Research Article
Circular Harmonic Decomposition Approach for Numerical Inversion of Circular Radon Transforms
@INPROCEEDINGS{10.4108/icst.valuetools.2011.245815, author={Ga\`{\i}l Rigaud and Ma\~{n} K. Nguyen and Alfred K. Louis }, title={Circular Harmonic Decomposition Approach for Numerical Inversion of Circular Radon Transforms}, proceedings={1st International ICST Workshop on New Computational Methods for Inverse Problems}, publisher={ACM}, proceedings_a={NCMIP}, year={2012}, month={6}, keywords={Radon transforms (RT) Circular Radon transform (CRT) Circular-arc Radon transform (CART) image reconstruction Circular Harmonic Decomposition (CHD) Compton scattering tomography (CST)}, doi={10.4108/icst.valuetools.2011.245815} }- Gaël Rigaud
Maï K. Nguyen
Alfred K. Louis
Year: 2012
Circular Harmonic Decomposition Approach for Numerical Inversion of Circular Radon Transforms
NCMIP
ICST
DOI: 10.4108/icst.valuetools.2011.245815
Abstract
Numerical inversions via circular harmonic decomposition for two classes of circular Radon transforms are established. The rst class deals with the Radon transform (RT) de- ned on circular arcs having a chord of xed length rotating around its middle point (CART) and the second is the RT de ned on a set of circles passing through a xed point of the plane (CRT). These circular Radon transforms arise from the modeling of di erent modalities in Compton scattering tomography (CST). Inversions via circular harmonic decomposition are used for image reconstructions in CST. Simulation results show the eciency and interest of this inversion method in imaging science.
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