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

• Published in: Information 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
• Language: English
• Published: Cham Springer International Publishing 2015
• Series: Lecture Notes in Computer Science
• Subjects: Aged; Aged, 80 and over; Alzheimer Disease - pathology; Cerebral Ventricles - pathology; Computer Simulation; Female; Gaussian Process Model; General Linear Model Approach; Humans; Image Interpretation, Computer-Assisted - methods; Image Time Series; Kronecker Product; Magnetic Resonance Imaging - methods; Male; Marginal Likelihood; Middle Aged; Models, Statistical; Normal Distribution; Pattern Recognition, Automated - methods; Reproducibility of Results; Sensitivity and Specificity; Spatio-Temporal Analysis; Time Factors
• ISBN: 9783319199917; 3319199919
• ISSN: 0302-9743; 1011-2499; 1611-3349; 1611-3349
• DOI: 10.1007/978-3-319-19992-4_49

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.