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Statistical methods in medical image estimation and sparse signal recovery
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Abstract [sv]

Denna avhandling presenterar arbete kring metoder för skattning av datortomografibilder (CT) från magnetiska resonanstomografibilder (MR) för ett antal diagnostiska och terapeutiska arbetsflöden. Studien demonstrerar även en metod för gles signalrekonstruktion, vilket är en mellanliggande metod för rekonstruktion av MR-bilder. Avhandlingen består av fyra artiklar. De tre första artiklarna handlar om att utveckla statistiska metoder för uppskattning av CT-bilder från MR-bilder. Här formuleras rumsliga och icke-rumsliga modeller för skattning av CT-bilder från MR-bilder, där de rumsliga modellerna inkluderar dolda Markov-modeller (HMM) och dolda Markov-slumpfältmodeller (HMRF), medan de icke-rumsliga modellerna består av Gaussiska mix-modeller (GMM) och skeva Gaussiska mixmodeller (SGMM). De statistiska modellerna skattas via en maximum-likelihoodansats, där EM-algoritmen används för GMM och SGMM, EM-gradientalgoritmen för HMRF samt Baum-Welch-algoritmen för HMM. Vi har även undersökt CTbildskattning med hjälp av GMM och övervakade statistiska inlärningsmetoder. Modellernas prestanda har utvärderats med hjälp av korsvalidering på faktiska data. Genom att jämföra prestandan hos modellernas CT-bildskattningar har vi observerat att GMM kombinerat med övervakad statistisk inlärning har den bästa prestandan, i synnerhet ifråga om benvävnad. Den fjärde artikeln behandlar en gles modellering inom signalrekonstruktion. Med hjälp av så kallade ”spike and slab priors” för signalen formulerade vi ett glest signalrekonstruktionsproblem och utvecklade en adaptiv algoritm för gles signalrekonstruktion. Den utvecklade algoritmen har bättre prestanda än den nyligen föreslagna iterativ konvex förfining (ICR)-algoritmen. De metoder som introducerats i detta arbete är bidrag till litteraturen inom så kallade ”lattice-processer” och signalbehandling. Resultaten levererar ett bidrag till forskningen kring ersättandet av CT-bilder med syntetiska eller pseudo-CTbilder, samt till effektiv gles signalrekonstruktion.

Place, publisher, year, edition, pages
Umeå: Umeå University , 2018. , p. 59
Series
Research report in mathematical statistics, ISSN 1653-0829 ; 63
Keywords [en]
Computed tomography, magnetic resonance imaging, Gaussian mixture model, skew-Gaussian mixture model, hidden Markov random field, hidden Markov model, supervised statistical learning, synthetic CT images, pseudo-CT images, spike and slab prior, adaptive algorithm
National Category
Probability Theory and Statistics Radiology, Nuclear Medicine and Medical Imaging
Identifiers
URN: urn:nbn:se:umu:diva-147751ISBN: 978-91-7601-890-3 (electronic)OAI: oai:DiVA.org:umu-147751DiVA, id: diva2:1206407
Public defence
2018-06-08, MA121, MIT-building, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2018-05-18 Created: 2018-05-16 Last updated: 2018-06-09Bibliographically approved
List of papers
1. Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images
Open this publication in new window or tab >>Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images
Show others...
2017 (English)Manuscript (preprint) (Other academic)
Abstract [en]

There is an interest to replace computed tomography (CT) images withmagnetic resonance (MR) images for a number of diagnostic and therapeuticworkflows. In this article, predicting CT images from a number of magnetic resonance imaging (MRI) sequences using regression approach isexplored. Two principal areas of application for estimated CT images aredose calculations in MRI based radiotherapy treatment planning and attenuationcorrection for positron emission tomography (PET)/MRI. Themain purpose of this work is to investigate the performance of hidden Markov (chain) models (HMMs) in comparison to hidden Markov random field (HMRF) models when predicting CT images of head. Ourstudy shows that HMMs have clear advantages over HMRF models in this particular application. Obtained results suggest that HMMs deservea further study for investigating their potential in modeling applications where the most natural theoretical choice would be the class of HMRFmodels.

