I'll present my thesis work at JSM 2024 Section on Statistics in Imaging

Abstract

In imaging denoising tasks, brain imaging data like functional magnetic resonance imaging (fMRI) or positron emission tomography (PET) scans often contain noise and artifacts. Kernel smoothing techniques are essential for smoothing these images and play a pivotal role in brain imaging analysis. While kernel smoothing has been extensively studied in statistics, certain challenges remain, especially in the multi-dimensional landscape. Many existing methods lack adaptive smoothing capabilities and numerical flexibility in high dimensional setting, hindering the achievement of optimal results. To address this, we present an efficient adaptive General Kernel Smoothing-Finite Element Method (GKS-FEM). This method exploits the equivalence between GKS and the general second-order parabolic partial differential equation (PDE) in high dimensions. Utilizing the Finite Element Method (FEM), we discretize the PDE, leading to efficient and robust numerical smoothing approaches. This study establishes a bridge between statistics and mathematics.

Qiuyi Wu

Postdoc Research Fellow

My research interests include functional data analysis, image processing and high dimensional data anlaysis.