Crofton's function and inversion formulas in real integral geometry

1991 ◽  
Vol 25 (1) ◽  
pp. 1-5 ◽  
Author(s):  
I. M. Gel'fand ◽  
M. I. Graev
Keyword(s):  
Integral Geometry ◽  
Inversion Formulas ◽  
And Inversion

scholarly journals Ranges and Inversion Formulas for Spherical Mean Operator and Its Dual

1995 ◽  
Vol 196 (3) ◽  
pp. 861-884 ◽  
Author(s):  
M.M. Nessibi ◽  
L.T. Rachdi ◽  
K. Trimeche
Keyword(s):  
Spherical Mean Operator ◽  
Inversion Formulas ◽  
Spherical Mean ◽  
And Inversion

scholarly journals Besov-Hankel norms in terms of the continuous Bessel wavelet transform

2021 ◽  
Author(s):  
Ashish Pathak ◽  
Dileep Kumar
Keyword(s):  
Wavelet Transform ◽  
Wavelet Coefficient ◽  
Inversion Formulas ◽  
And Inversion

Using the theory of continuous Bessel wavelet transform in $L^2 (\mathbb{R})$-spaces, we established the Parseval and inversion formulas for the $L^{p,\sigma}(\mathbb{R}^+)$- spaces. We investigate continuity and boundedness properties of Bessel wavelet transform in Besov-Hankel spaces. Our main results: are the characterization of Besov-Hankel spaces by using continuous Bessel wavelet coefficient.

The vertical slice transform on the unit sphere

2019 ◽  
Vol 22 (4) ◽  
pp. 899-917 ◽  
Author(s):  
Boris Rubin
Keyword(s):  
Unit Sphere ◽  
Radon Transform ◽  
Integral Geometry ◽  
Singular Value ◽  
Hypersingular Integrals ◽  
Inversion Formulas ◽  
Spherical Mean ◽  
Singular Value Decompositions ◽  
Vertical Slice ◽  
Class Of Functions

Abstract The vertical slice transform in spherical integral geometry takes a function on the unit sphere Sn to integrals of that function over spherical slices parallel to the last coordinate axis. This transform was investigated for n = 2 in connection with inverse problems of spherical tomography. The present article gives a survey of some methods which were originally developed for the Radon transform, hypersingular integrals, and the spherical mean Radon-like transforms, and can be adapted to obtain new inversion formulas and singular value decompositions for the vertical slice transform in the general case n ≥ 2 for a large class of functions.

Nonlocal inversion formulas in real integral geometry

1978 ◽  
Vol 11 (3) ◽  
pp. 173-179 ◽  
Author(s):  
I. M. Gel'fand ◽  
S. G. Gindikin
Keyword(s):  
Integral Geometry ◽  
Inversion Formulas

A brief comparison of some Kirchhoff integral formulas for migration and inversion

Geophysics ◽  
1991 ◽  
Vol 56 (8) ◽  
pp. 1164-1169 ◽  
Author(s):  
Paul Docherty
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Reflection Coefficients ◽  
Acoustic Wave Equation ◽  
Inversion Formulas ◽  
Kirchhoff Migration ◽  
Integral Formulas ◽  
The One ◽  
And Inversion ◽  
Kirchhoff Integral

Kirchhoff migration has traditionally been viewed as an imaging procedure. Usually, few claims are made regarding the amplitudes in the imaged section. In recent years, a number of inversion formulas, similar in form to those of Kirchhoff migration, have been proposed. A Kirchhoff‐type inversion produces not only an image but also an estimate of velocity variations, or perhaps reflection coefficients. The estimate is obtained from the peak amplitudes in the image. In this paper prestack Kirchhoff migration and inversion formulas for the one‐parameter acoustic wave equation are compared. Following a heuristic approach based on the imaging principle, a migration formula is derived which turns out to be identical to one proposed by Bleistein for inversion. Prestack Kirchhoff migration and inversion are, thus, seen to be the same—both in terms of the image produced and the peak amplitudes of the output.

scholarly journals Notes on explicit and inversion formulas for the Chebyshev polynomials of the first two kinds

2019 ◽  
Vol 20 (2) ◽  
pp. 1129 ◽  
Author(s):  
Feng Qi ◽  
Da-Wei Niu ◽  
Dongkyu Lim
Keyword(s):  
Chebyshev Polynomials ◽  
Inversion Formulas ◽  
And Inversion
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