MR KLEAN: a Generalized Acquisition-agnostic LLR k-Space Denoising Method for High-dimensional Imaging

High-dimensional and dynamic MRI are often limited by thermal noise, particularly in accelerated acquisitions. Although image-domain low-rank denoising methods (e.g., MP-PCA and NORDIC) are effective, their reliance on stationary noise distributions limits applicability to non-Cartesian sampling and advanced reconstructions. This work introduces Magnetic Resonance K-space Local low-rank Estimation for Attenuating Noise (MR KLEAN), a k-space low-rank denoising framework agnostic to acquisition trajectory and reconstruction strategy.

MR KLEAN exploits local low-rank structure in multichannel, high-dimensional k-space. Data are prewhitened using a noise-only scan to enforce independent and identically distributed, zero-mean, unit-variance noise. Casorati matrices from local k-space patches are denoised by singular-value thresholding, with thresholds set via Monte-Carlo simulations under known noise statistics. MR KLEAN was evaluated in (1) a Cartesian 3D FLASH phantom study, (2) an ASL study with spiral readout and compressed sensing reconstruction to assess generalizability and preservation of temporal information via resting-state connectivity analysis, and (3) an accelerated cardiac cine study assessing performance under rapid temporal dynamics.

MR KLEAN increased SNR and CNR in phantom studies. In vivo ASL showed reduced noise in perfusion images, improved relative SNR, and substantially enhanced resting-state networks detection. In cardiac imaging, noise was reduced and delineation of fine anatomical features improved while temporal fidelity was preserved across cardiac phases.

MR KLEAN provides robust, acquisition- and reconstruction-agnostic k-space denoising, improving image quality and allowing flexible spatial-temporal trade-offs. Results further support that high-dimensional k-space data retain intrinsic local low-rank structure analogous to image-space despite temporal signal variations.