Stochastic projection methods and applications to some nonlinear inverse problems of phase retrieving

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Stochastic projection methods and applications to some nonlinear inverse problems of phase retrieving. / Sabelfeld, Karl K.

In: Mathematics and Computers in Simulation, Vol. 143, 01.01.2018, p. 169-175.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{7e540b6f41e648a5877df1062a9062b5,

title = "Stochastic projection methods and applications to some nonlinear inverse problems of phase retrieving",

abstract = "In this short paper we present a stochastic projection based Monte Carlo algorithm for solving a nonlinear ill-posed inverse problem of recovering the phase of a complex-valued function provided its absolute value is known, under some additional information. The method is developed here for retrieving the step structure of the epitaxial films from the X-ray diffraction analysis. We suggest to extract some additional information from the measurements which makes the problem well-posed, and with this information, the method suggested works well even for noisy measurements. Results of simulations for a layer structure recovering problem with 26 sublayers are presented.",

keywords = "Epitaxial layers, Inverse problem, Phase retrieving, Stochastic projections, X-ray diffraction, ALGORITHM, INTEGRAL-EQUATIONS, CONVERGENCE, CRYSTALLOGRAPHY",

author = "Sabelfeld, {Karl K.}",

year = "2018",

month = jan,

day = "1",

doi = "10.1016/j.matcom.2016.08.001",

language = "English",

volume = "143",

pages = "169--175",

journal = "Mathematics and Computers in Simulation",

issn = "0378-4754",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Stochastic projection methods and applications to some nonlinear inverse problems of phase retrieving

AU - Sabelfeld, Karl K.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this short paper we present a stochastic projection based Monte Carlo algorithm for solving a nonlinear ill-posed inverse problem of recovering the phase of a complex-valued function provided its absolute value is known, under some additional information. The method is developed here for retrieving the step structure of the epitaxial films from the X-ray diffraction analysis. We suggest to extract some additional information from the measurements which makes the problem well-posed, and with this information, the method suggested works well even for noisy measurements. Results of simulations for a layer structure recovering problem with 26 sublayers are presented.

AB - In this short paper we present a stochastic projection based Monte Carlo algorithm for solving a nonlinear ill-posed inverse problem of recovering the phase of a complex-valued function provided its absolute value is known, under some additional information. The method is developed here for retrieving the step structure of the epitaxial films from the X-ray diffraction analysis. We suggest to extract some additional information from the measurements which makes the problem well-posed, and with this information, the method suggested works well even for noisy measurements. Results of simulations for a layer structure recovering problem with 26 sublayers are presented.

KW - Epitaxial layers

KW - Inverse problem

KW - Phase retrieving

KW - Stochastic projections

KW - X-ray diffraction

KW - ALGORITHM

KW - INTEGRAL-EQUATIONS

KW - CONVERGENCE

KW - CRYSTALLOGRAPHY

UR - http://www.scopus.com/inward/record.url?scp=84994156495&partnerID=8YFLogxK

U2 - 10.1016/j.matcom.2016.08.001

DO - 10.1016/j.matcom.2016.08.001

M3 - Article

AN - SCOPUS:84994156495

VL - 143

SP - 169

EP - 175

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

ER -

ID: 9445276