On the inversion of generalized Radon transforms over n-dimensional paraboloids

In this paper, we investigate the problem of determining a function from its surface integrals of the second type over n-dimensional circular paraboloids in Rn+1 with fixed focal length and fixed direction of symmetry axis, without any restrictions on their vertices. We obtain some inversion formulas with a method based on the Fourier transform and reducing the reconstruction problem to solving a Volterra integral equation of the first kind. We present some examples on the direct numerical implementations of the resulting inversion formulas.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we investigate the problem of determining a function from its surface integrals of the second type over n-dimensional circular paraboloids in Rn+1 with fixed focal length and fixed direction of symmetry axis. We obtain some inversion formulas with a method based on the Fourier transform and reducing the reconstruction problem to solving a Volterra integral equation of the first kind. We present some examples on the direct numerical implementations of the resulting inversion formulas.