Simultaneous Registration and Estimation of Fractional Anisotropy Profiles from Fragmented and Noisy Observations

• Activity Number: 334 - Functional and Geometric Approaches for Imaging Data
• Type: Invited
• Date/Time: Thursday, August 12, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistics in Imaging
• Author(s): Sebastian Kurtek* and James Matuk and Oksana Chkrebtii and Karthik Bharath
• Companies: The Ohio State University and Department of Statistics, The Ohio State University and The Ohio State University and University of Nottingham
• Keywords: function estimation; function registration; amplitude and phase variability; square root velocity function; Bayesian inference

Abstract

In many applications, smooth processes generate data that is recorded under a variety of observational regimes, such as dense sampling and sparse or fragmented observations that are often contaminated with noise. The statistical goal of registering and estimating the underlying functions from discrete observations has thus far been mainly approached sequentially without formal uncertainty propagation, or in an application-specific manner by pooling information across subjects. We propose a unified Bayesian framework for simultaneous registration and estimation, which is flexible enough to accommodate inference on individual functions under general observational regimes. Our ability to do this relies on the specification of informative prior models over the amplitude component of function variability using two different strategies: (1) data-driven, and (2) shape-restricted. The proposed framework builds on elastic functional data analysis to separately model amplitude and phase variability inherent in functional data. We validate the proposed approach using simulation studies and apply it to two datasets of fractional anisotropy from diffusion tensor imaging.