An Inversion Formula of the Radon Transform on the Heisenberg Group

2004 ◽  
Vol 47 (3) ◽  
pp. 389-397 ◽  
Author(s):  
Jianxun He
Keyword(s):  
Heisenberg Group ◽  
Radon Transform ◽  
Inversion Formula ◽  
Weak Sense

AbstractIn this paper we give an inversion formula of the Radon transform on the Heisenberg group by using the wavelets defined in [3]. In addition, we characterize a space such that the inversion formula of the Radon transform holds in the weak sense.

scholarly journals The Radon Transforms on the Generalized Heisenberg Group

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Tianwu Liu ◽  
Jianxun He
Keyword(s):  
Fourier Transform ◽  
Differential Operator ◽  
Heisenberg Group ◽  
Radon Transform ◽  
Inversion Formula ◽  
The Other ◽  
Radon Transforms

Let Hna be the generalized Heisenberg group. In this paper, we study the inversion of the Radon transforms on Hna. Several kinds of inversion Radon transform formulas are established. One is obtained from the Euclidean Fourier transform; the other is derived from the differential operator with respect to the center variable t. Also by using sub-Laplacian and generalized sub-Laplacian we deduce an inversion formula of the Radon transform on Hna.

INVERSION OF THE RADON TRANSFORM ASSOCIATED WITH THE CLASSICAL DOMAIN OF TYPE ONE

2005 ◽  
Vol 16 (08) ◽  
pp. 875-887 ◽  
Author(s):  
JIANXUN HE ◽  
HEPING LIU
Keyword(s):  
Wavelet Transform ◽  
Differential Operator ◽  
Lie Group ◽  
Radon Transform ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Weak Sense ◽  
Continuous Wavelet ◽  
Nilpotent Lie Group ◽  
Classical Domain

Let D(Ω,Φ) be the unbounded realization of the classical domain [Formula: see text] of type one. In general, its Šilov boundary [Formula: see text] is a nilpotent Lie group of step two. In this article we define the Radon transform on [Formula: see text], and obtain an inversion formula [Formula: see text] in terms of a determinantal differential operator. Moreover, we characterize a subspace of [Formula: see text] on which the Radon transform is a bijection. By use of the suitable continuous wavelet transform we establish a new inversion formula of the Radon transform in weak sense without the assumption of differentiability.

The d-plane radon transform on the torus $$ \mathbb{T}^n $$

2011 ◽  
Vol 14 (2) ◽  
Author(s):  
Ahmed Abouelaz
Keyword(s):  
Radon Transform ◽  
Inversion Formula ◽  
Flat Torus ◽  
Smooth Functions ◽  
Suitable Function

AbstractWe define and study the d-plane Radon transform, namely R, on the n-dimensional (flat) torus. The transformation R is obtained by integrating a suitable function f over all d-dimensional geodesics (d-planes in the torus). We specially establish an explicit inversion formula of R and we give a characterization of the image, under the d-plane Radon transform, of the space of smooth functions on the torus.

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