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| Title | The Doppler moment transform in Doppler tomography |
| Author/s | Fredrik Andersson |
| Department/s |
Centre for Mathematical Sciences
|
| Full-text | Full text is not available in this archive |
| Alternative location (URL) | http://dx.doi.org/10.1088/0266... Restricted Access (Alternative Location) |
| Publication/Series | INVERSE PROBLEMS |
| Publishing year | 2005 |
| Volume | 21 |
| Issue | 4 |
| Pages | 1249 - 1274 |
| Document type | Journal article |
| Status | published |
| Quality controlled | yes |
| Language | English |
| Publisher | IOP Publishing |
| Abstract 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. |
| Subject |
Mathematics and Statistics |
| ISBN/ISSN/Other |
ISSN: 0266-5611 |
| Research group | Harmonic Analysis and Applications |
