Speaker: JIAPING WANG (University of North Carolina - Chapel Hill)

Title: Multiscale Adaptive Smoothing Model for the Spatio-temporal Functional Data

Abstract: The fMRI has become popular and widely used in medical imaging. As the spatio-temporal functional data, the study of fMRI data often aims to analyze functional data with complex spatial and temporal correlation structures and varying activation patterns on a two-dimensional (2D) surface or in a 3D volume. The aim of this talk is to introduce a multiscale adaptive smoothing model (MASM) to enhance the quality of the 2D or 3D noisy functional images with the applications in the fMRI data. Compared with most statistical methods which smooth functions independently, MASM, however, is a comprehensive framework to simultaneously smooth the functions across all locations, specifically when accounting for the complex spatial dependence and patterns in 2D or 3D functional images. MASM has three features: being spatial, being hierarchical, and being adaptive. To hierarchically and spatially denoise functional images, MASM creates adaptive ellipsoids at each location to capture spatial dependence among imaging observations in neighboring locations.

To apply MASM to the study of fMRI data, we introduce two applications in this talk. One is estimating the hemodynamic response function (HRF) in the event fMRI data, which implements MASM in the frequency domain by integrating the spatial and temporal information to adaptively and accurately estimate HRFs pertaining to each stimulus sequence across all voxels in a 2D or 3D space. The 2nd is about the functional principal component analysis (fPCA) in which we combine MASM with the power algorithm to develop a new method called the multiscale adaptive fPCA. The finite sample performance of these applications is demonstrated in the simulations and the real data analyses. The consistency of the adaptive estimates under some mild conditions will be given in the future work.