# Automated characterization of noise distributions in diffusion MRI data

## TL;DR

This paper introduces two automated methods for estimating noise distributions in diffusion MRI data using only magnitude data, improving robustness and accuracy over existing techniques.

## Contribution

The paper presents novel automated algorithms based on moments and maximum likelihood for noise estimation in diffusion MRI, requiring no prior acquisition information.

## Key findings

- Methods are robust to artifacts and signal leakage.
- Estimated parameters are stable across repeated in vivo scans.
- Proposed algorithms outperform existing methods in noise estimation accuracy.

## Abstract

Knowledge of the noise distribution in diffusion MRI is the centerpiece to quantify uncertainties arising from the acquisition process. Accurate estimation beyond textbook distributions often requires information about the acquisition process, which is usually not available. We introduce two new automated methods using the moments and maximum likelihood equations of the Gamma distribution to estimate all unknown parameters using only the magnitude data. A rejection step is used to make the framework automatic and robust to artifacts. Simulations were created for two diffusion weightings with parallel imaging. Furthermore, MRI data of a water phantom with different combinations of parallel imaging were acquired. Finally, experiments on freely available datasets are used to assess reproducibility when limited information about the acquisition protocol is available. Additionally, we demonstrated the applicability of the proposed methods for a bias correction and denoising task on an in vivo dataset. A generalized version of the bias correction framework for non integer degrees of freedom is also introduced. The proposed framework is compared with three other algorithms with datasets from three vendors, employing different reconstruction methods. Simulations showed that assuming a Rician distribution can lead to misestimation of the noise distribution in parallel imaging. Results showed that signal leakage in multiband can also lead to a misestimation of the noise distribution. Repeated acquisitions of in vivo datasets show that the estimated parameters are stable and have lower variability than compared methods. Results show that the proposed methods reduce the appearance of noise at high b-value. The proposed algorithms herein can estimate both parameters of the noise distribution automatically, are robust to signal leakage artifacts and perform best when used on acquired noise maps.