Unique tomographic reconstruction of vector fields using boundary data
The problem of reconstructing a vector field v(r) from its line integrals (through some domain D) is generally undetermined since v(r) is defined by two component functions. When v(r) is decomposed into its irrotational and solenoidal components, it is shown that the solenoidal part is uniquely dete...
| Veröffentlicht in: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 1(1992), 3 vom: 15., Seite 406-12 |
|---|---|
| 1. Verfasser: | |
| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1992
|
| Zugriff auf das übergeordnete Werk: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society |
| Schlagworte: | Journal Article |
| Zusammenfassung: | The problem of reconstructing a vector field v(r) from its line integrals (through some domain D) is generally undetermined since v(r) is defined by two component functions. When v(r) is decomposed into its irrotational and solenoidal components, it is shown that the solenoidal part is uniquely determined by the line integrals of v(r). This is demonstrated in a particularly simple manner in the Fourier domain using a vector analog of the well-known projection slice theorem. In addition, under the constraint that v (r) is divergenceless in D, a formula for the scalar potential phi(r) is given in terms of the normal component of v(r) on the boundary D. An important application of vector tomography, i.e., a fluid velocity field from reciprocal acoustic travel time measurements or Doppler backscattering measurements, is considered |
|---|---|
| Beschreibung: | Date Completed 02.10.2012 Date Revised 25.02.2008 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1057-7149 |