Microlocal properties of the Radon transform on V-lines: A framework to reduce artifacts due to intrinsic missing data in linear Compton cameras

Abstract

Microlocal Analysis constitutes a theoretical framework based on Fourier analysis and differential geometry that provides a precise characterization of singularities in image reconstruction in the context of the classical Radon transform theory. Accurate descriptions of artifacts together with strategies to mitigate them have been proposed since it was introduced. Artifacts due to missing data are presumably the most challenging problem addressed by microlocal analysis. Recent extensions of these analytical concepts to the field of transmission Compton tomography show the efficacy of this theoretical framework. Conversely, in the case of Compton cameras, an emission technique wherein the issue of missing data is an intrinsic problem, these ideas are still unexplored. In this work we introduce a Radon transform over double V-lines, presenting its key properties for deriving a filtered back-projection formula. This theoretical groundwork enables us to outline an initial methodology utilizing microlocal analysis to develop a framework aimed at mitigating the main artifacts produced by the limited size of detectors in linear Compton cameras.