The Non-Local Bootstrap - Estimation of Uncertainty in Diffusion MRI

Diffusion MRI is a noninvasive imaging modality that allows for the estimation and visualization of white matter connectivity patterns in the human brain. However, due to the low signal-to-noise ratio (SNR) nature of diffusion data, deriving useful statistics from the data is adversely affected by different sources of measurement noise. This is aggravated by the fact that the sampling distribution of the statistic of interest is often complex and unknown. In situations as such, the bootstrap, due to its distribution-independent nature, is an appealing tool for the estimation of the variability of almost any statistic, without relying on complicated theoretical calculations, but purely on computer simulation. In this work, we present new bootstrap strategies for variability estimation of diffusion statistics in association with noise. In contrast to the residual bootstrap, which relies on a predetermined data model, or the repetition bootstrap, which requires repeated signal measurements, our approach, called the non-local bootstrap (NLB), is non-parametric and obviates the need for time-consuming multiple acquisitions. The key assumption of NLB is that local image structures recur in the image. We exploit this self-similarity via a multivariate non-parametric kernel regression framework for bootstrap estimation of uncertainty. Evaluation of NLB using a set of high-resolution diffusion-weighted images, with lower than usual SNR due to the small voxel size, indicates that NLB is markedly more robust to noise and results in more accurate inferences.