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Development, analysis and implementation of exact inversion formulas for cone beam vector tomography

Subject Area Mathematics
Term from 2014 to 2017
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 256416862
 
Inversion of the cone beam transform in the case of scalar functions has received much attention, and various efficient inversion formulas were derived during the past decade. The cone-beam geometry is of greatest relevance in view of practical applications. The cone-beam transform of vector fields has been studied much less, even though vector field tomography has a variety of interesting applications ranging from medical imaging to oceanography to plasma physics. One reason for less studies could be, in part, due to the fact that it is a much harder problem. Building on a recent key result of Prof. Schuster and Dr. Kazantsev, an inversion formula for the cone-beam transform of vector fields was obtained by Profs. Katsevich and Schuster in 2013. The formula consists of two additive terms. The first term is of the filtered-backprojection form, while the second term is more complicated and involves a four-dimensional integral which is numerically very costly. We propose to investigate the formula in more detail, and use the flexibilities built into the formula to simplify the second term. Then we propose to implement the formula in computer code and test its performance on numerical examples for different types of vector fields.
DFG Programme Research Grants
 
 

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