Multi-resolutional shape features via non-Euclidean wavelets: Applications to statistical analysis of cortical thickness

Abstract

Statistical analysis on arbitrary surface meshes such as the cortical surface is an important approach to understanding brain diseases such as Alzheimer’s disease (AD). Surface analysis may be able to identify specific cortical patterns that relate to certain disease characteristics or exhibit differences between groups. Our goal in this paper is to make group analysis of signals on surfaces more sensitive. To do this, we derive multi-scale shape descriptors that characterize the signal around each mesh vertex, i.e., its local context, at varying levels of resolution. In order to define such a shape descriptor, we make use of recent results from harmonic analysis that extend traditional continuous wavelet theory from the Euclidean to a non-Euclidean setting (i.e., a graph, mesh or network). Using this descriptor, we conduct experiments on two different datasets, the Alzheimer’s Disease NeuroImaging Initiative (ADNI) data and images acquired at the Wisconsin Alzheimer’s Disease Research Center (W-ADRC), focusing on individuals labeled as having Alzheimer’s disease (AD), mild cognitive impairment (MCI) and healthy controls. In particular, we contrast traditional univariate methods with our multi-resolution approach which show increased sensitivity and improved statistical power to detect a group-level effects. We also provide an open source implementation.

Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping

“…The present framework lacks a systematic approach in determining the spectral coverage for each wavelet scale; this is a limitation for the SGWT design in general, as also reported in other applications than fMRI (e.g., Kim et al, 2014;Li and Hamza, 2013). The adopted spectral partitioning in the design has been found empirically by visual assessment of the wavelets and their characteristic scale.…”

“…They have also been used to discriminate between healthy and pathological tissue by characterizing subtle changes in brain structure in a variety of diseases such as Alzheimer's disease, mild cognitive impairment and multiple sclerosis (Hackmack et al, 2012;Harrison et al, 2010). Interestingly, the recent proposal in Kim et al (2014), also uses the SGWT to derive multi-scale shape descriptors that can be used to detect group-level effects. However, the approach uses cortical surface reconstructions, and as such, it comes with benefits and limitations of interpolation between the surface and volume as we discussed earlier.…”

Second harmonic generation microscopy analysis of extracellular matrix changes in human idiopathic pulmonary fibrosis

“…[34][35][36] The wavelet transform decomposition provides both spatial and frequency domain information, which is intricately related to the scale and orientation of the texture features we seek to characterize in the image data. In this process, the wavelet function is placed on a specific location on the image to determine the correlation coefficients between this function and the local morphology.…”

Multi-resolution statistical analysis of brain connectivity graphs in preclinical Alzheimer's disease

“…The standard constructions are no longer applicable for non-Euclidean spaces. Based on recent work in harmonic analysis on spectral graph wavelets (Hammond et al, 2011) and using methods developed by our group to apply non-Euclidean wavelet based transformations to conduct shape analysis (Kim et al, 2012, 2014), we show how to perform multi-resolution wavelet analysis to connectivity graphs derived from DTI data. Multi-resolution wavelet analysis is ideal for improving sensitivity in both cases where sample sizes are low (often the case in patient-based studies), and where differences (effect sizes) may be small, often the case in studies of preclinical participants.…”