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A Framework for Discrete Integral Transformations I—The Pseudopolar Fourier Transform

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Israeli, Y. Shkolnisky
2008 SIAM Journal on Scientific Computing  
The algorithm relies on a discrete Fourier slice theorem, which associates the discrete Radon transform with the pseudo-polar Fourier transform [14] .  ...  The discrete 2D definition of the Radon transform is shown to be geometrically faithful as the lines used for summation exhibit no wraparound effects.  ...  The fast algorithms for the pseudo-polar Fourier transform provide fast forward and inverse algorithms for the discrete Radon transform.  ... 
doi:10.1137/060650283 fatcat:4d5rzevp4refvkbahnwegersze

Page 4858 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
(FIN-TUT-SG; Tampere Fast quantum -D Fourier and Radon transforms.  ...  The algorithms are based on the decomposition of the transform into a product of an n-dimensional discrete Radon transform and a family of parallel one-dimensional transforms.  ... 

3-D Discrete Analytical Ridgelet Transform

David Helbert, Philippe Carre, ric Andres
2006 IEEE Transactions on Image Processing  
This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform.  ...  The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain.  ...  Principles of the 3-D Discrete Radon Transform The discretization of the 3-D Radon transform is the extension of the 2-D discrete Radon transform method: 1) Compute the 3-D Discrete Fourier Transform of  ... 
doi:10.1109/tip.2006.881936 pmid:17153944 fatcat:u5v7waxsjfaobiqelzi7e5yjh4

Discrete analytical Ridgelet transform

Philippe Carre, Eric Andres
2004 Signal Processing  
This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform.  ...  The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain.  ...  Principles of the 3-D Discrete Radon Transform The discretization of the 3-D Radon transform is the extension of the 2-D discrete Radon transform method: 1) Compute the 3-D Discrete Fourier Transform of  ... 
doi:10.1016/j.sigpro.2004.07.009 fatcat:zu7hwjxnkrck7bv6jl52nc5tia

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

R Hielscher, D Potts, J Prestin, H Schaeben, M Schmalz
2008 Inverse Problems  
Based on a Fourier slice theorem the discrete inverse Radon transform of a function sampled on the product space S 2 × S 2 of two two-dimensional spheres is determined as the solution of a minimization  ...  This communication presents a novel approach to the numerical inversion of the one-dimensional Radon transform on SO(3).  ...  Acknowledgments The authors gratefully acknowledge financial support by Deutsche Forschungsgemeinschaft, grant "high resolution texture analysis" (PR 331/11, SCHA 465/15) and thank the referees and the  ... 
doi:10.1088/0266-5611/24/2/025011 fatcat:3oq2efczhvgvpjctiakr3acjia

Compressed sensing electron tomography

Rowan Leary, Zineb Saghi, Paul A. Midgley, Daniel J. Holland
2013 Ultramicroscopy  
Still demonstrates the feasibility of undersampled recovery, which is evidently of interest for some tomography applications.  ...  Experimental results For phantoms with the nanoparticle statistical properties, CS-ET recovery is markedly better than alternative methods.  ...  ET Radon data can be numerically transformed into 2D Fourier samples on a polar grid. From a computational perspective, these are non-uniform discrete Fourier transform (NDFT) samples.  ... 
doi:10.1016/j.ultramic.2013.03.019 pmid:23834932 fatcat:im76pmc4fndsdjhujzao7emyee

Fast numerical inversion of the attenuated Radon transform with full and partial measurements

Guillaume Bal, Philippe Moireau
2004 Inverse Problems  
The method is based on an extension of the fast slant stack algorithm developed for the Radon transform.  ...  We propose a numerical method to simulate and invert the two-dimensional attenuated Radon transform (AtRT) from full (360 • ) or partial (180 • ) measurements.  ...  The first author also acknowledges support from an Alfred P Sloan fellowship.  ... 
doi:10.1088/0266-5611/20/4/009 fatcat:dwanjr3hhjbqreygt7mmrg7rru

Irregular Sampling Of The Radon Transform Of Bandlimited Functions

Laurent Demaret, Thomas Wiese
2013 Zenodo  
Publication in the conference proceedings of SampTA, Bremen, Germany, 2013  ...  SAMPLING THEOREMS FOR THE RADON TRANSFORM The developments from the previous section allow us to apply the theory of bandlimited functions to the sampled Radon transform.  ...  Bandlimitedness conditions also appear implicitly in reconstruction techniques based on discretizations of the inverse Radon transform.  ... 
doi:10.5281/zenodo.54450 fatcat:sdbvioek5rcylpij5gytoqjxk4

