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Dissertations / Theses on the topic 'Radon transforms'

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Published: 4 June 2021
Last updated: 27 July 2024

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1

Grouy, Thibaut. "Radon-type transforms on some symmetric spaces." Doctoral thesis, Universite Libre de Bruxelles, 2019. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/285815.

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Dans cette thèse, nous étudions des transformées de type Radon sur certains espaces symétriques. Une transformée de type Radon associe à toute fonction continue à support compact sur une variété $M$ ses intégrales sur une classe $Xi$ de sous-variétés de $M$. Le problème sur lequel nous nous concentrons est l'inversion d'une telle transformée, c'est-à-dire déterminer la fonction à partir de ses intégrales sur les sous-variétés dans $Xi$. Nous présentons d'abord la solution de ce problème inverse due à Sigurdur Helgason et François Rouvière, entre autres, lorsque $M$ est un espace symétrique rie
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BARTOLUCCI, FRANCESCA. "Radon transforms: Unitarization, Inversion and Wavefront sets." Doctoral thesis, Università degli studi di Genova, 2020. http://hdl.handle.net/11567/997903.

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The first contribution of this thesis is a new approach based on the theory of group representations in order to solve in a general an unified way the unitarization and inversion problems for generalized Radon transform associated to dual pairs (G/K,G/H) of homogeneous spaces of a locally compact group G, where K and H are closed subgroups of G. Precisely, under some technical assumptions, if the quasi-regular representations of G acting on L^2(G/K) and L^2(G/H) are irreducible, then the Radon transform, up to a composition with a suitable pseudo-differential operator, can be extended to a uni
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3

Ambartsoumian, Gaik. "Spherical radon transforms and mathematical problems of thermoacoustic tomography." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1807.

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4

Webber, James. "Radon transforms and microlocal analysis in Compton scattering tomography." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/radon-transforms-and-microlocal-analysis-in-compton-scattering-tomography(c1ad3583-01ce-4147-8576-2e635090cb15).html.

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In this thesis we present new ideas and mathematical insights in the field of Compton Scattering Tomography (CST), an X-ray and gamma ray imaging technique which uses Compton scattered data to reconstruct an electron density of the target. This is an area not considered extensively in the literature, with only two dimensional gamma ray (monochromatic source) CST problems being analysed thus far. The analytic treatment of the polychromatic source case is left untouched and while there are three dimensional acquisition geometries in CST which consider the reconstruction of gamma ray source inten
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Pirbudak, Ozan. "Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms." Scholar Commons, 2019. https://scholarcommons.usf.edu/etd/7889.

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The goal of this study is the recovery of functions and finite parametric distributions from their spherical means over spheres and designing a general formula or algorithm for the reconstruction of a function f via its spherical mean transform. The theoretical study is and supported with a numerical implementation based on radar data. In this study, we approach the reconstruction problem in two different way. The first one is to show how the reconstruction problem could be converted to a Prony-type system of equations. After solving this Prony-type system of equations, one can extract the par
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6

Stazyk, Michael Walter. "Radon Transform in three dimensional image reconstruction from projections." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/28726.

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This thesis presents an algorithm for image reconstruction from projections intended for use in a new class of volume imaging PET scanners. The algorithm is based on the inversion of the three dimensional Radon Transform as it applies to the truncated cylindrical detector geometry and is derived from the X-ray Transform inversion given by the Orlov recovery operator. The algorithm is tested using Monte Carlo simulations of several phantom geometries and employs a single iterative step to include all detected events in the reconstruction. The reconstructed images are good representations of
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7

Adjei, Osei Nana. "The use of radon transforms and neural networks in image recognition." Thesis, Cranfield University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359966.

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8

Kakehi, Tomoyuki. "Range characterization of Radon transforms and ultrahyperbolic type of differential operators." 京都大学 (Kyoto University), 1993. http://hdl.handle.net/2433/86216.

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9

Donahue, Michael J. "The angle between null spaces of the radon and related transforms /." The Ohio State University, 1991. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487758680159321.

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10

Rigaud, Gaël. "Study of generalized Radon transforms and applications in Compton scattering tomography." Phd thesis, Université de Cergy Pontoise, 2013. http://tel.archives-ouvertes.fr/tel-00945739.

