Blind Deconvolution of Linear Systems with Multilevel Nonstationary Inputs

Li, Ta‐Hsin

doi:10.1214/aos/1176324542

Cited by 25 publications

(21 citation statements)

References 15 publications

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“…There are deconvolution problems in signal processsing when the probability distribution of the signal process {s(t)} is discrete with finitely many points of support such as in the finite alphabet transmission. These deconvolution problems were treated in [17,12]. The finite tone image deconvolution or debluriing problems were treated in [18] where the distribution of the pixels is two-tone (or finite-tone) without the stationarity assumption.…”

Section: If the Output Process {X(t)} Is Observed With An Independentmentioning

confidence: 99%

Rosenblatt’s Contributions to Deconvolution

Davis

Lii

Politis

2011

Selected Works of Murray Rosenblatt

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A simple model of deconvolution can be described as observing {x(t)} which is a convolution of a signal {s(t)} with a filter {f(j)},x = s*f. More specifically, we haveThe problem of deconvolution is to recover {s(t)} based on the output process {x(t)}. If the filter {f(j)} is known then the problem is fairly straightforward. The blind deconvolution, in signal processing terminology, is to recover {s(t)} based solely on {x(t)} without knowing {/(j)}. Statisticians may be more interested in the estimation of {f(j)} under certain conditions on {s(t)} and {/(j)}-This problem and its many variations have very broad applications in signal processing, image restoration, geo-exploration, seismology, radio astronomy among others [11,33,38,39].Assume that the signal random variables {s(t)} are independent and identically distributed with mean 0 and variance 1. Let the filter {f(j)} be a sequence of real constants such that oo

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Section: If the Output Process {X(t)} Is Observed With An Independentmentioning

confidence: 99%

Rosenblatt’s Contributions to Deconvolution

Davis

Lii

Politis

2011

Selected Works of Murray Rosenblatt

View full text Add to dashboard Cite

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“…Indeed, using a finite alphabet of cardinality d, one can force the equalizer output to belong to the desired alphabet using a combination of moments of order up to 2d. In fact, a possible way to force the equalizer output to belong to the desired constellation is to null the cost function [4], [5], [6] …”

Section: Problem Formulationmentioning

confidence: 99%

New Global Blind Equalization Using Two Constant Modulus Asymmetrical Modulations Proposals

Zaouche

Tatkeu

Dayoub

et al. 2008

VTC Spring 2008 - IEEE Vehicular Technology Conference

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A new global fractionally spaced blind equalization approach based on the use of pattern search optimization and two new constant modulus fourth order asymmetrical modulations schemes is proposed. Simulation results in terms of intersymbol interference and a new performance measure show that the proposed approach achieves perfect global convergence behavior together with correction of the random phase rotation of the constellation. The propagation environment is a frequency selective channel in the presence of Gaussian noise.

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“…If signal z n (n is the iteration number) can be represented as the output of an input signal x n acted upon by an operator (or machine) y n , then the problem of solving for x n and y n knowing z n (the convolution of the two) is called ''blind deconvolution'' (LI, 1995;CREPE et al, 1999). Normally the solution to this problem is non-unique and the number of solutions is infinite.…”

Section: Theorymentioning

confidence: 99%

A Study of the Adaptive Method for Decoupling Overlapping Seismic Records

Yang

Shen

et al. 2006

Pure appl. geophys.

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Signal extraction from overlapping seismic records is a common problem in geophysical data analysis. Identification and separation of multiple seismic arrivals, analysis of large earthquakes as multiple point sources, and calculation of the true yield of a large nuclear explosion from interfering small explosion, all hinge on our ability to effectively decouple two interfering wave signals. This paper presents a method for signal separation based on an adaptive filtering technique. We apply a semi-deconvolution algorithm to overlapping explosion records and S/SKS phase groups, and then perform noise reduction and signal decoupling under different a priori conditions and assess the stabilities using a variance reduction approach. We demonstrate, through numerical experiments and analysis of seismic station records, that the adaptive method can be both robust and practical for regional and teleseismic applications.

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Blind Deconvolution of Linear Systems with Multilevel Nonstationary Inputs

Cited by 25 publications

References 15 publications

Rosenblatt’s Contributions to Deconvolution

Rosenblatt’s Contributions to Deconvolution

New Global Blind Equalization Using Two Constant Modulus Asymmetrical Modulations Proposals

A Study of the Adaptive Method for Decoupling Overlapping Seismic Records

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