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A sampling theorem for the Radon transform of finite complexity objects
2002
IEEE International Conference on Acoustics Speech and Signal Processing
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ì ae í å ð ã j ä å ae ç è é Ó ð ò ë » ì ä ì ð ø · í î °ã ª ae É ã j î é ( ì î X ò I ae É ã ( ð ð À í j ø 7 è í è þ ¡ ã ( è » ó ae ç ä ç ễ ì i ó D ð m ç é ( è ã j ae É ð õ v ð û » ò ë D ã ( ð °ð k ê î ...
À P w 2 w Á ¥ Á Á õ ( ö v ë ç ò ë À ç ä å ae ç ì i ð ê ë » ã s ê d t q f v u 6 w A y P h 2 ç É ð ¡ ì ç è é 7 ä À ã ( ó ì & û å À í j ø ã s ê B ae ì ã ð k ê © ä & ç î ã ò ð õ ã ( è » ó X ê ë » ã s ê " ...
doi:10.1109/icassp.2002.1005963
fatcat:3syhnimk5zh6ncgcikzmjfqlke
A sampling theorem for the Radon transform of finite complexity objects
2002
IEEE International Conference on Acoustics Speech and Signal Processing
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ì ae í å ð ã j ä å ae ç è é Ó ð ò ë » ì ä ì ð ø · í î °ã ª ae É ã j î é ( ì î X ò I ae É ã ( ð ð À í j ø 7 è í è þ ¡ ã ( è » ó ae ç ä ç ễ ì i ó D ð m ç é ( è ã j ae É ð õ v ð û » ò ë D ã ( ð °ð k ê î ...
À P w 2 w Á ¥ Á Á õ ( ö v ë ç ò ë À ç ä å ae ç ì i ð ê ë » ã s ê d t q f v u 6 w A y P h 2 ç É ð ¡ ì ç è é 7 ä À ã ( ó ì & û å À í j ø ã s ê B ae ì ã ð k ê © ä & ç î ã ò ð õ ã ( è » ó X ê ë » ã s ê " ...
doi:10.1109/icassp.2002.5744015
dblp:conf/icassp/MaravicV02
fatcat:yboljocfinen3ntf57gucjr34i
Finite Radon Transform as Subcarriers Mapping Technique for OFDM System
2022
Journal of Communications Software and Systems
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Finite groups represent digital images; the Finite Radon Transform (FRAT) is then applied. ...
To overcome the periodization effect of a finite transform, Do and Vetterli [1] introduce a novel ordering of the FRAT coefficients. ...
THE FINITE RADON TRANSFORM (FRAT) The Finite Radon Transform (FRAT) has been discussed in many research papers and defined for 2-D images. ...
doi:10.24138/jcomss-2022-0043
fatcat:6ufdw62lx5c2ln6qmz6elywtza
Compressed sensing electron tomography
2013
Ultramicroscopy
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Still demonstrates the feasibility of undersampled recovery, which is evidently of interest for some tomography applications. ...
For biological tomograms, CS-ET matches or exceeds alternative methods, but by a smaller margin. ...
Each image is a projection of the rotated object, a sequence of images indexed by rotation angle is a tilt series. ...
doi:10.1016/j.ultramic.2013.03.019
pmid:23834932
fatcat:im76pmc4fndsdjhujzao7emyee
SPECTRAL PROPERTIES OF PROJECTION SIGNALS IN 3-D TOMOGRAPHY
2005
IFAC Proceedings Volumes
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Compared to the traditional progressive sampling method, a reduction of sampling points by the factor 4 is achieved. ...
On the basis of this result, an optimal interleaved sampling pattern is established. ...
The Radon transform and its 3-D extension are the underlying fundamental concept used for 2-D and 3-D tomography. Via Radon transform the projection signals and the image object are related. ...
doi:10.3182/20050703-6-cz-1902.00183
fatcat:u7u7hn472fhpvcbk3lvyv4z6l4
CT Reconstruction From Parallel and Fan-Beam Projections by a 2-D Discrete Radon Transform
2012
IEEE Transactions on Image Processing
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In this paper, we demonstrate the applicability of the inverse DRT for the reconstruction of a 2-D object from its continuous projections. ...
The discrete Radon transform (DRT) was defined by Abervuch et al. as an analog of the continuous Radon transform for discrete data. ...
FRAs are based on the Fourier slice theorem [2] , which states that the Fourier transform of a projection at angle is a radial slice through the 2-D Fourier transform of the object at direction . ...
doi:10.1109/tip.2011.2164416
pmid:21843992
fatcat:p457sxsep5blvbm5uzo4czjfbm
Relation-based variations of the discrete radon transform
1996
Computers and Mathematics with Applications
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The finite Radon transform was introduced by Bolker around 1976. Since then, many variations of the discrete Radon transform have been proposed. ...
