From Picoscale Pathology to Decascale Disease: Image Registration with a Scattering Transform and Varifolds for Manipulating Multiscale Data.

Advances in neuroimaging have yielded extensive variety in the scale and type of data available. Effective integration of such data promises deeper understanding of anatomy and disease-with consequences for both diagnosis and treatment. Often catered to particular datatypes or scales, current computational tools and mathematical frameworks remain inadequate for simultaneously registering these multiple modes of "images" and statistically analyzing the ensuing menagerie of data. Here, we present (1) a registration algorithm using a "scattering transform" to align high and low resolution images and (2) a varifold-based modeling framework to compute 3D spatial statistics of multiscale data. We use our methods to quantify microscopic tau pathology across macroscopic 3D regions of the medial temporal lobe to address a major challenge in the diagnosis of Alzheimer's Disease-the reliance on invasive methods to detect microscopic pathology.