Averages over hypersurfaces smoothness of generalized Radon transforms

1990 ◽  
Vol 54 (1) ◽  
pp. 165-188 ◽  
Author(s):  
C. D. Sogge ◽  
E. M. Stein
Keyword(s):  
Radon Transforms ◽  
Generalized Radon Transforms

scholarly journals Multilinear generalized Radon transforms and point configurations

2015 ◽  
Vol 27 (4) ◽  
Author(s):  
Loukas Grafakos ◽  
Allan Greenleaf ◽  
Alex Iosevich ◽  
Eyvindur Palsson
Keyword(s):  
Linear Case ◽  
General Mechanism ◽  
Radon Transforms ◽  
Graph Theoretic ◽  
Point Configurations ◽  
Generalized Radon Transforms

AbstractWe study multilinear generalized Radon transforms using a graph-theoretic paradigm that includes the widely studied linear case. These provide a general mechanism to study Falconer-type problems involving (

scholarly journals A fast butterfly algorithm for generalized Radon transforms

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. U41-U51 ◽  
Author(s):  
Jingwei Hu ◽  
Sergey Fomel ◽  
Laurent Demanet ◽  
Lexing Ying
Keyword(s):  
Integral Operator ◽  
Radon Transform ◽  
Model Space ◽  
Oscillatory Integral ◽  
Fourier Integral ◽  
Low Rank ◽  
Radon Transforms ◽  
Low Rank Approximation ◽  
Data Set ◽  
Generalized Radon Transforms

Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator and to construct a blockwise low-rank approximation of the kernel function. The overall structure follows the Fourier integral operator butterfly algorithm. For 2D data, the algorithm runs in complexity [Formula: see text], where [Formula: see text] depends on the maximum frequency and offset in the data set and the range of parameters (intercept time and slowness) in the model space. From a series of studies, we found that this algorithm can be significantly more efficient than the conventional time-domain integration.

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