Irregular Sampling of the Radon Transform of Bandlimited Functions [article]

Thomas Wiese, Laurent Demaret
2013 arXiv   pre-print
First, we prove that the Radon transform is a continuous L2-operator for certain classes of bandlimited signals.  ...  We provide conditions for exact reconstruction of a bandlimited function from irregular polar samples of its Radon transform.  ...  SAMPLING THEOREMS FOR THE RADON TRANSFORM The developments from the previous section allow us to apply the theory of bandlimited functions to the sampled Radon transform.  ... 
arXiv:1307.1151v1 fatcat:uaknufdkeve2hawistcqzrv3nu

Page 2581 of Mathematical Reviews Vol. , Issue 92e [page]

1992 Mathematical Reviews  
over a finite field is initiated chiefly by the possible applications of these transforms to problems of coding theory, combinatorics, and other branches of discrete mathematics.  ...  Summary: “We present a fast algorithm which evaluates a discrete Laplace transform with N points at M arbitrarily distributed points with C(N+M) work, where C depends only on the precision 44 INTEGRAL  ... 

Application of Radon Transform for Fast Solution of Boundary Value Problems for Elliptic PDE in Domains With Complicated Geometry [chapter]

Alexandre I. Grebennikov
2010 Matrix Methods: Theory, Algorithms and Applications  
Here we extend the proposed approach and construct another version of GRmethod based on application of the direct Radon transform [Radon (1917) ] to the PDE [Sigurdur (1999); Gelfand and Shapiro (1955)  ...  GRmethod consists in application of the Radon transform directly to the PDE and in reduction PDE to assemblage of Ordinary Differential Equations (ODE).  ...  Acknowledgement Author acknowledge to VIEP BUAP, SEP and CONACYT Mexico for the support of the part of this investigation in the frame of the Projects No GRA-EXC08-I and No CB-2006-1-57479.  ... 
doi:10.1142/9789812836021_0030 fatcat:2yzqk73l65ginihnqhbeelsi3e

Computational complexity lower bounds of certain discrete Radon transform approximations [article]

Timur M. Khanipov
2018 arXiv   pre-print
For the computational model where only additions are allowed, the Ω(n^2 n) lower bound on operations count with respect to image size n× n is obtained for two types of the discrete Radon transform implementations  ...  : the fast Hough transform and a generic strip pattern class which includes the classical Hough transform, implying the fast Hough transform algorithm asymptotic optimality.  ...  , Igor Polyakov and Alexey Savchik for verifying the proofs and locating a few misprints, and Andrey Gladkov for help with the FHT pictures.  ... 
arXiv:1801.01054v1 fatcat:a4s7vky6pfgbnimskdymbtukq4

Page 44 of Mathematical Reviews Vol. , Issue 88k [page]

1988 Mathematical Reviews  
Summary: “We describe the discrete Radon transform (DRT) and the exact inversion algorithm for it.  ...  This observation allows construction of fast direct and inverse transforms.  ... 

Binary Shape Normalization Using the Radon Transform [chapter]

Salvatore Tabbone, Laurent Wendling
2003 Lecture Notes in Computer Science  
This paper presents a novel approach to normalize binary shapes which is based on the Radon transform. The key idea of the paper is an original adaptation of the Radon transform.  ...  The binary shape is projected in Radon space for different levels of the (3-4) distance transform.  ...  cary over to the discrete Radon transform only approximately, due to errors of discretization.  ... 
doi:10.1007/978-3-540-39966-7_17 fatcat:wxiso37e6bfv3djxla6vbjcgnu

Central and Periodic Multi-Scale Discrete Radon Transforms

Óscar Gómez-Cárdenes, José G. Marichal-Hernández, Jonas Phillip Lüke, José M. Rodríguez-Ramos
2021 Applied Sciences  
The multi-scale discrete Radon transform (DRT) calculates, with linearithmic complexity, the summation of pixels, through a set of discrete lines, covering all possible slopes and intercepts in an image  ...  Central DRT can provide almost a 2× speedup over conventional DRT, probably becoming the faster Radon transform algorithm available, at the cost of ignoring 15% of the summations in the corners.  ...  The details on the formulation of the discrete Radon transform can be found there.  ... 
doi:10.3390/app112210606 fatcat:shm4glttqvgr5g63722fty35v4
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