The Doppler moment transform in Doppler tomography
Författare
Summary, in English
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.
Avdelning/ar
Publiceringsår
2005
Språk
Engelska
Sidor
1249-1274
Publikation/Tidskrift/Serie
Inverse Problems
Volym
21
Issue
4
Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
IOP Publishing
Ämne
- Mathematics
Status
Published
Forskningsgrupp
- Harmonic Analysis and Applications
ISBN/ISSN/Övrigt
- ISSN: 0266-5611