NUQ: A Noise Metric for Diffusion MRI via Uncertainty Discrepancy Quantification

Diffusion MRI (dMRI) is the only non-invasive technique sensitive to tissue micro-architecture, which can, in turn, be used to reconstruct tissue microstructure and white matter pathways. The accuracy of such tasks is hampered by the low signal-to-noise ratio in dMRI. Today, the noise is characterized mainly by visual inspection of residual maps and estimated standard deviation. However, it is hard to estimate the impact of noise on downstream tasks based only on such qualitative assessments. To address this issue, we introduce a novel metric, Noise Uncertainty Quantification (NUQ), for quantitative image quality analysis in the absence of a ground truth reference image. NUQ uses a recent Bayesian formulation of dMRI models to estimate the uncertainty of microstructural measures. Specifically, NUQ uses the maximum mean discrepancy metric to compute a pooled quality score by comparing samples drawn from the posterior distribution of the microstructure measures. We show that NUQ allows a fine-grained analysis of noise, capturing details that are visually imperceptible. We perform qualitative and quantitative comparisons on real datasets, showing that NUQ generates consistent scores across different denoisers and acquisitions. Lastly, by using NUQ on a cohort of schizophrenics and controls, we quantify the substantial impact of denoising on group differences.