Reconstruction of Sparse Signals in Impulsive Disturbance Environments

Stanković, Ljubiša; Daković, Miloš; Vujovic, Stefan

doi:10.1007/s00034-016-0334-3

Cited by 22 publications

(15 citation statements)

References 34 publications

(70 reference statements)

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“…In this paper, we mainly focused on the no noise environments. Recently, in Reference [33][34][35][36], the researchers focused on the reconstruction solutions for the original signal in the presence of noise corruption and several algorithms were proposed. In the future, we can use their ideas to improve our proposed method in anti-noise interference performance.…”

Section: Discussionmentioning

confidence: 99%

Stochastic Gradient Matching Pursuit Algorithm Based on Sparse Estimation

Zhao

Liu

2019

Electronics

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The stochastic gradient matching pursuit algorithm requires the sparsity of the signal as prior information. However, this prior information is unknown in practical applications, which restricts the practical applications of the algorithm to some extent. An improved method was proposed to overcome this problem. First, a pre-evaluation strategy was used to evaluate the sparsity of the signal and the estimated sparsity was used as the initial sparsity. Second, if the number of columns of the candidate atomic matrix was smaller than that of the rows, the least square solution of the signal was calculated, otherwise, the least square solution of the signal was set as zero. Finally, if the current residual was greater than the previous residual, the estimated sparsity was adjusted by the fixed step-size and stage index, otherwise we did not need to adjust the estimated sparsity. The simulation results showed that the proposed method was better than other methods in terms of the aspect of reconstruction percentage in the larger sparsity environment.

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Section: Discussionmentioning

confidence: 99%

Stochastic Gradient Matching Pursuit Algorithm Based on Sparse Estimation

Zhao

Liu

2019

Electronics

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“…, is used in minimization, [21,3,6,23]. The correct amplitude in the signal transform at the frequency k p , in the case if all signal samples were used, would be NA p .…”

Section: Additive Noise Influencementioning

confidence: 99%

“…Therefore, a signal reconstruction that would be based on the initial estimate (10) would worsen SNR, since N > M. An improvement can be expected only if we were able to remove the noisy samples in a selective manner so that the samples used in reconstruction are less noisy than the other samples, [23]. If such a criterion is used to selectively remove the noise samples then the reconstruction is improved if The agreement of the numerical statistical results with this simple theory in analysis of noise influence to the reconstruction of sparse signals is high.…”

Section: Additive Noise Influencementioning

confidence: 99%

“…In applications it could happen that some arbitrarily positioned samples of the signal are so heavily corrupted by disturbances that it is better to omit them and consider as unavailable in the analysis. This is especially true for the impulsive noise [4], [23]. As a study case, in this paper we will consider signals that are sparse in the Fourier transform domain.…”

Section: Introductionmentioning

confidence: 99%

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Noises in randomly sampled sparse signals

Stanković

2014

FACTA U EE

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Sparse signals can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Two main reconstruction directions are in the sparse transformation domain analysis of signals and the gradient based algorithms. In the transformation domain analysis, that will be considered here, the estimation of nonzero signal coefficients is based on the signal transform calculated using available samples only. The missing samples manifest themselves as a noise. This kind of noise is analyzed in the case of random sampling, when the sampling instants do not coincide with the sampling theorem instants. Analysis of the external noise influence to the results, with randomly sampled sparse signals, is done as well. Theory is illustrated and checked on statistical examples.

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“…Moreover, this transform domain has been convenient for the reconstruction of digital images with missing pixels and/or noise corruption using the sparsity assumption [21][22][23]. Measuring the 2 Mathematical Problems in Engineering 2D-DCT coefficients concentration (using the ℓ 1 -norm based measure) and varying missing samples values to obtain the sparsest possible solution leads to the prominent compressive sensing reconstruction results [20,23]. In the orthogonal matching pursuit (OMP) framework, successful reconstruction is easily obtained if the coefficients corresponding to signal component positions are successfully identified [12,[28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Error in the Reconstruction of Nonsparse Images

Brajović

Stanković

Daković

et al. 2018

Mathematical Problems in Engineering

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Sparse signals, assuming a small number of nonzero coefficients in a transformation domain, can be reconstructed from a reduced set of measurements. In practical applications, signals are only approximately sparse. Images are a representative example of such approximately sparse signals in the two-dimensional (2D) discrete cosine transform (DCT) domain. Although a significant amount of image energy is well concentrated in a small number of transform coefficients, other nonzero coefficients appearing in the 2D-DCT domain make the images be only approximately sparse or nonsparse. In the compressive sensing theory, strict sparsity should be assumed. It means that the reconstruction algorithms will not be able to recover small valued coefficients (above the assumed sparsity) of nonsparse signals. In the literature, this kind of reconstruction error is described by appropriate error bound relations. In this paper, an exact relation for the expected reconstruction error is derived and presented in the form of a theorem. In addition to the theoretical proof, the presented theory is validated through numerical simulations.

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Reconstruction of Sparse Signals in Impulsive Disturbance Environments

Cited by 22 publications

References 34 publications

Stochastic Gradient Matching Pursuit Algorithm Based on Sparse Estimation

Stochastic Gradient Matching Pursuit Algorithm Based on Sparse Estimation

Noises in randomly sampled sparse signals

Error in the Reconstruction of Nonsparse Images

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