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Since the advent of the first ionizing radiation imaging devices initiated by Godfrey Newbold Hounsfield and Allan MacLeod Cormack, Nobel Prizes in 1979, the requirement for new non-invasive imaging techniques has grown. These techniques rely upon the properties of penetration in the matter of X and gamma radiation for detecting a hidden structure without destroying the illuminated environment. They are used in many fields ranging from medical imaging to non-destructive testing through. However, the techniques used so far suffer severe degradation in the quality of measurement and reconstructe
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Courdurier, Matias. "Restricted measurements for the X-ray transform /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/5784.

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12

EASTON, ROGER LEE JR. "TWO-DIMENSIONAL SIGNAL PROCESSING IN RADON SPACE (OPTICAL SIGNAL, IMAGE PROCESSING, FOURIER TRANSFORMS)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183978.

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This dissertation considers a method for processing two-dimensional (2-D) signals (e.g. imagery) by transformation to a coordinate space where the 2-D operation separates into orthogonal 1-D operations. After processing, the 2-D output is reconstructed by a second coordinate transformation. This approach is based on the Radon transform, which maps a two-dimensional Cartesian representation of a signal into a series of one-dimensional signals by line-integral projection. The mathematical principles of this transformation are well-known as the basis for medical computed tomography. This approach
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Wade, Jeremy. "Summability of Fourier orthogonal expansions and a discretized Fourier orthogonal expansion involving Radon projections for functions on the cylinder /." Connect to title online (Scholars' Bank) Connect to title online (ProQuest), 2009. http://hdl.handle.net/1794/10245.

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14

Pedrick, Micah G. "Complexity of Linear Summary Statistics." Scholarship @ Claremont, 2017. https://scholarship.claremont.edu/hmc_theses/99.

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Families of linear functionals on a vector space that are mapped to each other by a group of symmetries of the space have a significant amount of structure. This results in computational redundancies which can be used to make computing the entire family of functionals at once more efficient than applying each in turn. This thesis explores asymptotic complexity results for a few such families: contingency tables and unranked choice data. These are used to explore the framework of Radon transform diagrams, which promise to allow general theorems about linear summary statistics to be stated and p
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15

Regnier, Rémi. "Approche de reconstruction d’images fondée sur l’inversion de certaines transformations de Radon généralisées." Thesis, Cergy-Pontoise, 2014. http://www.theses.fr/2014CERG0698/document.

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Depuis l'invention de la radiographie au début du vingtième siècle et des premiers radars lors la seconde guerre mondiale, le besoin de connaître notre environnement par différentes techniques d'imagerie n'a cessé de croître. Ce besoin a pris de multiples formes, allant de l'exploration d'une structure interne avec la prolifération des techniques d'imagerie non invasives à l'imagerie par satellite qui accompagna la conquête de l'espace. Nombre de systèmes d'imagerie ont donc été proposés pour arriver à créer les images les plus représentatives des milieux étudiés. Parmi eux la tomodensitométri
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Barrera, Cruz Marco Antonio. "Hybrid method algebraic/inverse radon transform for region of interest reconstruction of computed tomography images /." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.

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17

Goncharov, Fedor. "Transformations de Radon pondérées et leurs applications." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX029/document.

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Cette thèse est consacrée à l'étude des problèmes inverses des transformations de Radon pondérées dans les espaces euclidiens. D'une part, nos études sont motivées par l'application des transformations de Radon pondérées pour différentes tomographies, par exemple en tomographie d'émission (PET, SPECT), en tomographie de fluorescence et en tomographie optique. En particulier, nous développons une nouvelle approche de reconstruction pour les tomographies en 3D, où les données sont modélisées par des transformations des rayons pondérées le long des rayons parallèles à un plan fixe. À cet égard, n
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18

Rigaud, Gaël [Verfasser], and Alfred K. [Akademischer Betreuer] Louis. "Study of generalized radon transforms and applications in compton scattering tomography / Gaël Rigaud. Betreuer: Alfred K. Louis." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2014. http://d-nb.info/1053724705/34.

