𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Spherical Radon Transform and Related Wavelet Transforms

✍ Scribed by Boris Rubin

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
210 KB
Volume
5
Category
Article
ISSN
1063-5203

No coin nor oath required. For personal study only.

✦ Synopsis

Continuous wavelet transforms associated with the spherical Radon transform

For the operator R and for its inverse R 01 explicit representations are given in the wavelet form. As a consequence we obtain the characterization of the range of R.

πŸ“œ SIMILAR VOLUMES

Inversion of Fractional Integrals Relate
Inversion of Fractional Integrals Related to the Spherical Radon Transform
✍ Boris Rubin πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 317 KB

Explicit inversion formulas are obtained for the analytic family of fractional integrals (T : f )(x)=# n, : S n |xy| :&1 f ( y) dy on the unit sphere in R n+1 . Arbitrary complex : and n 2 are considered. In the ease :=0 the integral T : f coincides with the spherical Radon transform. For :>1 (:{1,

Wavelets on S3 and SO(3)β€”Their construct
Wavelets on S3 and SO(3)β€”Their construction, relation to each other and Radon transform of wavelets on SO(3)
✍ Swanhild Bernstein; Svend Ebert πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 385 KB

The paper at hand is concerned with creating a flexible wavelet theory on the three sphere S 3 and the rotation group SO(3). The theory of zonal functions and reproducing kernels will be used to develop conditions for an admissible wavelet. After explaining some preliminaries on group actions and so

Inversion of the Radon Transform on the
Inversion of the Radon Transform on the Laguerre Hypergroup by using Generalized Wavelets
✍ M.M. Nessibi; K. TrimΓ¨che πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 337 KB

We consider the Radon transform R , ␣ G 0, on the Laguerre hypergroup ␣ w w Ks 0, qΟ± ‫.ή’=‬ We characterize a space of infinitely differentiable and rapidly decreasing functions together with their derivatives such that R is a bijection ␣ from this space onto itself. We establish an inversion formula