Statistical analysis of fMRI using wavelets: Big Data, denoising, large‐p‐small‐n matrices

Abstract

AbstractOver the past decade functional Magnetic Resonance Imaging (fMRI) has been intensively used to study the complex functional network organization of the human brain and how it changes in time. An fMRI machine produces 3D time‐course cerebral images that contain hundreds of thousands of voxels and each voxel is scanned for hundreds of times. This potentially allows the researchers to explore functional connectivity on a voxel‐to‐voxel level, and also yields a number of serious statistical complications. First of all, the high‐dimension property of fMRI data turns it into Big Data. Furthermore, the study of functional brain network for so many voxels involves the problem of estimation of and simultaneous inference for large‐p‐small‐n cross‐covariance matrices. Furthermore, all problems should be solved in the presence of notoriously large fMRI noise which often forces statisticians to average signals over large areas instead of considering a network between individual voxels. An attractive alternative to the averaging, discussed in the paper, is a multiresolution wavelet analysis complemented by special procedures of estimating noise and estimation and simultaneous inference for cross‐covariance and cross‐correlation matrices for hundreds of thousands pairs of voxels, and it is fair to say that if wavelets have not been already known, fMRI applications would necessitates their creation. Both task and resting‐state fMRI are considered, and lessons from the wavelet analysis of ultra‐fast and conventional neuroplasticity fMRI experiments are presented. The article is self‐contained and does not require familiarity with wavelets or fMRI.This article is categorized under: Algorithms and Computational Methods > Numerical Methods Applications of Computational Statistics > Signal and Image Processing and Coding