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19

Sanja, Kostadinova. "Some classes of integral transforms on distribution spaces and generalized asymptotics." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2014. https://www.cris.uns.ac.rs/record.jsf?recordId=87772&source=NDLTD&language=en.

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In this doctoral dissertation several integral transforms are discussed.The first one is the Short time Fourier transform (STFT). We present continuity theorems for the STFT and its adjoint on the test function space <em>K</em><sub>1</sub>(ℝ<sup>n</sup>) and the topological tensor product <em>K</em><sub>1</sub>(ℝ<sup>n</sup>) &otimes; <em>U</em>(<strong>ℂ</strong><sup>n</sup>), where <em>U</em>(<strong>ℂ</strong><sup>n</sup>) is the space of entirerapidly decreasing functions in any horizontal band of&nbsp;<strong>ℂ</strong><sup>n</sup>. We then use such continuity results to develop a framewo
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20

Ahmad, Rizwan. "Data acquisition and reconstruction techniques for improved electron paramagnetic resonance (EPR) imaging." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1186602293.

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21

Moraes, Dione Cherpinsky. "Interpolação e regularização de dados sismicos usando a transformada de Radon linear (tau-up) 2D e 3D." [s.n.], 2004. http://repositorio.unicamp.br/jspui/handle/REPOSIP/265528.

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Orientadores: Rodrigo de Souza Portugal, Carlos Alves da Cunha Filho<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica, Instituto de Geociencias<br>Made available in DSpace on 2018-08-12T03:43:20Z (GMT). No. of bitstreams: 1 Moraes_DioneCherpinsky_M.pdf: 4463877 bytes, checksum: 6418a90fbf3389f9233ef9eb721da563 (MD5) Previous issue date: 2004<br>Resumo: Os levantamentos sísmicos são parametrizados para que os dados sejam adquiridos segundo uma malha regular. Tal regularidade quase nunca é possível, pois durante a aquisição dos dados ocorrem obstá
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22

Boukerbout, Hassina. "Analyse en ondelettes et prolongement des champs de potentiel : développement d'une théorie 3-D et application en géophysique /." Rennes : Géosciences-Rennes, 2004. http://catalogue.bnf.fr/ark:/12148/cb39995468z.

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23

Miqueles, Eduardo Xavier Silva. "A transformada generalizada atenuada de Radon = inversão, analitica, aproximações, metodos iterativos e aplicações em tomografia por fluorescencia." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307559.

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Orientador: Alvaro Rodolfo De Pierro<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-15T04:08:38Z (GMT). No. of bitstreams: 1 Miqueles_EduardoXavierSilva_D.pdf: 22019050 bytes, checksum: 05c0fc26d4ba49669bc4f5fc2a22fe5b (MD5) Previous issue date: 2010<br>Resumo: A Tomografia por Fluorescência de Raios X é uma nova técnica que combina a tomografia por transmissão de Raios X e a tomografia por emissão. Uma amostra de tecido (ou corpo) é bombardeada por Raios X de alta intensidade (gerad
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24

Coetzer, Johannes. "Off-line signature verification." Thesis, Stellenbosch : University of Stellenbosch, 2005. http://hdl.handle.net/10019.1/1355.

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Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2005.<br>A great deal of work has been done in the area of off-line signature verification over the past two decades. Off-line systems are of interest in scenarios where only hard copies of signatures are available, especially where a large number of documents need to be authenticated. This dissertation is inspired by, amongst other things, the potential financial benefits that the automatic clearing of cheques will have for the banking industry.
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25

Burnier-Mennessier, Catherine. "Identification en imagerie doppler : liens avec la transformée de Randon généralisée." Université Joseph Fourier (Grenoble), 1997. https://tel.archives-ouvertes.fr/tel-00686829.

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Le champ magnetique des etoiles joue un role essentiel dans leur evolution interne et dans l'interaction qu'elles entretiennent avec leur environnement. Il se manifeste, entre autre, par l'existence de structures inhomogenes a leur surface. Helas a de rares exceptions la resolution des telescopes reste insuffisante pour les resoudre spatialement. Ceci oblige donc a se tourner vers des methodes indirectes. Telle est le but de l'imagerie doppler. Apres un expose detaille du principe de l'imagerie doppler et quelques rappels sur la tomographie - transformee de radon classique - nous montrons que
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Dickerson, Jill. "Curvelets and the Radon Transform." Master's thesis, University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5626.

