Missing samples analysis in signals for applications to L-estimation and compressive sensing

Stanković, Ljubiša; Stanković, Srdjan; Amin, Moeness G.

doi:10.1016/j.sigpro.2013.07.002

Cited by 132 publications

(92 citation statements)

References 20 publications

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“…Signals that can be characterized by a small number of nonzero coefficients are referred to as sparse signals [1][2][3][4][5][6][7][8][9][10][11]. These signals can be reconstructed from a reduced set of measurements .…”

Section: Introductionmentioning

confidence: 99%

“…These signals can be reconstructed from a reduced set of measurements . The measurements represent linear combination of the sparsity (transform) domain coefficients [1,7,24]. Signal samples can be considered as measurements (observations) in the case when a linear signal transform is the sparsity domain.…”

Section: Introductionmentioning

confidence: 99%

“…The reduced number of measurements may appear due to different causes. In the CS applications, it arises as a consequence of intentional sampling strategy, aiming to reduce the signal acquisition time, equipment load, and subject exposure to potentially dangerous radiation during the acquisition in biomedical applications, or, simply, there is a particular interest to reduce the amount of acquired samples while preserving the complete information (compression) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. In certain cases, physical unavailability can be a cause of a reduced number of measurements.…”

Section: Introductionmentioning

confidence: 99%

“…In many applications, strong disturbances (noise) can significantly corrupt the signal samples. Such signals are processed by detecting and intentionally neglecting the corrupted measurements [7,9,23]. Regardless of their unavailability reasons, under certain reasonable conditions, missing samples can be reconstructed using well developed CS methods and algorithms [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…This leads to inevitable reconstruction errors. The reduction of the amount of available samples manifests as a transform domain noise [7,9]. During the reconstruction, this noise is completely cancelled out, if the sparsity assumption is strictly satisfied.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Error in the Reconstruction of Nonsparse Images

Brajović

Stanković

Daković

et al. 2018

Mathematical Problems in Engineering

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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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