Recovering missing connections in diffusion weighted mri using matrix completion

Abstract

Diffusion weighted magnetic resonance imaging (dwMRI) has become the dominant neuroimaging modality for estimating anatomical connectivity (AC). However, such AC estimation is prone to error due to missing connections resulting from crossing fibers and fiber endpoint uncertainty because of insufficient spatial resolution. Endeavors tackling this problem include improving fiber orientation estimation, applying heuristics to extrapolate fiber endpoints, and increasing spatial resolution. Refining fiber orientation estimation and tractography algorithms can only improve AC estimation to a certain extent, since the attainable improvement is constrained by the current limit on spatial resolution. We thus instead propose using matrix completion (MC) to recover missing connections. The underlying assumption is that the missing connections are intrinsically related to the observed entries of the AC matrix. A critical parameter that governs MC performance is the matrix rank. For this, we present a robust strategy that bypasses selection of a specific rank. Further, standard MC algorithms do not constrain the recovered entries to be non-negative, but this condition is necessary for fiber counts. We thus devise a method to interpolate negative entries based on neighborhood information. On synthetic data, our approach is able to accurately recover deleted AC matrix entries. On real data, AC estimated with our approach achieves higher IQ prediction accuracy than the original AC estimates, fiber endpoint extrapolation, and median filtering.