Theory and application of optimal linear resolution to MRI truncation artifacts, multiexponential decays and in vivo multiple sclerosis pathology
department or school: Science, Faculty of
department or school: Physics and Astronomy, Department of
data provider: DSpace
degree campus: UBCV
creator: Cover, Keith Sean
issued: 2009-10-10T00:00:00
issued: 2001
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
description: It is widely believed that one of the best way to proceed when analysing data is to generate estimates which fit the data. However, when the relationship between the unknown model and data is linear for highly underdetermined systems, is it common practice to find estimates with good linear resolution with no regard for fitting the data. For example, windowed Fourier transforms produces estimates that have good linear resolution but do not fit the data. Surprisingly, many researchers do not seem to be explicitly aware of this fact. This thesis presents a theoretical basis for the linear resolution which demonstrates that, for a wide range of problems, algorithms which produce estimates with good linear resolution can be a more powerful and convenient way of presenting the information in the data, than models that fit the data. Linear resolution was also applied to two outstanding problems in linear inverse theory. The first was the problem of truncation artifacts in magnetic resonance imaging (MRI). Truncation artifacts were heavily suppressed or eliminated by the choice of one of two novel Fourier transform windows. Complete elimination of truncation artifacts generally led to unexpectedly blurry images. Heavy suppression seemed to be the best compromise between truncation artifacts and blurriness. The second problem was estimating the relaxation distribution of a multiexponential system from its decay curve. This is an example where hundreds of papers have been written on the subject, yet almost no one has made a substantial effort to apply linear resolution. I found the application to be very successful. As an example, the algorithm was applied to the decay of MRI data from multiple sclerosis patients in an attempt to differentiate between various pathologies.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/13891
extent: 16432784 bytes
format: application/pdf
note: T H E O R Y A N D A P P L I C A T I O N OF O P T I M A L L I N E A R R E S O L U T I O N T O M R I T R U N C A T I O N A R T I F A C T S , M U L T I E X P O N E N T I A L D E C A Y S A N D IN VIVO M U L T I P L E SCLEROSIS P A T H O L O G Y By Keith S Cover B. Sc. (Physics) University of Waterloo, ltf&3 M. Sc. (Geophysics) University of British Columbia^ j 7 c? G A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS AND ASTRONOMY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 2001 © Keith S Cover, 2001 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Physics and Astronomy The University of British Columbia 6224 Agricultural Road Vancouver, Canada V6T 1Z1 Date: Abstract It is widely believed that one of the best way to proceed when analysing data is to generate estimates which fit the data. However, when the relationship between the unknown model and data is linear for highly underdetermined systems, is it common practice to find estimates with good linear resolution with no regard for fitting the data. For example, windowed Fourier transforms produces estimates that have good linear resolution but do not fit the data. Surprisingly, many researchers do not seem to be explicitly aware of this fact. This thesis presents a theoretical basis for the linear resolution which demonstrates that, for a wide range of problems, algorithms which produce estimates with …
has type: Thesis/Dissertation
date issued: 2001-11
is shown at: 10.14288/1.0085726
language: eng
degree discipline: Physics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/13891