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Random matrix theory (RMT) combined with principal component analysis hasresulted in a widely used MPPCA noise mapping and denoising algorithm, thatutilizes 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 wepropose a Universal Sampling Denoising (USD) pipeline to homogenize the noiselevel and decorrelate the noise in non-Cartesian sampled k-space data afterresampling to a Cartesian grid. In this way, the RMT approaches becomeapplicable to MRI of any non-Cartesian k-space sampling. We demonstrate thedenoising pipeline on MRI data acquired using radial trajectories, includingdiffusion MRI of a numerical phantom and ex vivo mouse brains, as well as invivo $T_2$ MRI of a healthy subject. The proposed pipeline robustly estimatesnoise level, performs noise removal, and corrects bias in parametric maps, suchas diffusivity and kurtosis metrics, and $T_2$ relaxation time. USD stabilizesthe variance, decorrelates the noise, and thereby enables the application ofRMT-based denoising approaches to MR images reconstructed from anynon-Cartesian data. In addition to MRI, USD may also apply to other medicalimaging techniques involving non-Cartesian acquisition, such as PET, CT, andSPECT.

Universal Sampling Denoising (USD) for noise mapping and noise removal of non-Cartesian MRI