COVLET: Covariance-Based Wavelet-Like Transform for Statistical Analysis of Brain Characteristics in Children

Abstract

Adolescence is a period of substantial experience-dependent brain development. A major goal of the Adolescent Brain Cognitive Development (ABCD) study is to understand how brain development is associated with various environmental factors such as socioeconomic characteristics. While ABCD study offers a large sample size, it still requires a sensitive method to detect subtle associations when studying typically developing children. Therefore, we propose a novel transform, i.e. covariance-based multi-scale transform (COVLET), which derives a multi-scale representation from a structured data (i.e., P features from N samples) that increases performance of downstream analyses. The theory driving our work stems from wavelet transform in signal processing and orthonormality of the principal components of a covariance matrix. Given the microstructural properties of brain regions from children enrolled in the ABCD study, we demonstrate a multi-variate statistical group analysis on family income using the multi-scale feature derived from brain structure and validate improvement in the statistical outcomes. Furthermore, our multi-scale descriptor reliably identifies specific regions of the brain that are susceptible to socioeconomic disparity.