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A Generalized Radon Transform on the Plane
Constructive Approximation, 2010The authors define a new generalized Radon transform \(R_{\alpha,\beta}\) on the plane for functions even on each variable. Such \(R_{\alpha,\beta}\) has natural connections with the bivariate Hankel transform, the generalized biaxially symmetric potential operator \(\Delta_{\alpha\beta}\), and the Jacobi polynomial \(P^{(\beta, \alpha)}_k(t)\).
Li, Zhongkai, Song, Futao
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The discrete periodic Radon transform
IEEE Transactions on Signal Processing, 1996In this correspondence, a discrete periodic Radon transform and its inversion are developed. The new discrete periodic Radon transform possesses many properties similar to the continuous Radon transform such as the Fourier slice theorem and the convolution property, etc. With the convolution property, a 2-D circular convolution can be decomposed into 1-
Daniel P K Lun, Wan-Chi Siu
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Radon transform for face recognition
Artificial Life and Robotics, 2010Face recognition is an important biometric because of its potential applications in many fields such as access control, surveillance, and human-computer interactions. In this article, an investigation of the effect of the step size for both the angle and the vector of the Radon transform on the performance of a face recognition system based on ...
Jamal Ahmad Dargham +3 more
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On the Invertibility of the Discrete Radon Transform
SIAM Journal on Discrete Mathematics, 1989Summary: The Radon transform is a useful device for analyzing multidimensional data. It is closely connected to what has become known as ``projection pursuit''. For the case of discrete data, theorems that address its invertibility are proven. Connections to the projective group over GF(2) and block designs naturally arise.
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On locality of Radon to Riesz transform
Signal Processing, 2016In this paper we present a novel approach to locally compute the Riesz transform from the knowledge of the Radon transform. Previous implementations of the Riesz transform are based on the Fourier or the Radon transforms and their inversion formulae, and therefore needs for the knowledge of the function or its Radon data on the whole domain.
Laurent Desbat, Valérie Perrier
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Wavelet localization of the Radon transform
IEEE Transactions on Signal Processing, 1994The authors develop an algorithm which significantly reduces radiation exposure in X-ray tomography, when a local region of the body is to be imaged. The algorithm uses the properties of wavelets to essentially localize the Radon transform. This algorithm differs from previous algorithms for doing local tomography because it recovers an approximation ...
Tim Olson, Joe DeStefano
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2008
In this article a special type of Radon transform (Kipriyanov-Radon transform K γ ) is considered and some properties of this transform are proved. The main results of this work are the inversion formulas of K γ , which were obtained with a help of general B-hypersingular integrals.
Ekaterina Gots, Lev Lyakhov
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In this article a special type of Radon transform (Kipriyanov-Radon transform K γ ) is considered and some properties of this transform are proved. The main results of this work are the inversion formulas of K γ , which were obtained with a help of general B-hypersingular integrals.
Ekaterina Gots, Lev Lyakhov
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2009
For a given function f defined in the plane, which may represent, for instance, the attenuation-coefficient function in a cross section of a sample, the fundamental question of image reconstruction calls on us to consider the value of the integral of f along a typical line l t , θ.
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For a given function f defined in the plane, which may represent, for instance, the attenuation-coefficient function in a cross section of a sample, the fundamental question of image reconstruction calls on us to consider the value of the integral of f along a typical line l t , θ.
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1998
The Radon transform, which was first discussed in 1912 by J. Radon, can be seen as a special case of a symmetry-preserving integral transform. The theory of this transformation is closely connected to Fourier transforms. The name Radon transform was first used by F. John in 1955.
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The Radon transform, which was first discussed in 1912 by J. Radon, can be seen as a special case of a symmetry-preserving integral transform. The theory of this transformation is closely connected to Fourier transforms. The name Radon transform was first used by F. John in 1955.
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Proceedings of International Conference on Image Processing, 2002
A convex elliptical region of the plane supports a positive-valued function of two variables whose Radon transform depends only on the slope of the integrating line: any two parallel lines that intersect the ellipse generate equal line integrals of the function. It is somewhat surprising that such a function exists.
Thomas L. Marzetta, Larry A. Shepp
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A convex elliptical region of the plane supports a positive-valued function of two variables whose Radon transform depends only on the slope of the integrating line: any two parallel lines that intersect the ellipse generate equal line integrals of the function. It is somewhat surprising that such a function exists.
Thomas L. Marzetta, Larry A. Shepp
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