Regularized 3D functional regression for brain image data via Haar wavelets

TL;DR

This paper introduces a regularized Haar wavelet-based method for analyzing 3D brain images, effectively capturing spatial information and identifying regions linked to cognitive impairment in elderly patients.

Contribution

It presents a novel regularized wavelet approach tailored for 3D brain image data, improving prediction and region identification in functional data analysis.

Findings

Effective in predicting cognitive outcomes

Identifies brain subregions associated with Alzheimer's

Outperforms existing methods in simulation studies

Abstract

The primary motivation and application in this article come from brain imaging studies on cognitive impairment in elderly subjects with brain disorders. We propose a regularized Haar wavelet-based approach for the analysis of three-dimensional brain image data in the framework of functional data analysis, which automatically takes into account the spatial information among neighboring voxels. We conduct extensive simulation studies to evaluate the prediction performance of the proposed approach and its ability to identify related regions to the outcome of interest, with the underlying assumption that only few relatively small subregions are truly predictive of the outcome of interest. We then apply the proposed approach to searching for brain subregions that are associated with cognition using PET images of patients with Alzheimer's disease, patients with mild cognitive impairment and normal controls.