Iterative time-reversal control for inverse problems

Kenrick Bingham; Yaroslav Kurylev; Matti Lassas; Samuli Siltanen

doi:10.3934/ipi.2008.2.63

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2008, Volume 2, Issue 1: 63-81. Doi: 10.3934/ipi.2008.2.63

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Iterative time-reversal control for inverse problems

1.
Helsinki University of Technology, Institute of Mathematics, P.O.Box 1100, 02015 TKK
2.
University College London, Department of Mathematics, Gower Street, London, WC1E 6BT
3.
Tampere University of Technology,Institute of Mathematics,, P.O. Box 553, 33101 Tampere

Received: March 31, 2007

Revised: May 31, 2007

Published: January 2008

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Abstract

A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave equation using focusing waves in unknown medium. The approach is computationally effective since the iteration lets the medium do most of the processing of the data.
The iterative time reversal scheme also gives an algorithm for approximating a given wave in a subset of the domain without knowing the coefficients of the wave equation.

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Mathematics Subject Classification: Primary: 35R30, 93B05.

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