Abstract
A spherical Radon transform whose integral domain is a sphere has many applications in partial differential equations as well as tomography. This paper is devoted to the spherical Radon transform which assigns to a given function its integrals over the set of spheres passing through the origin. We present a relation between this spherical Radon transform and the regular Radon transform, and we provide a new inversion formula for the spherical Radon transform using this relation. Numerical simulations were performed to demonstrate the suggested algorithm in dimension 2.
| Original language | English |
|---|---|
| Pages (from-to) | 1029-1039 |
| Number of pages | 11 |
| Journal | Communications on Pure and Applied Analysis |
| Volume | 15 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 2016 |
Keywords
- Circular-arc
- Compton
- Radon
- Spherical
- Tomography
- Transform