Publisher
p. 17
Keywords
computed tomography, magnetic resonance imaging, pseudo-CT, hidden Markov model, hidden Markov random field, unsupervised modeling, radiotherapy, attenuation correction
National Category
Probability Theory and Statistics Medical Image Processing
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-141547 (URN)
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
Funder
Swedish Research Council, 340-2013-5342
Available from: 2017-11-07 Created: 2017-11-07 Last updated: 2018-06-09
2. Model-based Estimation of Computed Tomography Images
Open this publication in new window or tab >>Model-based Estimation of Computed Tomography Images
2017 (English)Manuscript (preprint) (Other academic)
Abstract [en]

There is a growing interest to get a fully MR based radiotherapy. The most important development needed is to obtain improved bone tissue estimation. Existing model-based methods have performed poorly on bone tissues. This paper aims to obtainimproved estimation of bone tissues. Skew-Gaussian mixture model (SGMM) isproposed to further investigate CT image estimation from MR images. The estimation quality of the proposed model is evaluated using leave-one-out cross-validation method on real data. In comparison with the existing model-based approaches, the approach utilized in this paper outperforms in estimation of bone tissues, especiallyon dense bone tissues.

Publisher
p. 17
Keywords
computed tomography; magnetic resonance imaging; CT image estimation; model-based estimation; skew-normal mixture model
National Category
Probability Theory and Statistics Medical Image Processing
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-141546 (URN)
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
Funder
Swedish Research Council, 340-2013-5342
Available from: 2017-11-07 Created: 2017-11-07 Last updated: 2018-06-09
3. Computed Tomography Image Estimation by Statistical Learning Methods
Open this publication in new window or tab >>Computed Tomography Image Estimation by Statistical Learning Methods
(English)Manuscript (preprint) (Other academic)
Abstract [en]

There is increasing interest in computed tomography (CT) image estimations from magnetic resonance (MR) images. The estimated CT images canbe utilised for attenuation correction, patient positioning, and dose planningin diagnostic and radiotherapy workflows. This study presents a statisticallearning method for CT image estimation. We have used predefined tissuetype information in a Gaussian mixture model to explore the estimation.The performance of our method was evaluated using cross-validation on realdata. In comparison with the existing model-based CT image estimationmethods, the proposed method has improved the estimation, particularly inbone tissues. Evaluation of our method shows that it is a promising methodto generate CT image substitutes for the implementation of fully MR-basedradiotherapy and PET/MRI applications.

Keywords
Computed tomography, magnetic resonance imaging, CT image estimation, pseudo-CT image, supervised learning, Gaussian mixture model
National Category
Probability Theory and Statistics Radiology, Nuclear Medicine and Medical Imaging
Identifiers
urn:nbn:se:umu:diva-147720 (URN)
Available from: 2018-05-15 Created: 2018-05-15 Last updated: 2018-06-09
4. Adaptive algorithm for sparse signal recovery
Open this publication in new window or tab >>Adaptive algorithm for sparse signal recovery
2018 (English)Manuscript (preprint) (Other academic)
Abstract [en]

Spike and slab priors play a key role in inducing sparsity for sparse signal recovery. The use of such priorsresults in hard non-convex and mixed integer programming problems. Most of the existing algorithms to solve the optimization problems involve either simplifying assumptions, relaxations or high computational expenses. We propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the presented optimization problem. The algorithm is based on the one-to-onemapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternatingdirection method of multipliers to recover the signal corresponding to the updated support. Experiments on synthetic data and real-world images show that the proposed AADMM algorithm provides superior performance and is computationally cheaper, compared to the recently developed iterative convex refinement (ICR) algorithm.

Publisher
p. 16
Keywords
sparsity, adaptive algorithm, sparse signal recovery, spike and slab priors
National Category
Probability Theory and Statistics Computational Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-146386 (URN)
Funder
Swedish Research Council, 340-2013-534
Available from: 2018-04-07 Created: 2018-04-07 Last updated: 2018-06-09

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Bayisa, Fekadu Lemessa

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