Paper Info
Title
Recovering The Initial Data Of The Wave Equation From Neumann Traces
Abstract
We study the problem of recovering the initial data (f; 0) of the standard wave equation from the Neumann trace (the normal derivative) of the solution on the boundary of convex domains in arbitrary spatial dimension. Among others, this problem is relevant for tomographic image reconstruction including photoacoustic tomography. We establish explicit inversion formulas of the back-projection type that recover the initial data up to an additive term defined by a smoothing integral operator. In the case that the boundary of the domain is an ellipsoid, the integral operator vanishes, and hence we obtain an analytic formula for recovering the initial data from Neumann traces of the wave equation on ellipsoids.
Year
DOI
Venue
2021
10.1137/20M1362322
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
DocType
Volume
image reconstruction, wave equation, inversion formula, Neumann trace, computed tomography
Journal
53
Issue
ISSN
Citations 
2
0036-1410
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Florian Dreier100.68
Markus Haltmeier27414.16