Spelling suggestions: "subject:"[een] INVERSE PROBLEMS"" "subject:"[enn] INVERSE PROBLEMS""
41 |
Spherical radon transforms and mathematical problems of thermoacoustic tomographyAmbartsoumian, 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.
|
42 |
Stochastic inversion of pre-stack seismic data to improve forecasts of reservoir productionVarela Londoño, Omar Javier. January 2003 (has links)
Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.
|
43 |
Stochastic inversion of pre-stack seismic data to improve forecasts of reservoir productionVarela Londoño, Omar Javier 25 July 2011 (has links)
Not available / text
|
44 |
Inverse Problems in Soft Tissue Elastography using Boundary Element MethodsBerger, Hans-Uwe January 2009 (has links)
Elastography is an emerging functional imaging technique of current
clinical research interest due to a direct relation between
mechanical material parameters, especially the tissue stiffness, and
tissue pathologies such as cancer. Digital Image Elasto-Tomography
(DIET) is a new method that aims to develop elastographic techniques
and create a simplified, improved breast cancer screening process.
The elastic material information of breast tissue is reconstructed
in the DIET concept from mechanically excited steady-state harmonic
motion observed on the surface of the breast. While this inversion
process has been traditionally approached using finite element
methods, this surface-orientated problem is naturally suited to the
use of Boundary Element Methods (BEMs) requiring the discretization
only on the surface of the domain and on the interface of a
potential inclusion. As only approximate information is available
about breast tissue material parameters, this thesis presents the
development of BEM based inverse problem algorithms suitable for the
reconstruction of all material parameters in a proportionally damped
isotropic linear elastic solid, where only the material density is
known. The highly nonlinear identification process of a potential
inclusion is treated through the combination of a systematic
Grid-Search with gradient descent techniques. This algorithm is
extended to a three-step algorithm that performs a background
material parameter estimation before the subsequent identification
of an inclusion and thus provides a confident indication for the
differentiation between cancerous and healthy breast tissue. The
development of these algorithms is illustrated by several simulation
studies highlighting important reconstruction behaviors relevant to
the elastographic inverse problem. A first experimental test on a
silicon based breast phantom is presented.
|
45 |
On Inverse Problems for a Beam with AttachmentsMir Hosseini, Farhad 05 December 2013 (has links)
The problem of determining the eigenvalues of a vibrational system having multiple lumped attachments has been investigated extensively. However, most of the research conducted in this field focuses on determining the natural frequencies of the combined system assuming that the characteristics of the combined vibrational system are known (forward problem). A problem of great interest from the point of view of engineering design is the ability to impose certain frequencies on the vibrational system or to avoid certain frequencies by modifying the characteristics of the vibrational system (inverse problem). In this thesis, the effects of adding lumped masses to an Euler-Bernoulli beam on its frequencies and their corresponding mode shapes are investigated for simply-supported as well as fixed-free boundary conditions. This investigation paves the way for proposing a method to impose two frequencies on a system consisting of a beam and a lumped mass by determining the magnitude of the mass as well as its position along the beam.
|
46 |
Deblurring with Framelets in the Sparse Analysis SettingDanniels, Travis 23 December 2013 (has links)
In this thesis, algorithms for blind and non-blind motion deblurring
of digital images are proposed. The non-blind algorithm is based on a convex program
consisting of a data fitting term and a sparsity-promoting regularization term.
The data fitting term is the squared l_2 norm of the residual between the blurred image
and the latent image convolved with a known blur kernel.
The regularization term
is the l_1 norm of the latent image under a wavelet frame (framelet) decomposition.
This convex program is solved with the first-order primal-dual algorithm proposed by Chambolle and Pock. The proposed blind deblurring algorithm
is based on the work of Cai, Ji, Liu, and Shen.
It works by embedding the proposed non-blind algorithm in an alternating minimization scheme
and imposing additional constraints in order
to deal with the challenging non-convex nature of the blind deblurring problem.
Numerical experiments are performed on artificially and naturally blurred images,
and both proposed algorithms are found to be competitive with recent deblurring methods. / Graduate / 0544 / tdanniels@gmail.com
|
47 |
Inverse Problems in Portfolio Selection: Scenario Optimization FrameworkBhowmick, Kaushiki 10 1900 (has links)
A number of researchers have proposed several Bayesian methods for portfolio selection, which combine statistical information from financial time series with the prior beliefs of the portfolio manager, in an attempt to reduce the impact of estimation errors in distribution parameters on the portfolio selection process and the effect of these errors on the performance of 'optimal' portfolios in out-of-sample-data.
This thesis seeks to reverse the direction of this process, inferring portfolio managers’ probabilistic beliefs about future distributions based on the portfolios that they hold. We refer to the process of portfolio selection as the forward problem and the process of retrieving the implied probabilities, given an optimal portfolio, as the inverse problem. We attempt to solve the inverse problem in a general setting by using a finite set of scenarios. Using a discrete time framework, we can retrieve probabilities associated with each of the scenarios, which tells us the views of the portfolio manager implicit in the choice of a portfolio considered optimal.
We conduct the implied views analysis for portfolios selected using expected utility maximization, where the investor's utility function is a globally non-optimal concave function, and in the mean-variance setting with the covariance matrix assumed to be given.
We then use the models developed for inverse problem on empirical data to retrieve the implied views implicit in a given portfolio, and attempt to determine whether incorporating these views in portfolio selection improves portfolio performance out of sample.
|
48 |
Velocity estimation from seismic data by nonlinear inversion and characterization of gas hydrate deposits offshore OregonWang, Chengshu, January 2003 (has links) (PDF)
Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.
|
49 |
A two dimensional inverse boundary value problem in radiation transport /Tamasan, Alexandru Cristian. January 2002 (has links)
Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 60-67).
|
50 |
Velocity estimation from seismic data by nonlinear inversion and characterization of gas hydrate deposits offshore Oregon /Wang, Chengshu, January 2003 (has links)
Thesis (Ph. D.)--University of Texas at Austin, 2003. / Available also in an electronic version.
|
Page generated in 0.0319 seconds