Open this publication in new window or tab >>2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]
This thesis is carried out within two projects ‘Statistical modelling and intelligentdata sampling in Magnetic resonance imaging (MRI) and positron-emission tomography(PET) measurements for cancer therapy assessment’ and ‘WindCoE -Nordic Wind Energy Center’ during my PhD study. It mainly focuses on applicationsof Bayesian hierarchical models (BHMs) and theoretical developments ofcompressive sensing (CS). Under the first project, Paper I improves the quantityestimation of MRI parametric imaging by utilizing inherent dependent structure inthe image through BHMs; Paper III constructs a theoretically unbiased and asymptoticallynormal estimator of sparsity of a sparsified MR image by using a BHM;Paper IV extends block sparsity estimation from real-valued signal recovery tocomplex-valued signal recovery. It also demonstrates the importance of accuratelyestimating the block sparsity through a sensitivity analysis; Paper V proposes anew measure, i.e. q-ratio block constrained minimal singular value, of measurementmatrix for block sparse signal recovery. An algorithm for computing thisnew measure is also presented. In the second project, Paper II estimates the uncertaintyof Weather Research and Forecasting (WRF) model’s daily-mean 2-metertemperature in a cold region by using a BHM. It is a computationally cheaper andfaster alternative to traditional ensemble approach. In summary, this thesis makessignificant contributions in improving and optimizing the estimation proceduresof parameters of interest in MRI and WRF in practice, and developing the novelestimators and measure under the framework of CS in theory.
Place, publisher, year, edition, pages
Umeå: Umeå University, 2019. p. 35
Series
Research report in mathematical statistics, ISSN 1653-0829 ; 69
Keywords
Magnetic resonance imaging, Bayesian hierarchical models, Weather Research and Forecasting, Compressive sensing, Block sparsity, Multivariate isotropic symmetric a-stable distribution, q-ratio block constrained minimal singular value
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-165285 (URN)978-91-7855-148-4 (ISBN)
Public defence
2019-12-17, N450, Naturvetarhuset, Umeå University, Umeå, 13:00 (English)
Opponent
Supervisors
2019-11-262019-11-192023-09-14Bibliographically approved