scholarly journals Time-invariant radon transform by generalized Fourier slice theorem

2017 ◽  
Vol 11 (3) ◽  
pp. 501-519 ◽  
Author(s):  
Ali Gholami ◽  
◽  
Mauricio D. Sacchi ◽  
Keyword(s):  
Radon Transform ◽  
Slice Theorem ◽  
Time Invariant ◽  
Fourier Slice Theorem

scholarly journals The Radon transform on SO(3): a Fourier slice theorem and numerical inversion

2008 ◽  
Vol 24 (2) ◽  
pp. 025011 ◽  
Author(s):  
R Hielscher ◽  
D Potts ◽  
J Prestin ◽  
H Schaeben ◽  
M Schmalz
Keyword(s):  
Radon Transform ◽  
Numerical Inversion ◽  
Slice Theorem ◽  
Fourier Slice Theorem

scholarly journals Robust Digital Image Reconstruction via the Discrete Fourier Slice Theorem

2014 ◽  
Vol 21 (6) ◽  
pp. 682-686 ◽  
Author(s):  
Shekhar S. Chandra ◽  
Nicolas Normand ◽  
Andrew Kingston ◽  
Jeanpierre Guedon ◽  
Imants Svalbe
Keyword(s):  
Image Reconstruction ◽  
Digital Image ◽  
Slice Theorem ◽  
Fourier Slice Theorem

scholarly journals Deprojection of Galaxies: How Much Can Be Learned?

1987 ◽  
Vol 127 ◽  
pp. 397-398 ◽  
Author(s):  
George B. Rybicki
Keyword(s):  
Symmetry Axis ◽  
Three Dimensional ◽  
Light Distribution ◽  
Axially Symmetric ◽  
Simple Criterion ◽  
Slice Theorem ◽  
Intrinsic Shape ◽  
Model Independent ◽  
Fourier Slice Theorem

A general discussion, based on the ht “Fourier Slice Theorem,” is given for the problem of deprojecting the observed light distribution of galaxies to obtain their intrinsic three dimensional light distribution or “shape.” Several results are obtained: 1) A model-independent deprojection of an axially symmetric galaxy is shown to be possible only if the symmetry axis lies in the plane of the sky. 2) A simple criterion is given to test whether two different galaxies can have the same intrinsic shape, based solely on their observed projections. 3) It is shown that a homogeneous class of galaxies can be deprojected using a sufficiently large number of projections of random perspective.

A Robust and Efficient Sparse Time-Invariant Radon Transform in the Mixed Time–Frequency Domain

2019 ◽  
Vol 57 (10) ◽  
pp. 7558-7566 ◽  
Author(s):  
Benfeng Wang ◽  
Yingqiang Zhang ◽  
Wenkai Lu ◽  
Jianhua Geng
Keyword(s):  
Frequency Domain ◽  
Radon Transform ◽  
Time Frequency ◽  
Time Invariant

On resolution and uniqueness in anisotropic crosshole traveltime tomography

Geophysics ◽  
1998 ◽  
Vol 63 (4) ◽  
pp. 1184-1189 ◽  
Author(s):  
Paul R. Williamson
Keyword(s):  
Velocity Field ◽  
Radon Transform ◽  
P Wave ◽  
Traveltime Tomography ◽  
Slice Theorem ◽  
Spatial Frequencies ◽  
Specific Calculations ◽  
Dc Component ◽  
Spatially Varying ◽  
Spatial Support

The inclusion of anisotropy in P-wave traveltime tomography has been undertaken by several authors and in all cases some loss of resolution and uniqueness compared to the isotropic problem was observed. The origin of this problem is analysed for straight‐ray tomography using the Radon transform and the projection slice theorem. This analysis shows that the separation of the anisotropy from the isotropic velocity field can only be guaranteed for the dc component. Resolution at higher spatial frequencies depends upon the spatial support of the object, that is the separation of the holes in crosshole work, and the range of ray angles available. Specific calculations in the crosshole case suggest that even in media known to be horizontally stratified, it will probably be difficult to estimate spatially varying elliptical anisotropy at wavelengths less than a few times smaller than the hole separation, and Thomsen’s parameter, delta at wavelengths less than the hole separation itself. These results broadly agree with the empirical observations in the literature.

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