Explicit Circular Harmonic Inversions of Exponential Radon Transform

TL;DR

This paper introduces new formulas for inverting the exponential Radon transform using circular harmonics, providing insights into range conditions and their implications for complex and real coefficients.

Contribution

It presents three novel inversion formulas for the exponential Radon transform with complex coefficients and analyzes their range conditions, linking Novikov's condition to traditional ones.

Findings

Derived three circular harmonic inversion formulas for the exponential Radon transform.

Established two different range conditions for the transform.

Proved that Novikov's range condition implies the traditional range condition for real coefficients.

Abstract

Using Plemelj formula we obtain three circular harmonic inversion formulas of the exponential Radon transform with complex coefficients. We also derive two different range conditions and prove that Novikov's range condition does imply the traditional range condition for real coefficients.