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Topic: Radon transform

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	Radon transform - InformationBlast
		The Radon transform integrates a function over lines in the plane, mapping a function of position to a function of the slope and the y-intercept.
		This transform in two dimensions and three dimensions (where a function is integrated over planes) was introduced in a 1917 paper by Johann Radon, who provided formulae for the inverse transform (reconstruction problem).
		A discrete Radon transform is a Hough transform.
	www.informationblast.com /Radon_transform.html (137 words)

	Radon transform package (Site not responding. Last check: 2007-11-05)
		A Radon transform is an array of size radii * angles * angles, where the radial size (NCOL) is the same as the edge of the image, and the number of angles (NTHETA) covers the range 0 - 2*PI.
		Because half of this angular range is redundant, a smaller transform is calculated with the number of angles covering 0 - PI equal to the image edge size (NTHETA/2 = NCOL).The POCS filter imposes consistency on a Radon transform and can be used to fill in missing points.
		There are three actions defined to do the forward and backward transformations, and the POCS filtering.
	www.niams.nih.gov /rcn/labbranch/lsbr/software/bsoft/radon/Radon.html (616 words)

	World Intellectual Property Organization (Site not responding. Last check: 2007-11-05)
		To obtain the backprojection of the Radon transform, the value of a particular point on a plane is calculated using the values of all the lines that go through the particular point.
		The transformation of the function that causes the backprojection to be the inverse is a wavelet transformation because it satisfies"the wavelet condition" (that the average value of the function is zero).
		The afferent inputs are inversions of the radon transforms.
	www.wipo.int /ipdl/IPDL-CIMAGES/view/pct/getbykey5?KEY=01/54059.010726&ELEMENT_SET=DECL (8674 words)

	Free Radon Test Kits
		Radon gas is a very potent carcinogen and children are particularly susceptible.
		Radon testing is essential before putting a house on the market to allow time for radon mitigation and before buying a house or basement remodeling.
		Radon test kits are inexpensive and your family’s health is at stake.
	free-radon-test-kits.com (681 words)

	Generalized Radon Transform Processing (Site not responding. Last check: 2007-11-05)
		Our interactive Radon analysis tools allow geophysicists to perform real-time transforms on selected gates within a data ensemble, design complex filters in the transform window, apply the filters, evaluate the results, iterate the preceding steps and finally output the batch job parameterization for subsequent production processing.
		Undesirable coherent noise, such as multiple contamination, may be targeted in the transform and rejected in the Radon domain prior to the inverse transform.
		Alternatively, this undesirable energy may be transformed back to the time domain for subtraction from the input data within the program.
	www.geotrace.com /Generalized%20Radon%20Transform%20Processing.htm (210 words)

	Citations: The Radon Transform and Some of its Applications - Deans (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		The Radon transform (projection) of an image is defined as line integrals across the image [10] It is well known that pure translational motion in an image results in translation of the projections
		) or as the plane wave integral (John (1955) The T 1 n transformation in a specific direction represents the projection of the n dimensional function on the hyperplanes that are perpendicular to this direction.
		....transform to the slices Rf( In this section we develop a digital procedure which is inspired by this viewpoint, and is realizable on n by n numerical arrays, 3.
	citeseer.ist.psu.edu /context/106693/0 (2473 words)

	Relationship Between Auto Chirplet FF Plane and Radon Transform
		The Radon transform (also known as the Hough transform) is formulated as a family of line integrals through a two-dimensional function.
		The Radon transform provides us with a simple means of computing the FF plane of the autochirplet transform, by using the Wigner distribution, and arriving at a transform space that tells us basically the same information as the chirplet FF-plane, except that we benefit from the greater resolution of the Wigner distribution.
		Thus we may be tempted to use the slope-intercept form of the Radon transform, except that we would prefer to have a parameterization in that matches the FF plane rather than the CF plane, for reasons previously discussed.
	www.wearcam.org /chirplet/node21.html (602 words)

