Session S08 - Inverse Problems and Applications

Wednesday, July 14, 16:30 ~ 17:00 UTC-3

A new toric Radon transform and its application in imaging.

Marcela Morvidone

Centro de Matemática Aplicada - Universidad Nacional de San Martín, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk we present a new toric Radon transform which models a Comtpon scattering tomography system in three dimensions. Compton scattering tomography is an emerging scanning technique with attractive applications in several fields such as non-destructive testing and medical imaging. The modality proposed here employs a fixed radiation source and a single detector moving on a spherical surface. The Radon transform modeling the data consists of integrals on toric surfaces. We show the invertibility of the toric Radon transform which ensures that the desired image of the object under study may be recovered from the measured data. We illustrate this through numerical reconstructions in three dimensions using a regularized approach.

Joint work with Javier Cebeiro (Universidad Nacional de San Martín, Argentina), Diana Rubio (Universidad Nacional de San Martín, Argentina), Cecilia Tarpau (Universite de Cergy-Pontoise, France) and Mai K. Nguyen (Universite de Cergy-Pontoise, France).

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