Circular Harmonic Decomposition Approach for Numerical Inversion of Circular Radon Transforms

Gaël Rigaud (1) , Mai K. Nguyen (1) , Alfred K. Louis (2)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes
2 IAM - Fachbereich Mathematik Universität des Saarlandess

Numerical inversions via circular harmonic decomposition for two classes of circular Radon transforms are established. The first class deals with the Radon transform (RT) defi ned on circular arcs having a chord of fixed length rotating around its middle point (CART) and the second is the RT de fined on a set of circles passing through a fixed 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 efficiency and interest of this inversion method in imaging science.

Mots clés: Radon transforms (RT); Circular Radon transform (CRT); Circular-arc Radon transform (CART); image reconstruction; Circular Harmonic Decomposition (CHD); Compton scattering tomography (CST)

Domaines: Imagerie médicale

Gaël Rigaud, Mai K. Nguyen, Alfred K. Louis. Circular Harmonic Decomposition Approach for Numerical Inversion of Circular Radon Transforms. 1st International ICST workshop on New Computational Methods for Inverse Problems (NCMIP), May 2011, Cachan, France. pp.1. ⟨hal-00665828⟩