On the reconstruction of nonsparse time-frequency signals with sparsity constraint from a reduced set of samples

Stanković, Isidora; Ioana, Cornel; Daković, Miloš

doi:10.1016/j.sigpro.2017.07.036

Cited by 19 publications

(9 citation statements)

References 15 publications

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“…This proves the expression (19). It remains to prove the expressions (20) and (21). Since w = e −j2lπ/N , we have that the real and imaginary part of w k are respectively equal to ℜ(w k ) = cos 2klπ N and ℑ(w k ) = − sin 2klπ N for every k = 1, 2, .…”

Section: Proofs Of the Resultsmentioning

confidence: 99%

“…Proof of Corollary 2.5. In order to prove Corollary 2.5, observe that by (21) of Theorem 2.4, we have…”

Section: Proofs Of the Resultsmentioning

confidence: 99%

“…In [27, Section 2] (cf. [28, Section II] and [21]) [21,Section 2]), the authors considered a set of N signal values Θ given by Θ = {s(1), s(2), . .…”

Section: Motivation Definitions and Related Examplesmentioning

confidence: 99%

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On some discrete random variables arising from recent study on statistical analysis of compressive sensing

Meštrović¹

2018

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The recent paper [27] provides a statistical analysis for efficient detection of signal components when missing data samples are present. Here we focus our attention to some complex-valued discrete random variables X l (m, N ) (0 ≤ l ≤ N − 1, 1 ≤ M ≤ N ), which are closely related to the random variables investigated by LJ. Stanković, S. Stanković and M. Amin in [27]. In particular, by using a combinatorial approach, we prove that for l = 0 the expected value of X l (m, N ) is equal to zero, and we deduce the expression for the variance of the random variables X l (m, N ). The same results are also deduced for the real part U l (m, N ) and the imaginary part V l (m, N ) of X l (m, N ), as well as the facts that the kth moments of U l (m, N ) and V l (m, N ) are equal to zero for every positive integer k which is not divisible by N/ gcd(N, l). Moreover, some additional assertions and examples concerning the random variables X l (m, N ), U l (m, N ) and V l (m, N ) are also presented.

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Section: Proofs Of the Resultsmentioning

confidence: 99%

“…Proof of Corollary 2.5. In order to prove Corollary 2.5, observe that by (21) of Theorem 2.4, we have…”

Section: Proofs Of the Resultsmentioning

confidence: 99%

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On some discrete random variables arising from recent study on statistical analysis of compressive sensing

Meštrović¹

2018

Preprint

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“…Proof of Proposition 2.4. Since by the assumption, N and l are relatively prime positive integers, then the multiset Φ(l, N) defined by (1) consists of N distinct elements, and it can be written as (17) Φ(l, N) = {1, w, w 2 , . .…”

Section: Proofs Of the Resultsmentioning

confidence: 99%

A note on some sub-Gaussian random variables

Meštrović¹

2018

Preprint

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In [8] the author of this paper continued the research on the complexvalued discrete random variables X l (m, N ) (0 ≤ l ≤ N − 1, 1 ≤ M ≤ N ) recently introduced and studied in [24]. Here we extend our results by considering X l (m, N ) as sub-Gaussian random variables. Our investigation is motivated by the known fact that the so-called Restricted Isometry Property (RIP) introduced in [4] holds with high probability for any matrix generated by a sub-Gaussian random variable. Notice that sensing matrices with the RIP play a crucial role in Theory of compressive sensing.Our main results concern the proofs of the lower and upper bound estimates of the expected values of the random variableswhere U l (m, N ) and U l (m, N ) are the real and the imaginary part of X l (m, N ), respectively. These estimates are also given in terms of related sub-Gaussian norm• ψ2 considered in [28]. Moreover, we prove a refinement of the mentioned upper bound estimates for the real and the imaginary part of X l (m, N ).

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“…In order to characterize a transient phenomenon, new methods have been developed that complement those listed above. The most important are based on a new space of interpretation that exploits the sparsity of the transient given by compressive sensing [9,10], the phase diagram analysis as way to analyze electrical transients [11], and the entropy defined in the time-frequency domain [12]. In this state-of-the-art context, the idea behind our contribution is to consider the entropy as a statistical notion of the system that can highlight the specific time where transient phenomena occur.…”

Section: Introductionmentioning

confidence: 99%

Entropy-Based Characterization of the Transient Phenomena—Systemic Approach

et al. 2021

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The difficulties of predictive maintenance of power grids are related to the large spread of electrical infrastructures and the definition of early warning indicators. Such indicator is the partial discharge activities—which can be very informative about the rising insulation problems of electrical materials. However, the detection and the localization of the partial discharges are very complicate tasks and are currently subject to intensive studies in both theoretical and practical domains. The traditional way to approach the global surveillance of partial discharge sources is to first detect it and the second is to attempt to localize their positions. Despite the numerous proposed approaches, based on advanced transient signal processing tools, there is no any operational technique to efficiently asses the partial discharge sources in a real power network. In this context, our paper proposes a new approach based on the global evaluation of entropy of transient phenomena detected in a power network, without needing any localization of the sources of these phenomena. We will show that this approach provides an effective evaluation of partial discharges sources. Moreover, since the technique requires a reduced number of sensors, it is very advantageous to use in real contexts.

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On the reconstruction of nonsparse time-frequency signals with sparsity constraint from a reduced set of samples

Cited by 19 publications

References 15 publications

On some discrete random variables arising from recent study on statistical analysis of compressive sensing

On some discrete random variables arising from recent study on statistical analysis of compressive sensing

A note on some sub-Gaussian random variables

Entropy-Based Characterization of the Transient Phenomena—Systemic Approach

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