidence: 99%

Analysis of gradient based algorithm for signal reconstruction in the presence of noise

Jokic

Ljindita

Kadovic

2015

2015 4th Mediterranean Conference on Embedded Computing (MECO)

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Abstract-Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy signal coefficients can be considered as missing ones, since they have wrong values due to the noise. The reconstruction of these coefficients is demanding task, considered within the Compressive sensing area. Signal with large number of missing samples can be recovered, if certain conditions are satisfied. There is a number of algorithms used for signal reconstruction. In this paper we have analyzed the performance of iterative gradient-based algorithm for sparse signal reconstruction. The parameters influence on the optimal performances of this algorithm is tested. Two cases are observed: non-noisy and noisy signal case. The theory is proved on examples.

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Adaptive Variable Step Algorithm for Missing Samples Recovery in Sparse Signals

Cited by 2 publications

References 0 publications

Reconstruction of Randomly Sampled Sparse Signals Using an Adaptive Gradient Algorithm

Reconstruction of Randomly Sampled Sparse Signals Using an Adaptive Gradient Algorithm

Analysis of gradient based algorithm for signal reconstruction in the presence of noise

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