• Refine Query
  • Source
  • Publication year
  • to
  • Language
  • 22
  • 9
  • 5
  • 3
  • 1
  • 1
  • 1
  • Tagged with
  • 49
  • 49
  • 13
  • 10
  • 9
  • 9
  • 9
  • 7
  • 7
  • 6
  • 5
  • 5
  • 4
  • 4
  • 4
  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Duality and Radon transform for symmetric spaces

Helgason, S. 07 1900 (has links)
First published in the Bulletin of the American Mathematical Society in Vol.69, 1963, published by the American Mathematical Society
2

A duality in integral geometry; some generalizations of the Radon transform

Helgason, Sigurdur January 1964 (has links)
First published in the Bulletin of the American Mathematical Society in Vol.70, 1964, published by the American Mathematical Society
3

New developments for imaging energetic photons

Palmer, Max John January 1997 (has links)
No description available.
4

The Dual Horospherical Radon Transform for Polynomials

vinberg@ebv.pvt.msu.su 10 September 2001 (has links)
No description available.
5

On Invertibility of the Radon Transform and Compressive Sensing

Andersson, Joel January 2014 (has links)
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 weights are involved they must solve a certain differentialequation and fulfill some regularity assumptions.In Paper C we present some new constant bounds. Firstly we presenta version of the theorem of uniform recovery of random sampling matrices,where explicit constants have not been presented before. Secondly we improvethe condition when the so-called restricted isometry property implies the nullspace property. / <p>QC 20140228</p>
6

Radon-Fourier transforms on symmetric spaces and related group representations

Helgason, S. January 1965 (has links)
First published in the Bulletin of the American Mathematical Society in Vol.71, 1965, published by the American Mathematical Society
7

Applications of the Radon transform, Stratigraphic filtering, and Object-based stochastic reservoir modeling

Nowak, Ethan J. 03 February 2005 (has links)
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 indicative of subsurface fractures. The geometry of primary reflections and diffractions on synthetic common-shot-gather data indicate that Radon filters can predict and model primary reflections upon inverse transformation. These modeled primaries can then be adaptively subtracted from the input gather to enhance the diffractions. Second, I examine the amplitude distortions at near and far offsets caused by free-surface multiple removal using Radon filters. These amplitudes are often needlessly reduced due to a truncation effect when the commonly used, unweighted least-squares solution is applied. Synthetic examples indicate that a weighted solution to the transformation minimizes this effect and preserves the reflection amplitudes. Third, a novel processing flow was developed to generate a stacked seismic section using the Radon transform. This procedure has the advantage over traditional summation of normal moveout corrected common midpoint gathers because it circumvents the need to perform manual and interpretive velocity analysis. The fourth study involves the detection of thin layers in periodic layerstacks. Numerical modeling of acoustic wave propagation suggests that the sinusoidal components of an incident signal with a wavelength that corresponds to the periodicity of the material be preferentially reflected. Isolating the different portions of the reflected wavefield and calculating the energy spectra may provide evidence of thin periodic layers which are deterministically unresolvable on their own. Object-based reservoir modeling often incorporates the use of lithology logs, deterministic seismic interpretation, architectural element analysis, geologic intuition, and modern and outcrop analogs. This last project consists of a pilot study where a more quantitative approach to define the statistical parameters currently derived through geologic intuition and analogs was developed. This approach utilizes a simulated annealing optimization technique for inversion and the pilot study shows that it can improve the correlation between synthesized and control logs. / Ph. D.
8

A generalization of the Funk–Radon transform to circles passing through a fixed point

Quellmalz, Michael 29 June 2016 (has links) (PDF)
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 an inversion formula of the generalized Radon transform.
9

A surfacelet-based method for constructing geometric models of microstructure

Jeong, Namin 07 January 2016 (has links)
Integration of material composition, microstructure, and mechanical properties with geometry information enables many product development activities, including design, analysis, and manufacturing. To address such needs, models of material composition have been integrated into CAD systems, creating systems called heterogeneous CAD modeling. In order to support the heterogeneous CAD system, extensive process-structure-property relationships have to be captured and integrated into current CAD system. A new method for reverse engineering of materials will be presented such that microstructure models can be constructed and used in the heterogeneous CAD system. Reverse engineering of material consists of three parts: image analysis, structure-property-process relationship, and repository. In this research, an image processing method, which comprises the Radon transform and the wavelet transform, will be used in order to recognize geometric features from a microstructure image. Recognizing geometric features can be obtained by combinations of three techniques, masking, clustering, and high frequency component on wavelet transform, that are integrated with the Radon transform. Then, recognized geometric features can be used to construct an explicit geometric model of microstructure. The proposed work will provide an explicit mathematical method to recognize and to quantify microstructure features from an image. In addition, explicit geometric models of microstructure can be automatically constructed and utilized to get effective mechanical properties, establishing structure-property relationship of the material. In order to demonstrate this, polymer nano-composite sample and metal alloy sample will be used.
10

Spherical radon transforms and mathematical problems of thermoacoustic tomography

Ambartsoumian, Gaik 02 June 2009 (has links)
The spherical Radon transform (SRT) integrates a function over the set of all spheres with a given set of centers. Such transforms play an important role in some newly developing types of tomography as well as in several areas of mathematics including approximation theory, integral geometry, inverse problems for PDEs, etc. In Chapter I we give a brief description of thermoacoustic tomography (TAT or TCT) and introduce the SRT. In Chapter II we consider the injectivity problem for SRT. A major breakthrough in the 2D case was made several years ago by M. Agranovsky and E. T. Quinto. Their techniques involved microlocal analysis and known geometric properties of zeros of harmonic polynomials in the plane. Since then there has been an active search for alternative methods, which would be less restrictive in more general situations. We provide some new results obtained by PDE techniques that essentially involve only the finite speed of propagation and domain dependence for the wave equation. In Chapter III we consider the transform that integrates a function supported in the unit disk on the plane over circles centered at the boundary of this disk. As is common for transforms of the Radon type, its range has an in finite co-dimension in standard function spaces. Range descriptions for such transforms are known to be very important for computed tomography, for instance when dealing with incomplete data, error correction, and other issues. A complete range description for the circular Radon transform is obtained. In Chapter IV we investigate implementation of the recently discovered exact backprojection type inversion formulas for the case of spherical acquisition in 3D and approximate inversion formulas in 2D. A numerical simulation of the data acquisition with subsequent reconstructions is made for the Defrise phantom as well as for some other phantoms. Both full and partial scan situations are considered.

Page generated in 0.1417 seconds