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Computed Tomography (CT) is the standard in medical imaging field. In this study, we look at the curvelet transform in an attempt to use it as a basis for representing a function. In doing so, we seek a way to reconstruct a function from the Radon data that may produce clearer results. Using curvelet decomposition, any known function can be represented as a sum of curvelets with corresponding coefficients. It can be shown that these corresponding coefficients can be found using the Radon data, even if the function is unknown. The use of curvelets has the potential to solve partial or truncated
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Bisset, D. A. "Seismic migration using the radon transform." Thesis, University of Strathclyde, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382336.

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su, vinberg@ebv pvt msu. "The Dual Horospherical Radon Transform for Polynomials." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1064.ps.

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29

Hielscher, Ralf. "The Radon transform on the rotation group." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek &quot;Georgius Agricola&quot, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:105-3614018.

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Ein zentrales Problem der quantitativen Texturanalyse ist die numerische Inversion der eindimensionalen Radontransformation auf der Lie--Gruppe SO(3) aller Rotationen im dreidimensionalen euklidischen Raum. In der vorliegenden Dissertation wird die Lösbarkeit und Eindeutigkeit dieses inversen Problems untersucht und Fehlerabschätzungen unter Berücksichtigung unvollständiger und fehlerbehafteter Daten hergeleitet. Weiterhin wird ein Algorithmus zur Lösung des inversen Problems vorgeschlagen, welcher auf einer Diskretisierung mittels radialer Basisfunktionen basiert und schnelle Fouriermethoden
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Quellmalz, Michael. "A generalization of the Funk–Radon transform to circles passing through a fixed point." Universitätsbibliothek Chemnitz, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-192513.

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The Funk–Radon transform assigns to a function on the two-sphere its mean values along all great circles. We consider the following generalization: we replace the great circles by the small circles being the intersection of the sphere with planes containing a common point ζ inside the sphere. If ζ is the origin, this is just the classical Funk–Radon transform. We find two mappings from the sphere to itself that enable us to represent the generalized Radon transform in terms of the Funk–Radon transform. This representation is utilized to characterize the nullspace and range as well as to prove
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31

Mano, Gen. "Radon transform of functions supported on a homogeneous cone." 京都大学 (Kyoto University), 2007. http://hdl.handle.net/2433/136742.

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32

Andersson, Joel. "On Invertibility of the Radon Transform and Compressive Sensing." Doctoral thesis, KTH, Matematik (Avd.), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-141837.

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This thesis contains three articles. The first two concern inversion andlocal injectivity of the weighted Radon transform in the plane. The thirdpaper concerns two of the key results from compressive sensing.In Paper A we prove an identity involving three singular double integrals.This is then used to prove an inversion formula for the weighted Radon transform,allowing all weight functions that have been considered previously.Paper B is devoted to stability estimates of the standard and weightedlocal Radon transform. The estimates will hold for functions that satisfy an apriori bound. When wei
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33

Elouedi, Inès. "Transformée de Radon discrète généralisée multidirectionnelle, formalisme théorique et aplications en reconnaissance de formes." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1187/document.

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La transformée de Radon généralisée est une extension de la transformée de Radon qui généralise ses courbes de projection. Ce mémoire présente de nouveaux formalismes théoriques à la transformée de Radon Généralisée discrète. Les approches proposées dans ce mémoire ont différentes propriétés. Nous citons principalement : l'aspect modèle où chaque point dans l'espace de Radon correspond à un modèle dans l'espace spatial. Il est le résultat de la somme des pixels appartenant au modèle, la projection multidirectionnelle dans le sens que le domaine transformé de Radon se constituera au fur et à me
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Recur, Benoît. "Précision et qualité en reconstruction tomographique : algorithmes et applications." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14113/document.

