Paper Info
Title
Recovering a Function from Circular Means or Wave Data on the Boundary of Parabolic Domains.
Abstract
Determining a function from its circular means with restricted centers is crucial for many modern medical imaging and remote sensing applications. Examples include photo- and thermoacoustic tomography, ultrasound imaging, and synthetic aperture radar. In this paper we derive an explicit inversion formula for the case where the centers of the circles of integration are restricted to the boundary of parabolic domains. A similar result is obtained for recovering the initial data of the wave equation from data on the boundary of a parabolic domain. These results show that the universal back-projection formulas, previously known to be exact for half-spaces, discs, and ellipsoids, are also exact for parabolic domains. We further present numerical simulations supporting our theoretical results. There, we also include two previously proposed strategies (dynamic aperture length correction and weight factor correction) accounting for the truncation of the parabola in practical applications.
Year
DOI
Venue
2015
10.1137/140960219
SIAM JOURNAL ON IMAGING SCIENCES
Keywords
Field
DocType
circular means,wave equation,photoacoustic tomography,Radon transform,inversion formula,universal back-projection,parabolic domain
Truncation,Ellipsoid,Mathematical optimization,Mathematical analysis,Synthetic aperture radar,Remote sensing application,Dynamic aperture,Wave equation,Radon transform,Mathematics,Parabola
Journal
Volume
Issue
ISSN
8
1
1936-4954
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Markus Haltmeier142.48
Sergiy Pereverzyev Jr.212.09