Paper Info
Title
Universal Inversion Formulas for Recovering a Function from Spherical Means.
Abstract
The problem of reconstruction of a function from spherical means is at the heart of several modern imaging modalities and other applications. In this paper we derive universal back-projection-type reconstruction formulas for recovering a function in arbitrary dimension from averages over spheres centered on the boundary of an arbitrarily shaped bounded convex domain with smooth boundary. Provided that the unknown function is supported inside that domain, the derived formulas recover the unknown function up to an explicitly computed integral operator. For elliptical domains the integral operator is shown to vanish and hence we establish exact inversion formulas for recovering a function from spherical means centered on the boundary of elliptical domains in arbitrary dimension.
Year
DOI
Venue
2014
10.1137/120881270
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
spherical means,reconstruction formula,inversion formula,wave equation,universal back-projection,Radon transform,photoacoustic tomography,thermoacoustic tomography
Imaging modalities,Mathematical analysis,Inversion (meteorology),Regular polygon,Operator (computer programming),SPHERES,Wave equation,Radon transform,Mathematics,Bounded function
Journal
Volume
Issue
ISSN
46
1
0036-1410
Citations 
PageRank 
References 
11
0.73
2
Authors
1
Name
Order
Citations
PageRank
Markus Haltmeier17414.16