On discrete X-ray transform

TL;DR

This paper investigates a discrete version of the X-ray transform, proposing a non-overdetermined reconstruction method, extending it to weighted cases, and exploring its connections to the continuous transform.

Contribution

It introduces a non-overdetermined reconstruction approach for the discrete X-ray transform and extends the framework to weighted and attenuated variants.

Findings

Proposes a non-overdetermined reconstruction method.

Extends the discrete X-ray transform to weighted and attenuated cases.

Explores the relationship between discrete and continuous X-ray transforms.

Abstract

We consider a discrete version of X-ray transform going back, in particular, to Strichartz (1982). We suggest non-overdetermined reconstruction for this discrete transform. Extensions to weighted (attenuated) analogues are given. Connections to the continuous case are presented.