	Radon
		According to the American Cancer Society, radon is the second leading cause of lung cancer in the United States and is associated with 15,000 to 22,000 lung cancer deaths each year.
		Radon, a naturally occurring form of radiation that results from the decaying elements inside of rocks, is found all over the world.
		Radon was widely discussed in the media when it was first identified as a problem in homes, but as the newness wore off so has its time in the media limelight.
	www.RadonSecrets.com (2231 words)

	ccmm97 abstract: Dym (Site not responding. Last check: 2007-11-05)
		An algorithm which can (among other things) compute the Radon Transform very efficiently (all rays in all directions are computed in O(nlogn) operations, with n the number of pixels in the image) is presented in [1].
		The original Radon Transform is `coarsened' to the point where it repesents a Transform of a two by two (coarse) image.
		These serve as an initial guess for the next stage, which uses a finer version of the coarsened Radon Transform, and which results in a four by four image, which, in turn, is interpolated to provide the initial values for the next stage.
	www.mgnet.org /mgnet/Conferences/CopperMtn97/dym.html (359 words)

	The general quadratic Radon transform (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		The general quadratic Radon transform in two dimensions is investigated.
		Whereas the classical Radon transform of a smooth function represents the integration over all lines, the general quadratic Radon transform integrates over all conic sections.
		Firstly, the parabolic isofocal Radon transform, i.e., the restriction of the general quadratic Radon transform to all parabolae with focus in the origin is defined and illustrated.
	citeseer.ist.psu.edu /354848.html (339 words)

	Dissertation: The Radon Transform on Finite Groups (Site not responding. Last check: 2007-11-05)
		The Radon transform and related integral transforms belong to the area known as inverse problems in which the reconstruction of a function from its projection or averages is a central point of study.
		What is interesting is that the Radon transform is an operator originally defined on two-dimensional real space or three dimmensional real space or but the above areas of applications all rely on some discretized version of the transform.
		To summarize, we investigate the Radon transform associated with the group of k -tuples whose components belong to the group of integers modulo n, and the transform associated to the group of invertible matrices of rank 2 over a finite field modulo a stabilizer subgroup of the matrices.
	userwww.sfsu.edu /~velasque/thesis.html (354 words)

	Citebase - The Radon transform of functions of matrix argument
		This transform assigns to a function $f$ on the matrix space the integrals of $f$ over the so-called matrix planes, the linear manifolds determined by the corresponding matrix equations.
		We introduce a new integral transform $T^\lam f$, $\lam \in C^m$, on the Stiefel manifold of orthonormal $m$-frames in $R^n$ which generalizes the $\lam$-cosine transform on the Grassmann manifold of $m$-dimensional linear subspaces of $R^n$.
		The paper is devoted to interrelation between the zeta distribution and the Radon transform on the space of $n \times m$ real matrices.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0406573 (1905 words)

	Daniel Trad Home Page~
		This transform achieves better resolution than the standard Radon transform as a consequence of enforcing sparseness in the transformed space.
		One of the most interesting aspects of looking at transformations performed in terms of inversion is the shaping or tailoring of the basis functions for the data and model spaces by means of data and model weights.
		The first chapter contains a simple introduction to the high resolution Radon transform that may be useful for those interested in the main concept and the bibliography.
	www.geop.ubc.ca /~dtrad/dtrad.html (453 words)

	RADON (Site not responding. Last check: 2007-11-05)
		This function can be used to return either the Radon transform, which transforms lines through an image to points in the Radon domain, or the Radon backprojection, where each point in the Radon domain is transformed to a straight line in the image.
		The transform is divided into two regions, one for nearly-horizontal lines ( q £ 45 ° ; 135 °£ q £ 180 °), and the other for steeper lines (45 ° < q < 135 °), where q is assumed to lie on the interval [0 °, 180 ° ].
		The bottom image is the Radon backprojection, after filtering all noise except for the two strong horizontal stripes in the middle image.
	idlastro.gsfc.nasa.gov /idl_html_help/R3.html (1155 words)

