  Diffusion magnetic resonance imaging datasets suffer from low Signal-to-Noise
Ratio, especially at high b-values. Acquiring data at high b-values contains
relevant information and is now of great interest for microstructural and
connectomics studies. High noise levels bias the measurements due to the
non-Gaussian nature of the noise, which in turn can lead to a false and biased
estimation of the diffusion parameters. Additionally, the usage of in-plane
acceleration techniques during the acquisition leads to a spatially varying
noise distribution, which depends on the parallel acceleration method
implemented on the scanner. This paper proposes a novel diffusion MRI denoising
technique that can be used on all existing data, without adding to the scanning
time. We first apply a statistical framework to convert the noise to Gaussian
distributed noise, effectively removing the bias. We then introduce a spatially
and angular adaptive denoising technique, the Non Local Spatial and Angular
Matching (NLSAM) algorithm. Each volume is first decomposed in small 4D
overlapping patches to capture the structure of the diffusion data and a
dictionary of atoms is learned on those patches. A local sparse decomposition
is then found by bounding the reconstruction error with the local noise
variance. We compare against three other state-of-the-art denoising methods and
show quantitative local and connectivity results on a synthetic phantom and on
an in-vivo high resolution dataset. Overall, our method restores perceptual
information, removes the noise bias in common diffusion metrics, restores the
extracted peaks coherence and improves reproducibility of tractography. Our
work paves the way for higher spatial resolution acquisition of diffusion MRI
datasets, which could in turn reveal new anatomical details that are not
discernible at the spatial resolution currently used by the diffusion MRI
community.
