Numerical inversion and uniqueness of a spherical radon transform restricted with a fixed angular span

In this paper, we study a spherical Radon transform that maps a function to its surface integrals over spheres restricted with a fixed angular span. Such transform is relevant for various image reconstruction problems arising in medical, radar and sonar imaging. This paper contains uniqueness results for the spherical Radon transform in the case of a fixed angular span, valid when the support of the image function is inside or outside the data acquisition sphere. Furthermore, we present simulation results for the numerical inversion in the special case of the spherical cap Radon transform.