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- Bayisa, Fekadu Lemessa, 1984-
(författare)
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Statistical methods in medical image estimation and sparse signal recovery
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis presents work on methods for the estimation of computed tomography (CT) images from magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. The study also demonstrates sparse signal recovery method, which is an intermediate method for magnetic resonance image reconstruction. The thesis consists of four articles. The first three articles are concerned with developing statistical methods for the estimation of CT images from MR images. We formulated spatial and non-spatial models for CT image estimation from MR images, where the spatial models include hidden Markov model (HMM) and hidden Markov random field model (HMRF) while the non-spatial models incorporate Gaussian mixture model (GMM) and skewed-Gaussian mixture model (SGMM). The statistical models are estimated via a maximum likelihood approach using the EM-algorithm in GMM and SGMM, the EM gradient algorithm in HMRF and the Baum–Welch algorithm in HMM. We have also examined CT image estimation using GMM and supervised statistical learning methods. The performance of the models is evaluated using cross-validation on real data. Comparing CT image estimation performance of the models, we have observed that GMM combined with supervised statistical learning method has the best performance, especially on bone tissues. The fourth article deals with a sparse modeling in signal recovery. Using spike and slab priors on the signal, we formulated a sparse signal recovery problem and developed an adaptive algorithm for sparse signal recovery. The developed algorithm has better performance than the recent iterative convex refinement (ICR) algorithm. The methods introduced in this work are contributions to the lattice process and signal processing literature. The results are an input for the research on replacing CT images by synthetic or pseudo-CT images, and for an efficient way of recovering sparse signal.
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| 2. |
- Wang, Jianfeng, 1984-
(författare)
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Enhanced block sparse signal recovery and bayesian hierarchical models with applications
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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