  Random matrix theory (RMT) combined with principal component analysis has
resulted in a widely used MPPCA noise mapping and denoising algorithm, that
utilizes the redundancy in multiple acquisitions and in local image patches.
RMT-based denoising relies on the uncorrelated identically distributed noise.
This assumption breaks down after regridding of non-Cartesian sampling. Here we
propose a Universal Sampling Denoising (USD) pipeline to homogenize the noise
level and decorrelate the noise in non-Cartesian sampled k-space data after
resampling to a Cartesian grid. In this way, the RMT approaches become
applicable to MRI of any non-Cartesian k-space sampling. We demonstrate the
denoising pipeline on MRI data acquired using radial trajectories, including
diffusion MRI of a numerical phantom and ex vivo mouse brains, as well as in
vivo $T_2$ MRI of a healthy subject. The proposed pipeline robustly estimates
noise level, performs noise removal, and corrects bias in parametric maps, such
as diffusivity and kurtosis metrics, and $T_2$ relaxation time. USD stabilizes
the variance, decorrelates the noise, and thereby enables the application of
RMT-based denoising approaches to MR images reconstructed from any
non-Cartesian data. In addition to MRI, USD may also apply to other medical
imaging techniques involving non-Cartesian acquisition, such as PET, CT, and
SPECT.