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Il existe un grand nombre de modalités permettant l'acquisition d'un objet de manière non destructrice (Scanner à Rayons X, micro-scanner, Ondes Térahertz, Microscopie Électronique de Transmission, etc). Ces outils acquièrent un ensemble de projections autour de l'objet et une étape de reconstruction aboutit à une représentation de l'espace acquis. La principale limitation de ces méthodes est qu'elles s'appuient sur une modélisation continue de l'espace alors qu'elles sont exploitées dans un domaine fini. L'étape de discrétisation qui en résulte est une source d'erreurs sur les images produite
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Giannakidis, Archontis. "Solving the inverse radon transform for vector field tomographic data." Thesis, University of Surrey, 2009. http://epubs.surrey.ac.uk/804891/.

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36

Quellmalz, Michael. "A generalization of the Funk–Radon transform to circles passing through a fixed point." Technische Universität Chemnitz, 2015. https://monarch.qucosa.de/id/qucosa%3A20372.

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The Funk–Radon transform assigns to a function on the two-sphere its mean values along all great circles. We consider the following generalization: we replace the great circles by the small circles being the intersection of the sphere with planes containing a common point ζ inside the sphere. If ζ is the origin, this is just the classical Funk–Radon transform. We find two mappings from the sphere to itself that enable us to represent the generalized Radon transform in terms of the Funk–Radon transform. This representation is utilized to characterize the nullspace and range as well as to prove
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37

Sadiq, Kamran. "On the range of the Attenuated Radon Transform in strictly convex sets." Doctoral diss., University of Central Florida, 2014. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/6349.

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In the present dissertation, we characterize the range of the attenuated Radon transform of zero, one, and two tensor fields, supported in strictly convex set. The approach is based on a Hilbert transform associated with A-analytic functions of A. Bukhgeim. We first present new necessary and sufficient conditions for a function to be in the range of the attenuated Radon transform of a sufficiently smooth function supported in the convex set. The approach is based on an explicit Hilbert transform associated with traces of the boundary of A-analytic functions in the sense of A. Bukhgeim. We the
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Moustafa, Moustafa Abdel-Azim. "Feature recognition using a fast radon transform-based computer vision system." Thesis, Cranfield University, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305610.

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39

Patterson, Richard Sven. "Acoustic modelling of near borehole anolmalies via the generalised radon transform." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/59049.

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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1992.<br>Includes bibliographical references (leaves 89-91).<br>by Richard Sven Patterson.<br>M.S.
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Guerrero, prado Patricio. "Reconstruction tridimensionnelle des objets plats du patrimoine à partir du signal de diffusion inélastique." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLV035/document.

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La caractérisation tridimensionnelle de matériaux anciens plats est restée une activité non évidente à accomplir par des méthodes classiques de tomographie à rayons X en raison de leur morphologie anisotrope et de leur géométrie aplatie.Pour surmonter les limites de ces méthodologies, une modalité d'imagerie basée sur le rayonnement diffusé Compton est étudiée dans ce travail. La tomographie classique aux rayons X traite les données de diffusion Compton comme du bruit ajouté au processus de formation d'image, tandis que dans la tomographie du rayonnement diffusé, les conditions sont définies d
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Benchoufi, Mehdi. "Théorie microlocale des faisceaux pour la transformation Radon." Electronic Thesis or Diss., Sorbonne université, 2020. http://www.theses.fr/2020SORUS475.

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Le sujet de cette thèse est une approche microlocale de la transformation de Radon. Il s’agit d’appliquer à la dualité projective complexe et réelle les techniques initiées dans l’article fondateur de Sato-Kashiwara-Kawai de 1972 et de retrouver, reformuler, améliorer des travaux d’analyse plus classiques sur ce sujet, en particulier ceux de G. Henkin ou S. Gindikin. La dualité projective vue sous l’angle microlocal et faisceautique est apparue pour la première fois dans un travail important de J-L. Brylinski sur les faisceaux pervers, travail repris ensuite par D’Agnolo et Schapira dans le ca
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Panton, Mark Stuart. "Off-line signature verification using ensembles of local Radon transform-based HMMs." Thesis, Stellenbosch : Stellenbosch University, 2011. http://hdl.handle.net/10019.1/6903.

