Workshop on Bioimaging I, Fri, 16 Nov, 2007
Speaker: Frank Natterer
Abstract
We model ultrasound tomography by the Helmholtz equation with spatially
variant speed of sound and attenuation. We study various approximate
solutions of the inverse problem: Born, Rytov and eikonal approximation. We
give an explicit error estimate for the Born approximation and investigate
its applicability to ultrasound mamography. Finally we describe an iterative
inversion method. It is based on the algebraic reconstruction technique
(ART) of computerized tomography. The projection and backprojection step of
ART is replaced by solving the initial value problem and the final value
problem, respectively, of the Helmholtz equation. This can be interpreted as
consecutive time reversal in frequency space. The stability of this process
is guaranteed by low pass filtering with the bandwidth of the incoming wave,
as can be shown by energy type estimates. We demonstrate the efficacy of the
method by computer simulations.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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