Synthetic focusing in ultrasound modulatedtomography

Peter Kuchment; Leonid Kunyansky

doi:10.3934/ipi.2010.4.665

Article Contents

2010, Volume 4, Issue 4: 665-673. Doi: 10.3934/ipi.2010.4.665

This issue Previous Article The Gauss-Bonnet-Grotemeyer Theorem in space forms Next Article Diffusion reconstruction from very noisy tomographic data

Synthetic focusing in ultrasound modulated tomography

Peter Kuchment^1, and
Leonid Kunyansky^2,

1.
Mathematics Department, Texas A&M University, College Station, TX 77843-3368
2.
Mathematics Department, University of Arizona, Tucson, AZ 85721

Received: December 31, 2008

Revised: April 30, 2009

Published: October 2010

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Abstract

Several hybrid tomographic methods utilizing ultrasound modulation have been introduced lately. Success of these methods hinges on the feasibility of focusing ultrasound waves at an arbitrary point of interest. Such focusing, however, is difficult to achieve in practice. We thus propose a way to avoid the use of focused waves through what we call synthetic focusing, i.e. by reconstructing the would-be response to the focused modulation from the measurements corresponding to realistic unfocused waves. Examples of reconstructions from simulated data are provided. This non-technical paper describes only the general concept, while technical details will appear elsewhere.

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Mathematics Subject Classification: Primary: 44A12, 92C55; Secondary: 65R32.

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