Workshop on Bioimaging I, Tue, 13 Nov, 2007
Speaker: Leonid Kunyansky
Abstract
We discuss explicit formulas for the reconstruction of
a function from its integrals over a family of spheres,
or for the inversion of the spherical mean Radon transform.
The need for such an inversion arises in problems of
thermo- and photo- acoustic tomography. Our approach is based
on finding scalar products of the unknown functions with
certain radial basis functions. As a result, we obtain a
closed-form inversion formula of a filtration-backprojection
type for the case when the centers of the integration spheres
lie on a sphere surrounding the support of the unknown
function.
Our approach also yields an explicit series solution for
certain other measuring surfaces, namely for those surrounding
a region whose eigenfunctions of the Dirichlet Laplacian
are explicitly known. Among such surfaces are cube, finite
cylinder, half-sphere etc. The simplest measurement surface
is the cubic one. For the latter case we present a fast
reconstruction algorithm capable of reconsrtucting 3-D images
thousands times faster than the backprojection-type methods.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
This page was made with 100% valid HTML & CSS - Send comments to Webmaster
Today's date and time is 04/20/24 - 10:12 CEST and this file (/specsem/ssqbm/participants/abstracts/index.php) was last modified on 12/18/12 - 11:01 CEST