title: Multi-resolutional brain network filtering and analysis via wavelets on non-Euclidean space.
abstract: 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.
authors: University of Wisconsin, Madison, USA.
authors: Won Hwa
authors: WH
authors: Kim
authors: University of Wisconsin, Madison, USA.
authors: Nagesh
authors: N
authors: Adluru
authors: University of Wisconsin, Madison, USA.
authors: Moo K
authors: MK
authors: Chung
authors: Southeastern Louisiana University, Hammond, USA.
authors: Sylvia
authors: S
authors: Charchut
authors: University of Illinois, Chicago, USA.
authors: Johnson J
authors: JJ
authors: GadElkarim
authors: University of California, Los-Angeles, USA.
authors: Lori
authors: L
authors: Altshuler
authors: University of California, Los-Angeles, USA.
authors: Teena
authors: T
authors: Moody
authors: University of Illinois, Chicago, USA.
authors: Anand
authors: A
authors: Kumar
authors: University of Wisconsin, Madison, USA.
authors: Vikas
authors: V
authors: Singh
authors: University of Illinois, Chicago, USA.
authors: Alex D
authors: AD
authors: Leow
mesh_terms: D000328:Adult; D000465:Algorithms; D001714:Bipolar Disorder / Q000175:diagnosis / Q000503:physiopathology*; D001921:Brain / Q000503:physiopathology*; D005260:Female; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008297:Male; D009415:Nerve Net / Q000503:physiopathology*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D058067:Wavelet Analysis