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 -