Abstract

Non-invasive imaging based on wave scattering remain sa difficult problem in those cases where the forward map can only be adequately simulated by solving the appropriate partial-differential equation. We develop a method for solving linear PDEs which is efficient and exact, trading off computation time against storage requirements. The method is based on using the present solution within the Woodbury formula for updating solutions away from changes in the trial image, or state. Hence the method merges well with typical Metropolis-Hastings algorithms using localized update. The scaling of the method as a function of image size and measurement set size is given. We conclude that this method is considerably more efficient than earlier algorithms that we have used to demonstrate sampling for inverse problems in this class.

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