  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 not
usually available. We introduce a new method where a change of variable
naturally gives rise to a particular form of the gamma distribution for
background signals. The first moments and maximum likelihood estimators of this
gamma distribution 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 method automatic and robust to artifacts. Experiments
on synthetic datasets show that the proposed method can reliably estimate both
the degrees of freedom and the standard deviation. The worst case errors range
from below 2% (spatially uniform noise) to approximately 10% (spatially
variable noise). Repeated acquisitions of in vivo datasets show that the
estimated parameters are stable and have lower variances than compared methods.
