Efficient Gaussian Process-Based Modelling and Prediction of Image Time Series

In this work we propose a novel Gaussian process-based spatio-temporal model of time series of images. By assuming separability of spatial and temporal processes we provide a very efficient and robust formulation for the marginal likelihood computation and the posterior prediction. The model adaptiv...

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Bibliographic Details
Published inInformation Processing in Medical Imaging Vol. 24; pp. 626 - 637
Main Authors Lorenzi, Marco, Ziegler, Gabriel, Alexander, Daniel C., Ourselin, Sebastien
Format Book Chapter Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2015
SeriesLecture Notes in Computer Science
Subjects
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ISBN9783319199917
3319199919
ISSN0302-9743
1011-2499
1611-3349
1611-3349
DOI10.1007/978-3-319-19992-4_49

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Summary:In this work we propose a novel Gaussian process-based spatio-temporal model of time series of images. By assuming separability of spatial and temporal processes we provide a very efficient and robust formulation for the marginal likelihood computation and the posterior prediction. The model adaptively accounts for local spatial correlations of the data, and the covariance structure is effectively parameterised by the Kronecker product of covariance matrices of very small size, each encoding only a single direction in space. We provide a simple and flexible framework for within- and between-subject modelling and prediction. In particular, we introduce the Hoffman-Ribak method for efficient inference on posterior processes and its uncertainty. The proposed framework is applied in the context of longitudinal modelling in Alzheimer’s disease. We firstly demonstrate the advantage of our non-parametric method for modelling of within-subject structural changes. The results show that non-parametric methods demonstrably outperform conventional parametric methods. Then the framework is extended to optimize complex parametrized covariate kernels. Using Bayesian model comparison via marginal likelihood the framework enables to compare different hypotheses about individual change processes of images.
Bibliography:G. Ziegler—Joint first author. Data used in preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (http://adni.loni.usc.edu/). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report.
ISBN:9783319199917
3319199919
ISSN:0302-9743
1011-2499
1611-3349
1611-3349
DOI:10.1007/978-3-319-19992-4_49