	Prof. Dr.-Ing. Fernando Puente León - MST - TUM (Site not responding. Last check: 2007-11-05)
		The Radon transform maps linear signal components onto pronounced extrema which can be detected very robustly.
		In the paper, the increase of the signal-to-noise ratio for such structures in the Radon domain is discussed quantitatively.
		Moreover, the application of the Radon transform for image enhancement is demonstrated.
	www.vms.ei.tum.de /publ/at102002.html (240 words)

	Related Papers
		There is a section on the fast wavelet transform, a section that relates the coefficients in a wavelet expansion of a function to its smoothness properties, and a final section on applications.
		Abstract: Because the Radon transform is a smoothing transform, any noise in the Radon data becomes magnified when the inverse Radon transform is applied.
		(For the Radon transform, $\alpha=1/2$, and the optimal value of $\beta_0$ is $d/2-\alpha=1/2$ in two dimensions.) We give a new proof of the rate of convergence of wavelet shrinkage that allows us to estimate rather sharply the best shrinkage parameter.
	www.math.purdue.edu /~lucier/692/related_papers_summaries.html (1490 words)

	Sigurdur Helgason - Publications
		The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds.
		Applications of the Radon transform to representations of semisimple Lie groups.
		Spherical functions, spherical representations and correspondence theorems for the spherical Fourier transform, Colloque sur les fonctions sphériques et la théorie des groupes, Nancy, 5-9, 1971.
	www-math.mit.edu /~helgason/publications.html (670 words)

	Color Density Contrasting in an Image using the Radon Transform (Site not responding. Last check: 2007-11-05)
		The Radon transform is applied to the filtered image.
		The transform is scaled to only include the values above the mean of the transform.
		The scaled results are backprojected by the Radon transform.
	www.rsinc.com /services/techtip.asp?ttid=3176&PV=YES (316 words)

	Mixed Fourier-Radon reconstruction of irregularly and sparsely sampled seismic data (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		Abstract: Seismic data irregularly sampled in two dimensions is transformed to the Fourier/Radon domain using a least squares formulation where the inverse transform, from the Fourier/Radon to the spatial domain is used as a forward model.
		By a proper choice of the region of support, the total number of parameters is limited (yet such that the actual data is optimally contained), leading to a stable inversion.
		1.1 : Parabolic Radon transform and x-squared fk-transform -..
	citeseer.ist.psu.edu /205243.html (277 words)

	e-Prints Soton - Use of the 3D radon transform to examine the properties of oceanic Rossby waves
		Use of the 3D radon transform to examine the properties of oceanic Rossby waves
		We review the methods for obtaining information on Rossby wave velocity from altimetry data, particularly the two-dimensional Radon transform. ; Unfortunately the use of longitude-time plots, although it allows the estimation of the zonal phase speeds, does not give any information on the speed vector when the propagation of the waves is not purely zonal (east-west).
		We show how the two-dimensional Radon Transform can be generalised to three dimensions, enabling not only the true propagation velocity component to be determined, but also the direction of the waves and thus any deviation from the pure-westward case.
	eprints.soton.ac.uk /120 (810 words)

	The general quadratic Radon transform
		the restriction of the general quadratic Radon transform to all parabolae with focus in the origin, is defined and illustrated.
		We show its intense relation to the classical Radon transform, deduce a support theorem, formulate an extension of the support theorem and derive an inversion formula.
		We show how the general quadratic Radon transform can be derived from the integrals over all parabolae by solving the related Cauchy problem.
	stacks.iop.org /0266-5611/14/615 (289 words)

