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

TL;DR

This paper introduces the Universal Sampling Denoising (USD) pipeline that homogenizes and decorrelates noise in non-Cartesian MRI data, enabling effective RMT-based denoising across various sampling schemes and potentially other imaging modalities.

Contribution

The authors propose a novel USD pipeline that preprocesses non-Cartesian MRI data to make RMT-based denoising applicable, addressing a key limitation of existing methods.

Findings

USD effectively homogenizes noise levels in non-Cartesian MRI data.

USD decorrelates noise, stabilizing variance for RMT application.

The pipeline improves parametric map accuracy in diffusion and T2 MRI.

Abstract

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.