On the inversion of generalized Radon transforms over n-dimensional paraboloids
Z. Ustaoglu
article (Uluslararası, Hakemli) | Yazar(lar): Z. Ustaoglu | Yıl: 2024 | Dergi/Kurum: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | İndeks: WOS.SCI | DOI: 10.1016/j.jmaa.2023.127799 | Anahtar Kelimeler: Generalized Radon transform, Inversion formula, Paraboloid — Özet: In this paper, we investigate the problem of
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.