Vector field reconstruction via quaternionic setting
| Autor: | Patcharee Wongsason |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Unit sphere
Vector field reconstruction Solenoidal vector field Radon transform General Mathematics Mathematical analysis General Engineering Geometry 01 natural sciences 030218 nuclear medicine & medical imaging 010101 applied mathematics 03 medical and health sciences 0302 clinical medicine Cone (topology) Physics::Accelerator Physics Vector field 0101 mathematics Quaternion Mathematics Vector potential |
| Zdroj: | Mathematical Methods in the Applied Sciences. |
| ISSN: | 0170-4214 |
| DOI: | 10.1002/mma.4637 |
| Popis: | We propose the reconstruction of the solenoidal part of a vector field supported in the unit ball in 3 dimensions by using cone beam data from a curve surrounding it, and this curve satisfies the Tuy's condition of order 3. We use the quaternionic inversion formula to decompose the solenoidal part of a vector field into 2 parts. To recover the first one, which is the main part of the solenoidal component, another definition of a cone beam transform containing both Doppler and transverse data will be introduced. The second part will be reconstructed by using information from the first part as in Katsevich and Schuster's work with less data. |
| Databáze: | OpenAIRE |
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