An exact inversion formula for cone beam vector tomography
Abbreviated Journal Title
RECONSTRUCTION ALGORITHM; IMPLEMENTATION; TRANSFORM; FIELDS; Mathematics, Applied; Physics, Mathematical
In this paper, we present an exact inversion formula for the cone beam transform of vector fields. This transform is the mathematical model for vector tomography with cone beam data. The cone beam data consist of line integrals of a vector field along rays which emanate from points on a given source trajectory. It is known that an exact reconstruction of the solenoidal part of the searched for vector field is possible if the trajectory satisfies the Tuy condition of order 3. We derive an inversion formula under the assumption that the source trajectory satisfies Tuy's condition of order 3 and the vector field is smooth and compactly supported. This formula thus represents an analogue of the known inversion formulas for the scalar cone beam transform.
"An exact inversion formula for cone beam vector tomography" (2013). Faculty Bibliography 2010s. 4190.