Inversion formulas for quarter-spherical Radon transforms

Abstract

The applications of spherical Radon transforms include synthetic aperture radar, sonar tomography, and medical imaging modalities. A spherical Radon transform maps a function to its integrals over a family of spheres. Recently, several types of incomplete spherical Radon transforms have received attention in research. This study examines two types of quarter-spherical Radon transforms that assign a function to its integral over a quarter of a sphere: 1) center of a quarter sphere of integration on a plane, and 2) center on a line and the rotation of the quarter sphere. Furthermore, we present inversion formulas for these two quarter-spherical Radon transforms.

Keywords

• photoacoutic
• tomography
• radon transform
• inversion
• a quarter sphere