| Statistical analysis of brain images/image-derived measures plays a central role in discovering associations between different brain regions and covariates. When this framework is used to analyze neurodegenerative diseases such as Alzheimer's disease (AD), the major goal is to identify, ideally early on, which of the brain regions show abnormal variations due to the disease, so that we can provide intervention and treatment to slow down the progression of the disease. Unfortunately, there are several factors that make this statistical analysis problematic. In most brain imaging studies, the sample size is limited (typically up to only a few hundreds) due to the high cost of scans and difficulties in recruiting participants depending on diseases or risk factors. In many cases, thus, it may not be sufficient to robustly achieve statistically meaningful outcome especially when the effect size is small in the preclinical stages. Moreover, there are many nuisance factors that affects the analyses. To deal with the challenges above, in this thesis, we propose novel multi-resolution frameworks which we will develop and experimentally evaluate on a variety of neuroimaging data. These frameworks make use of recent work from harmonic analysis literature which implement "wavelet transform" in non-Euclidean spaces, so that we can adopt the multi-resolution scheme not only for imaging data in the Euclidean space but for image derived measures represented in non-Euclidean spaces such as cortical thickness on brain meshes and brain connectivity. We describe the algorithmic development and how such methods can help evaluate novel scientific hypothesis. For each framework, we demonstrate extensive experimental results to show that the frameworks improve statistical outcome over traditional approaches and can be easily adopted for real data analyses. |
