Automated characterization of noise distributions in diffusion MRI data

Abstract

Knowledge of the noise distribution in magnitude diffusion MRI images is the centerpiece to quantify uncertainties arising from the acquisition process. The use of parallel imaging methods, the number of receiver coils and imaging filters applied by the scanner, amongst other factors, dictate the resulting signal distribution. Accurate estimation beyond textbook Rician or noncentral chi distributions often requires information about the acquisition process (e.g., coils sensitivity maps or reconstruction coefficients), which is usually not available. We introduce two new automated methods using the moments and maximum likelihood equations of the Gamma distribution to estimate noise distributions as they explicitly depend on the number of coils, making it possible 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 using stationary and spatially varying noncentral chi noise distributions were created for two diffusion weightings with SENSE or GRAPPA reconstruction and 8, 12 or 32 receiver coils. Furthermore, MRI data of a water phantom with different combinations of parallel imaging were acquired on a 3T Philips scanner along with noise-only measurements. Finally, experiments on freely available datasets from a single subject acquired on a 3T GE scanner 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 acquired on a 3T Siemens scanner. 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 on the acquired datasets 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 for the bias correction and denoising task 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.

Keywords: Diffusion MRI; GRAPPA; Gamma distribution; Noise estimation; Parallel acceleration; SENSE.