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The Doppler moment transform in Doppler tomography

Andersson, Fredrik LU (2005) In Inverse Problems 21(4). p.1249-1274
Abstract
The problem of reconstructing two-dimensional vector fields from tomographic measurements based on Doppler techniques is addressed. Measurements are made along lines, from which distributions of the field component parallel to the line are obtained. A new transform, the Doppler moment transform, which extracts local information from such data, is introduced. In contrast to most previous approaches in vector tomography that are only able to treat solenoidal fields, the Doppler moment transform provides information also of the irrotational part of the field. Specifically, it gives rise to partial differential equations in the field components. Properties of the new transform and the corresponding equations are discussed, shedding light on... (More)
The problem of reconstructing two-dimensional vector fields from tomographic measurements based on Doppler techniques is addressed. Measurements are made along lines, from which distributions of the field component parallel to the line are obtained. A new transform, the Doppler moment transform, which extracts local information from such data, is introduced. In contrast to most previous approaches in vector tomography that are only able to treat solenoidal fields, the Doppler moment transform provides information also of the irrotational part of the field. Specifically, it gives rise to partial differential equations in the field components. Properties of the new transform and the corresponding equations are discussed, shedding light on questions of uniqueness. It is also shown that the differential equations can be combined to form algebraic equations in the field components. Finally, a reconstruction scheme is constructed and some numerical experiments are provided. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Inverse Problems
volume
21
issue
4
pages
1249 - 1274
publisher
IOP Publishing
external identifiers
  • wos:000231612700005
  • scopus:23244460962
ISSN
0266-5611
DOI
10.1088/0266-5611/21/4/004
language
English
LU publication?
yes
id
bf110f9c-5aae-4310-8cdc-a4cd120878f0 (old id 226307)
alternative location
http://www.iop.org/EJ/abstract/0266-5611/21/4/004
date added to LUP
2007-09-13 16:59:11
date last changed
2017-01-01 05:19:23
@article{bf110f9c-5aae-4310-8cdc-a4cd120878f0,
  abstract     = {The problem of reconstructing two-dimensional vector fields from tomographic measurements based on Doppler techniques is addressed. Measurements are made along lines, from which distributions of the field component parallel to the line are obtained. A new transform, the Doppler moment transform, which extracts local information from such data, is introduced. In contrast to most previous approaches in vector tomography that are only able to treat solenoidal fields, the Doppler moment transform provides information also of the irrotational part of the field. Specifically, it gives rise to partial differential equations in the field components. Properties of the new transform and the corresponding equations are discussed, shedding light on questions of uniqueness. It is also shown that the differential equations can be combined to form algebraic equations in the field components. Finally, a reconstruction scheme is constructed and some numerical experiments are provided.},
  author       = {Andersson, Fredrik},
  issn         = {0266-5611},
  language     = {eng},
  number       = {4},
  pages        = {1249--1274},
  publisher    = {IOP Publishing},
  series       = {Inverse Problems},
  title        = {The Doppler moment transform in Doppler tomography},
  url          = {http://dx.doi.org/10.1088/0266-5611/21/4/004},
  volume       = {21},
  year         = {2005},
}