A Quasi Monte Carlo Method for Large-Scale Inverse Problems

Nick Polydorides; Mengdi Wang; Dimitri P. Bertsekas

doi:10.1007/978-3-642-27440-4_36

A Quasi Monte Carlo Method for Large-Scale Inverse Problems

Nick Polydorides, Mengdi Wang, Dimitri P. Bertsekas

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

We consider large-scale linear inverse problems with a simulation-based algorithm that approximates the solution within a low-dimensional subspace. The algorithm uses Tikhonov regularization, regression, and low-dimensional linear algebra calculations and storage. For sampling efficiency, we implement importance sampling schemes, specially tailored to the structure of inverse problems. We emphasize various alternative methods for approximating the optimal sampling distribution and we demonstrate their impact on the reduction of simulation noise. The performance of our algorithm is tested on a practical inverse problem arising from Fredholm integral equations of the first kind.

Original language	English (US)
Title of host publication	Monte Carlo and Quasi-Monte Carlo Methods 2010
Publisher	Springer New York LLC
Pages	623-637
Number of pages	15
ISBN (Print)	9783642274398
DOIs	https://doi.org/10.1007/978-3-642-27440-4_36
State	Published - 2012
Externally published	Yes
Event	9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010 - Warsaw, Poland Duration: Aug 15 2010 → Aug 20 2010

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	23
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010
Country/Territory	Poland
City	Warsaw
Period	8/15/10 → 8/20/10

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/978-3-642-27440-4_36

Cite this

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title = "A Quasi Monte Carlo Method for Large-Scale Inverse Problems",

abstract = "We consider large-scale linear inverse problems with a simulation-based algorithm that approximates the solution within a low-dimensional subspace. The algorithm uses Tikhonov regularization, regression, and low-dimensional linear algebra calculations and storage. For sampling efficiency, we implement importance sampling schemes, specially tailored to the structure of inverse problems. We emphasize various alternative methods for approximating the optimal sampling distribution and we demonstrate their impact on the reduction of simulation noise. The performance of our algorithm is tested on a practical inverse problem arising from Fredholm integral equations of the first kind.",

author = "Nick Polydorides and Mengdi Wang and Bertsekas, {Dimitri P.}",

year = "2012",

doi = "10.1007/978-3-642-27440-4_36",

language = "English (US)",

isbn = "9783642274398",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "623--637",

booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2010",

note = "9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010 ; Conference date: 15-08-2010 Through 20-08-2010",

}

Polydorides, N, Wang, M & Bertsekas, DP 2012, A Quasi Monte Carlo Method for Large-Scale Inverse Problems. in Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics and Statistics, vol. 23, Springer New York LLC, pp. 623-637, 9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010, Warsaw, Poland, 8/15/10. https://doi.org/10.1007/978-3-642-27440-4_36

TY - GEN

T1 - A Quasi Monte Carlo Method for Large-Scale Inverse Problems

AU - Polydorides, Nick

AU - Wang, Mengdi

AU - Bertsekas, Dimitri P.

PY - 2012

Y1 - 2012

N2 - We consider large-scale linear inverse problems with a simulation-based algorithm that approximates the solution within a low-dimensional subspace. The algorithm uses Tikhonov regularization, regression, and low-dimensional linear algebra calculations and storage. For sampling efficiency, we implement importance sampling schemes, specially tailored to the structure of inverse problems. We emphasize various alternative methods for approximating the optimal sampling distribution and we demonstrate their impact on the reduction of simulation noise. The performance of our algorithm is tested on a practical inverse problem arising from Fredholm integral equations of the first kind.

AB - We consider large-scale linear inverse problems with a simulation-based algorithm that approximates the solution within a low-dimensional subspace. The algorithm uses Tikhonov regularization, regression, and low-dimensional linear algebra calculations and storage. For sampling efficiency, we implement importance sampling schemes, specially tailored to the structure of inverse problems. We emphasize various alternative methods for approximating the optimal sampling distribution and we demonstrate their impact on the reduction of simulation noise. The performance of our algorithm is tested on a practical inverse problem arising from Fredholm integral equations of the first kind.

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DO - 10.1007/978-3-642-27440-4_36

M3 - Conference contribution

AN - SCOPUS:84893613808

SN - 9783642274398

T3 - Springer Proceedings in Mathematics and Statistics

SP - 623

EP - 637

BT - Monte Carlo and Quasi-Monte Carlo Methods 2010

PB - Springer New York LLC

T2 - 9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010

Y2 - 15 August 2010 through 20 August 2010

ER -

A Quasi Monte Carlo Method for Large-Scale Inverse Problems

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