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Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images
University of Tartu, Estonia.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Chalmers University of Technology, Sweden.
University of Tartu, Estonia.
Show others and affiliations
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.

Place, publisher, year, edition, pages
2017. , p. 17
Keywords [en]
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: urn:nbn:se:umu:diva-141547OAI: oai:DiVA.org:umu-141547DiVA, id: diva2:1155314
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
Funder
Swedish Research Council, 340-2013-5342Available from: 2017-11-07 Created: 2017-11-07 Last updated: 2018-06-09
In thesis
1. Statistical methods in medical image estimation and sparse signal recovery
Open this publication in new window or tab >>Statistical methods in medical image estimation and sparse signal recovery
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
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:nbn:se:umu:diva-147751 (URN)978-91-7601-890-3 (ISBN)
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

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arXiv:1705.01727

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Bayisa, FekaduYu, Jun

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