TY - GEN

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

AU - Polydorides, Nick

AU - Wang, Mengdi

AU - Bertsekas, Dimitri P.

N1 - Funding Information:
Research is supported by the Cyprus Program at MIT Energy Initiative, the LANL Information of Science and Technology Institute, and by NSF Grant ECCS-0801549.

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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U2 - 10.1007/978-3-642-27440-4_36

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 -