Advances in resting state fMRI and diffusion weighted imaging (DWI) have led to much interest in studies that evaluate hypotheses focused on how brain connectivity networks show variations across clinically disparate groups. However, various sources of error (e.g., tractography errors, magnetic field distortion, and motion artifacts) leak into the data, and make downstream statistical analysis problematic. In small sample size studies, such noise have an unfortunate effect that the differential signal may not be identifiable and so the null hypothesis cannot be rejected. Traditionally, smoothing is often used to filter out noise. But the construction of convolving with a Gaussian kernel is not well understood on arbitrarily connected graphs. Furthermore, there are no direct analogues of scale-space theory for graphs — ones which allow to view the signal at multiple resolutions. We provide rigorous frameworks for performing ’multi-resolutional’ analysis on brain connectivity graphs. These are based on the recent theory of non-Euclidean wavelets. We provide strong evidence, on brain connectivity data from a network analysis study (structural connectivity differences in adult euthymic bipolar subjects), that the proposed algorithm allows identifying statistically significant network variations, which are clinically meaningful, where classical statistical tests, if applied directly, fail.
This research is supported by NIH R01AG040396, NIH R01AG021155, NSF RI1116584, NSF RI1252725, the Wisconsin Partnership Proposal, UW ADRC, and UW ICTR (1UL1RR025011), NIH grants P30 AG010129, K01 AG030514, NIH R01 AG027161 and Waisman Core grant P30 HD003352-45.