Inversions of the windowed ray transform

TL;DR

This paper introduces inversion formulas for the windowed ray transform, a generalization of the analytic-signal transform, facilitating the extension of functions from real to complex space.

Contribution

The paper provides new inversion formulas for the windowed ray transform, advancing the mathematical understanding of this generalized transform.

Findings

Derived multiple inversion formulas for the windowed ray transform

Extended the analytic-signal transform to higher dimensions

Enhanced methods for function extension from real to complex space

Abstract

The windowed ray transform is a natural generalization of the "Analytic-Signal Transform" which is developed to extend arbitrary functions from $\RR^n$ to $\CC^n$. We present several inversion formulas here.