# An approach to the spherical mean Radon transform with detectors on a line

## TL;DR

This paper introduces a new consistency-based method for inverting the 2D spherical Radon transform with detectors on a line, providing a practical iterative algorithm for functions supported on one side of the line, relevant to tomography.

## Contribution

It proposes a novel consistency method and iterative formula for approximate inversion of the 2D spherical Radon transform with line detectors, addressing the lack of exact formulas.

## Key findings

- Proved local description of the reconstruction process.
- Developed a practical iterative algorithm for functions on one side of a line.
- Applicable to thermo- and photo-acoustic tomography problems.

## Abstract

The article suggests a new approach what is called a consistency method for the inversion of the spherical Radon transform in 2D with detectors on a line. It is known that there is not an exact inversion formula in 2D. By means of the method was proved that the reconstruction has a local description and found a new iteration formula which give an practical algorithm to recover an unknown function supported completely on one side of a line $L$ from its spherical means over circles centered on the line $L$. Such an inversion is required in problems of thermo- and photo-acoustic tomography.