Iterative time-reversal control for inverse problems | Zendy

Kenrick Bingham | Zendy; Yaroslav Kurylev | Zendy; Matti Lassas | Zendy; Samuli Siltanen | Zendy

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Iterative time-reversal control for inverse problems

Author(s) -

Kenrick Bingham,

Yaroslav Kurylev,

Matti Lassas,

Samuli Siltanen

Publication year - 2008

Publication title -

inverse problems and imaging

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.755

H-Index - 40

eISSN - 1930-8345

pISSN - 1930-8337

DOI - 10.3934/ipi.2008.2.63

Subject(s) - wave equation , inverse problem , iterative method , inverse , scheme (mathematics) , boundary (topology) , computer science , acoustic wave equation , mathematics , time domain , domain (mathematical analysis) , algorithm , mathematical optimization , mathematical analysis , wave propagation , physics , optics , geometry , computer vision

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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