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

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  • Sabelfeld, Karl K.

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.

Suggested Citation

  • Sabelfeld, Karl K., 2018. "Stochastic projection methods and applications to some nonlinear inverse problems of phase retrieving," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 169-175.
    • Handle: RePEc:eee:matcom:v:143:y:2018:i:c:p:169-175
    DOI: 10.1016/j.matcom.2016.08.001
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    References listed on IDEAS

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    1. Sabelfeld, K.K. & Mozartova, N.S., 2011. "Sparsified Randomization algorithms for low rank approximations and applications to integral equations and inhomogeneous random field simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 295-317.
    2. Sabelfeld K. & Mozartova N., 2009. "Sparsified Randomization Algorithms for large systems of linear equations and a new version of the Random Walk on Boundary method," Monte Carlo Methods and Applications, De Gruyter, vol. 15(3), pages 257-284, January.
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