Reconstruction algorithm for 3D Compton scattering imaging with incomplete data

Abstract

Compton scattering describes the scattering of a photon after its collision with an electron. The recent developments of spectral cameras, able to collect photons in terms of energy, open the way to a new imaging concept: 3D Compton scattering imaging (CSI), which seeks to exploit the scattered radiation as a vector of information while a specimen of interest is illuminated by a monochromatic ionizing source. Focusing on modelling the first-order scattering, image reconstruction from CSI data remains a difficult challenge. In particular, physical constraints (detector and architecture of the scanner) lead to various incompleteness scenario within the data and thus streak artifacts when using filtered backprojection type formulas. This paper addresses the problem of recovering an object under study using CSI data subject to incompleteness and assuming only first-order scattering. The proposed method consists of suitably tuning the multiplicative Kaczmarz algorithm and is implemented and tested for two architectures of the scanner. Furthermore, the modality on CSI considered here presents the advantage of not requiring any rotation of the source or object.