Novel Denoising Method for Magnetic Resonance Velocimetry Using Split-and-Overlap Singular Value Decomposition*

Singular value decomposition (SVD) is a powerful tool for denoising 3D data like magnetic resonance velocimetry (MRV), but its effectiveness is often limited by unclear basis selection criteria. To address this, we propose a novel method that splits the data matrix into overlapping subdomains, applies SVD, and reconstructs the data using the main basis for noise reduction. We validated this method with synthetic MRV data generated from simulated flow through a square duct contaminated with Gaussian noise, as well as real MRV data from phantom experiments using the same geometry and flow conditions. Additionally, we tested the filter's performance on in vivo thoracic aorta MRV data. Evaluations were conducted using peak velocity-to-noise ratio (PVNR), noise reduction rate, divergence reduction rate, and velocity consistency. Results showed that the split-and-overlap SVD (SOSVD) technique reduced Gaussian noise in synthetic data by 79% with a PVNR of 10-30 dB. In vitro tests showed a noise reduction of 39% and a divergence reduction of 52%. For in vivo thoracic aorta MRV data, the SOSVD technique significantly minimized noise and enhanced velocity consistency, improving overall image quality. These findings demonstrate the potential of the SOSVD technique to significantly improve clinical hemodynamic analysis.