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Thesis (MSc)--Stellenbosch University, 2011.<br>ENGLISH ABSTRACT: An off-line signature verification system attempts to authenticate the identity of an individual by examining his/her handwritten signature, after it has been successfully extracted from, for example, a cheque, a debit or credit card transaction slip, or any other legal document. The questioned signature is typically compared to a model trained from known positive samples, after which the system attempts to label said signature as genuine or fraudulent. Classifier fusion is the process of combining individual classifiers,
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Hugonnet, Pierre. "La transformée de Radon généralisée et ses applications à la sismique." Pau, 1998. https://tel.archives-ouvertes.fr/tel-01511030.

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La transformée de Radon d'une image multi-dimensionnelle consiste à intégrer cette image sur des familles d'hypersurfaces (de courbes pour une image 2d). La décomposition de Radon consiste à exprimer une image comme une superposition d'hypersurfaces affectées d'une certaine amplitude (combinaison linéaire d'hypersurfaces). C'est donc un problème inverse linéaire. Nous étudions d'abord les propriétés des différentes décompositions 2d et des courbes d'intégration utilisées en sismique d'exploration pétrolière. L'étude de l'échantillonnage des différentes variables permet de confirmer des règles
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Palmer, Max John. "New developments for imaging energetic photons." Thesis, University of Southampton, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243171.

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45

Hielscher, Ralf. "The Radon transform on the rotation group inversion and application to texture analysis /." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=985235330.

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46

Nowak, Ethan J. "Applications of the Radon transform, Stratigraphic filtering, and Object-based stochastic reservoir modeling." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/29691.

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The focus of this research is to develop and extend the application of existing technologies to enhance seismic reservoir characterization. The chapters presented in this dissertation constitute five individual studies consisting of three applications of the Radon transform, one aspect of acoustic wave propagation, and a pilot study of generating a stochastic reservoir model. The first three studies focus on the use of the Radon transform to enhance surface-recorded, controlled-source seismic data. First, the use of this transform was extended to enhance diffraction patterns, which may be ind
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Wang, Ping Ph D. Massachusetts Institute of Technology. "Imaging of structure at and near the core mantle boundary using a generalized radon transform." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40966.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2007.<br>Includes bibliographical references (p. [163]-175).<br>In this thesis, concepts from inverse scattering and modem statistics are combined into a powerful tool for imaging interfaces in Earth's deep interior. Specially, a generalized Radon transform (GRT) approach is developed to image heterogeneity at and near interfaces in Earth's lowermost mantle with broadband, three-component seismograms from Global Seismograph Networks (GSN). With this GRT method I transformed ~100,000 tra
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CLOUGH, ANNE VIRGINIA. "A MATHEMATICAL MODEL OF SINGLE-PHOTON EMISSION COMPUTED TOMOGRAPHY (RADON TRANSFORM, COMPTON SCATTER, ATTENUATION, NUCLEAR MEDICINE)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/188142.

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Single-photon emission computed tomography (SPECT) is a nuclear-medicine imaging technique that has been shown to provide clinically useful images of radionuclide distributions within the body. The problem of quantitative determination of tomographic activity images from a projection data set leads to a mathematical inverse problem which is formulated as an integral equation. The solution of this problem then depends on an accurate mathematical model as well as a reliable and efficient inversion algorithm. The effects of attenuation and Compton scatter within the body have been incorporated in
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MONTI, MATTEO. "Some aspects of Analysis on symmetric spaces and homogeneous trees: from Radon transform to Bergman spaces." Doctoral thesis, Università degli studi di Genova, 2022. http://hdl.handle.net/11567/1093794.

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The thesis is focused on the Analysis on two classes of non Euclidean spaces: the symmetric spaces of the noncompact type and the homogeneous trees. I first solve in both the settings the problem of the Unitarization of the Radon transform. The last chapter is devoted to the study of the harmonic Bergman spaces on homogeneous trees.
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Lamm, Rosalee Alicia. "Fine scale imaging of structures at and near the mantle transition zone using a generalized Radon transform." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/37280.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2006.<br>Includes bibliographical references (p. 34-37).<br>We apply a generalized Radon transform (GRT) to the study of the transition zone discontinuities. The transition zone discontinuities, e.g. the '410' and '660', result from mineral phase changes that occur at depths constrained by temperature and chemistry, and can provide information about the conditions of the mantle within the transition zone. Previous global studies of topography on the transition zone discontinuities use SS
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