Resolution Enhancement in Magnetic Resonance Imaging by Frequency Extrapolation
Bibliographic record
Abstract
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.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".