The Doppler moment transform in Doppler tomography
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/226307
- author
- Andersson, Fredrik LU
- organization
- publishing date
- 2005
- 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
- 2016-04-01 12:38:22
- date last changed
- 2022-01-27 07:50:26
@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}},
doi = {{10.1088/0266-5611/21/4/004}},
volume = {{21}},
year = {{2005}},
}