Volume 42, pp. 177-196, 2014.

Data completion and stochastic algorithms for PDE inversion problems with many measurements

Farbod Roosta-Khorasani, Kees van den Doel, and Uri Ascher

Abstract

Inverse problems involving systems of partial differential equations (PDEs) with many measurements or experiments can be very expensive to solve numerically. Assuming that all experiments share the same set of receivers, in a recent paper we examined both stochastic and deterministic dimensionality reduction methods to reduce this computational burden. In the present article we consider the more general and practically important case where receivers are not shared across experiments. We propose a data completion approach to alleviate this problem. This is done by means of an approximation using an appropriately restricted gradient or Laplacian regularization, extending existing data for each experiment to the union of all receiver locations. Results using the method of simultaneous sources (SS) with the completed data are then compared to those obtained by a more general but slower random subset (RS) method which requires no modifications.

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Key words

stochastic algorithm, data completion, inverse problem, partial differential equation, many experiments, DC resistivity

AMS subject classifications

65N21, 65C05

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