Paper Info
Title
Inversion of circular means and the wave equation on convex planar domains
Abstract
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary @?@W of a smooth convex bounded domain @W@?R^2. As a main result we establish back-projection type inversion formulas that recover any initial data with support in @W modulo an explicitly computed smoothing integral operator K"@W. For circular and elliptical domains the operator K"@W is shown to vanish identically and hence we establish exact inversion formulas of the back-projection type in these cases. Similar results are obtained for recovering a function from its mean values over circles with centers on @?@W. Both reconstruction problems are, amongst others, essential for the hybrid imaging modalities photoacoustic and thermoacoustic tomography.
Year
DOI
Venue
2013
10.1016/j.camwa.2013.01.036
Computers & Mathematics with Applications
Keywords
Field
DocType
convex planar domain,back-projection type inversion formula,operator k,initial data,circular mean,hybrid imaging modalities photoacoustic,elliptical domain,integral operator k,exact inversion formula,dimensional wave equation,back-projection type,w modulo,photoacoustic imaging,wave equation,radon transform
Mathematical optimization,Mathematical analysis,Modulo,Regular polygon,Smoothing,Planar,Operator (computer programming),Wave equation,Radon transform,Mathematics,Bounded function
Journal
Volume
Issue
ISSN
65
7
Comput. Math. Appl. 65 (2013) 1025-1036
Citations 
PageRank 
References 
7
0.87
6
Authors
1
Name
Order
Citations
PageRank
Markus Haltmeier17414.16