In this paper, we first propose a variation of the discrete Radon transform which is based on a binary relation. ...
bcB In this paper, we will consider a more general variation of the Radon transformation that will unify most variations of the finite Radon transformation. ...
doi:10.1016/0898-1221(95)00208-1
fatcat:jnllqppo7ngvbcfpfysln5juvy
The Radon transform on SO(3): a Fourier slice theorem and numerical inversion
2008
Inverse Problems
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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). ...
editor for their helpful comments and valuable suggestions. ...
doi:10.1088/0266-5611/24/2/025011
fatcat:3oq2efczhvgvpjctiakr3acjia
Page 6861 of Mathematical Reviews Vol. , Issue 2001I
[page]
2001
Mathematical Reviews
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This sampling theorem is used to give a formula reconstructing a function from the samples of its Radon transform. ...
) Irregular sampling and the Radon transform. ...
The raised-cosine wavelets in computerized tomography
2004
Applicable Analysis
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In Computerized Tomography (CT), an image must be recovered from its sampled projections in the form of values of the Radon transform. ...
In this work a method of recovering the image is based on the properties of the raised-cosine wavelet. This wavelet has a closed form which allows for certain precomputations and avoids convolution. ...
Mathematically, this is exactly the Radon transform R f ðtÞ of the object function. More details on the theory and applications of the Radon transform can be found in [7] . ...
doi:10.1080/00036810310001632862
fatcat:wqhpuhqfmveufk7xv6w4xitx2a
A Framework for Discrete Integral Transformations I—The Pseudopolar Fourier Transform
2008
SIAM Journal on Scientific Computing
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The algorithm relies on a discrete Fourier slice theorem, which associates the discrete Radon transform with the pseudo-polar Fourier transform [14] . ...
The Radon transform is a fundamental tool in many areas. For example, in reconstruction of an image from its projections (CT scanning). ...
We can now given an explicit formula for the adjoint Radon transform. Theorem 3.11. ...
doi:10.1137/060650283
fatcat:4d5rzevp4refvkbahnwegersze
Investigation of the noise properties of a new class of reconstruction methods in diffraction tomography
1999
International journal of imaging systems and technology (Print)
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From the estimated Radon transforms, one can readily reconstruct the object function by using a variety of existing reconstruction algorithms. ...
This strategy leads to the development of an infinite class of estimation methods, that from the measured scattered data, can estimate the Radon transform of the scattering object function. ...
According to the central slice theorem, the 1D FT of the Radon transform corresponds to the 2D FT of the scattering object function a(r, ) in a polar coordinate system. ...
doi:10.1002/(sici)1098-1098(1999)10:6<437::aid-ima5>3.0.co;2-0
fatcat:ooflswc27vcspa36tbquvtqtl4
The discrete diffraction transform
2008
IMA Journal of Applied Mathematics
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Unlike the DRT, though, this transform cannot be used for reconstruction of the object from the set of rotated projections. ...
We prove that when the DDT is applied to a set of samples of a continuous object, it approximates a set of continuous vertical diffracted projections of a horizontally sheared object and a set of continuous ...
Actually, the 2D Radon transform of a discrete object along a line can be viewed as a 'discrete projection' of the object. ...
doi:10.1093/imamat/hxn010
fatcat:kxmah2rlhfg6digtymwhuuqpwa
An interesting feature of the radon transform
1995
Applied Mathematics Letters
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It is shown that the reconstructed image in two-dimensional, parallel beam tomography has an imaginary component which, while zero for perfect data, is of necessity nonzero with real world data. ...
The first is as an indicator function of the efficacy of corrective measures taken to correct flaws in the original data or in the processing technique. ...
SECTION 2 The Radon transform of the two-dimensionai attenuation coefficient f(x, y) consists of straight line integrals of f(x, y) along rays or beams in a plane through the three-dimensionai object to ...
doi:10.1016/0893-9659(95)00051-q
fatcat:wt6usnelnra2dmqxxuquemndvi
Regularization Methods for Phase Retrieval and Phase Contrast Tomography
2015
Abstract and Applied Analysis
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In this work, the convergence properties of regularization approaches for phase retrieval and phase contrast tomography are investigated. ...
Yet, the functional framework and the convergence properties of the methods have not been studied in detail. ...
convergence theorem, the Fourier transform is a continuous function. ...
doi:10.1155/2015/943501
fatcat:bdwhysrnvrgwdlhkk6jnym37wi
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