| Zugriffsnummer |
47259 |
| Dokumenttyp |
Dissertation
|
| Peer Review |
unbekannt |
| Sprache |
Englisch
|
| Titel |
Bayesian data analysis for magnetic resonance fingerprinting |
| Autor(in); Institution |
Metzner, Selma; 8.4, Mathematische Modellierung und Datenanalyse, PTB-Berlin
|
| Quelle/Jahr |
(2021), 125 S.
|
| Dissertationsvermerk |
Dissertation, Technische Universität Berlin, 2021 |
| DOI |
|
| Freie Schlagworte |
quantitative MRI ; Bayesian statistics ; magnetic resonance fingerprinting ; quantitative MR-Bildgebung ; Bayessche Statistik |
| Zusammenfassung |
Magnetic resonance imaging is a medical imaging technique which is widely used in clinical practice. It is non-invasive and provides
a good tissue contrast. However, usually only qualitative images are obtained. In quantitative MRI biological tissue properties are measured which enhances the reliability of diagnostics. Standard methods in qMRI require long acquisition times and usually just measure a single parameter. Magnetic Resonance Fingerprinting is a recent approach to qMRI that allows for the simultaneous estimation of the tissue-related parameters within short acquisition time. The main idea of MRF is to conduct a series of measurements that are highly undersampled in the Fourier domain and perform a template matching between approximately reconstructed magnetization courses and modeled magnetization courses stored in a pre-computed dictionary. The goal of this thesis is to apply Bayesian statistics to further enhance the data analysis of MRF. Advantages of a Bayesian approach include the possibility to incorporate available prior knowledge and to obtain a posterior distribution for the sought parameters. The posterior can be used to assign uncertainties and to make probability statements. This can be particularly useful when assessing diagnostics or therapy monitoring. The first contribution of this thesis is a Bayesian uncertainty quantification for the dictionary-based MRF estimates. The data analysis of the original MRF approach is shown to be equivalent to a maximum likelihood estimation for a particular statistical model, and a Bayesian inference is developed based on this model. Analytical expressions for the posterior are derived and numerical techniques utilizing the pre-computed dictionary lead to a fast probability characterization. The second contribution of this thesis is the development of a Bayesian inference for MRF data based on direct modeling in the Fourier domain.
The advantage is that significantly better estimates can be achieved when aliasing errors are the dominant uncertainty source of the dictionary-based MRF data analysis. However, the challenge is that a large-scale regression problem is faced. A general class of large-scale regression problems together with several classes of (improper) prior distributions is considered and theoretical properties of the posterior such as the existence of moments are explored. These results apply to MRF but can also be used for many other large-scale regression problems. Spatial smoothness of the parameters can be modeled through Gaussian Markov Random Field or so-called partition priors, and the potential advantage of such prior information is explored for MRF. The results of thesis demonstrate that the Bayesian inference developed for the original, dictionary-based MRF approach yields both a reliable uncertainty quantification and the possibility to make probability statements about the sought parameters for the first time.
Furthermore, when aliasing errors are the dominating source of uncertainty for the dictionary-based MRF approach, the developed large-scale Bayesian inference can substantially improve the estimation. Additionally, the inclusion of valuable prior information can improve estimation quality for MRF substantially. The enhancement of data analysis for MRF developed in this thesis is expected to support MRF and its potential future application in clinical practice. |
