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On the Radon Transform and Linear Transformations of Images
Proceedings of the 2019 2nd International Conference on Digital Medicine and Image Processing, 2019We present a novel original method for estimating and recovering a general geometric transformation which is applied to an image. Our main tool is the Radon Transform; we develop analysis to address the behavior of this transform under a Linear Transformation in terms of the singular value decomposition of the Transformation's matrix.
Fawaz Hjouj, Mohamed Soufiane Jouini
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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 fast discrete Radon transform
[Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, 1992An explicit relationship between the continuous and discrete time Radon transforms is derived. A generalized least-squares solution to the inversion problem is proposed, and a new inverse counterpart to the fast Radon transform (FRT) algorithm (IFRT) is derived.
Brian T. Kelley, Vijay K. Madisetti
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Radon Transform on Sobolev Spaces
Siberian Mathematical Journal, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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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-
Tai-Chiu Hsung +2 more
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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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