LIDS REPORT 2822 1 Approximate Solution of Large-Scale Linear Inverse Problems with Monte Carlo Simulation ∗

We consider the approximate solution of linear ill-posed inverse problems of high dimension 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 use variance reduction/importance sampling schemes, specially tailored to the structure of inverse problems. We demonstrate the implementation of our algorithm in a series of practical large-scale examples arising from Fredholm integral equations of the first kind. November 2009

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