Resolution Enhancement in Magnetic Resonance Imaging by Frequency Extrapolation

This thesis focuses on spatial resolution enhancement of magnetic resonance imaging (MRI). In particular, it addresses methods of performing such enhancement in the Fourier domain.
\n
\nAfter a brief review of Fourier theory, the thesis reviews the physics of the MRI acquisition process in order to introduce a mathematical model of the measured data. This model is later used to develop and analyze methods for resolution enhancement, or "super-resolution'', in MRI. 
\n
\nWe then examine strategies of performing super-resolution MRI (SRMRI). We begin by exploring strategies that use multiple data sets produced by spatial translations of the object being imaged, to add new information to the reconstruction process. This represents a more detailed mathematical examination of the author's Master's work at the University of Calgary. Using our model of the measured data developed earlier in the thesis, we describe how the acquisition strategy determines the efficacy of the SRMRI process that employs multiple data sets.
\n
\nThe author then explores the self-similarity properties of MRI data in the 
\nFourier domain as a means of performing spatial resolution enhancement.
\nTo this end, a fractal-based method over (complex-valued) Fourier
\nTransforms of functions with compact spatial support, derived from a
\nfractal transform in the spatial domain, is explored. It is shown that
\nthis method of "Iterated Fourier Transform Systems" (IFTS) can be tailored to
\nperform frequency extrapolation, hence spatial resolution enhancement.
\n
\nThe IFTS method, however, is limited in scope, as it assumes that a
\nspatial function f(x) may be approximated by linear combinations of
\nspatially-contracted and range-modified copies of the entire function.
\nIn order to improve the approximation, we borrow from traditional
\nfractal image coding in the spatial domain, where subblocks of an
\nimage are approximated by other subblocks, and employ such a
\nblock-based strategy in the Fourier domain. An examination of the
\nstatistical properties of subblock approximation errors shows that, in
\ngeneral, Fourier data can be locally self-similar. Furthermore, we
\nshow that such a block-based self-similarity method is actually
\nequivalent to a special case of the auto-regressive moving average (ARMA) modeling method.
\n
\nThe thesis concludes with a chapter on possible future research directions in SRMRI.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.