Approximate Reconstruction from Circular and Spherical Mean Radon Transform Data

2013 ◽  
pp. 155-165
Author(s):  
W. Madych
Keyword(s):  
Radon Transform ◽  
Spherical Mean ◽  
Approximate Reconstruction

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.

scholarly journals Range descriptions for the spherical mean Radon transform

2007 ◽  
Vol 248 (2) ◽  
pp. 344-386 ◽  
Author(s):  
Mark Agranovsky ◽  
Peter Kuchment ◽  
Eric Todd Quinto
Keyword(s):  
Radon Transform ◽  
Spherical Mean

To recovering the moments from the spherical mean Radon transform

2020 ◽  
Vol 490 (2) ◽  
pp. 124334
Author(s):  
Rafik H. Aramyan ◽  
Robert M. Mnatsakanov
Keyword(s):  
Radon Transform ◽  
Spherical Mean
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