	Untitled Document (Site not responding. Last check: 2007-11-05)
		The Radon transform is a fundamental tool in many areas.
		Radon transform lacks a coherent discrete deinition for 2D and 3D discrete
		for which the transform is rapidly computable and invertible.
	www.cs.tau.ac.il /bulletin-abstract/Advanced%20Seminar%20in%20Image%20Procassing/27-10-2002.htm (286 words)

	discrete mathematics: mathematics, 32 applied computerized classics (Site not responding. Last check: 2007-11-05)
		For the student of the Radon transform and its many applications, this book is a must.
		It's all here: the Radon transform in a multidimensional setting, the X-ray transform (a closely related transform), general theorems for the Fourier transform of the Radon transform, and theorems on the range of the Radon transform.
		He also offers much material on other allied transforms, the exponential Radon transform and the Radon transform for nonuniform attenuation, one of the major unsolved problems of mathematical physics.
	www.programming123.com /detail/discrete_mathematics/discrete_mathematics_0898714931.html (215 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		Spacing for the Radon transform in the tilting angle.
		Usually only the Fourier transform of the Radon transform is needed.
		Use this option to compute the Fourier transform of the Radon transform of a volume or image in a single step.
	www.cnb.uam.es /~bioinfo/NewXmipp/Applications/Src/Radon_Transform/Help/radon_transform.html (222 words)

	Citations: High-speed computation of the radon transform and backprojection using an expandable multiprocessor ... (Site not responding. Last check: 2007-11-05)
		Shieh, K. Current, P. Hurst, and I. Agi, "" High--speed computation of the radon transform and backprojection using an expandable multiprocessor architecture "," IEEE Trans.
		....image space and Radon space, requiring the implementation of the forward Radon transform as well [19, 5] If 3 D reconstruction is required, the computation time can easily take hours to complete.
		High-speed computation of the radon transform and backprojection using an expandable multiprocessor architecture.
	citeseer.ist.psu.edu /context/280638/0 (321 words)

	A Fast and Accurate Multilevel Inversion of the Radon Transform
		A Fast and Accurate Multilevel Inversion of the Radon Transform: SIAM Journal on Applied Mathematics Vol.
		A number of imaging technologies reconstruct an image function from its Radon projection using the convolution backprojection method.
		Radon transform, inversion of the Radon transform, computed tomography, convolution backprojection, multilevel, Fourier-domain postprocessing
	epubs.siam.org /sam-bin/dbq/article/32425 (206 words)

	OUP: Universality of the Radon Transform: Ehrenpreis
		The first part of the book discusses parametric and nonparametric Radon transforms, Harmonic Functions and Radon transform on Algebraic Varieties, nonlinear Radon and Fourier transforms, Radon transform on groups, and Radon transform as the interrelation of geometry and analysis.
		VII.2 The nilpotent (horocyclic) Radon transform on G/K
		VIII Radon transform as the interrelation of geometry and analysis
	www.oup.co.uk /isbn/0-19-850978-2 (542 words)

	Multi-parameter DMO in anisotropic media using the generalized Radon transform (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		Multi-parameter DMO in anisotropic media using the generalized Radon transform (1996)
		Abstract: Dip moveout (DMO), as part of the transformation to zero-offset (TZO), is a process that transforms data collected at finite source-receiver offsets to data that would be collected at zero-offset.
		The aim of this paper is to extend the TZO and DMO processes to elastic media and develop dynamically correct transformations of wave field data.
	citeseer.lcs.mit.edu /dehoop96multiparameter.html (372 words)

	Publication Listing: Berkman Sahiner, Ph.D. (Site not responding. Last check: 2007-11-05)
		Sahiner B. and A.E. Yagle, "Time-frequency distribution inversion of the Radon transform," IEEE Trans.
		Sahiner B. and A.E. Yagle, "On the use of wavelets in inverting the Radon transform," Proc.
		Sahiner B. and A.E. Yagle, "Iterative inversion of the Radon transform using image-adaptive wavelet constraints," Proc.
	alpha3.rad.med.umich.edu /pblctns/bspub/bspub.html (2535 words)

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