Improved Quantitative 23 Na MRI via Denoising With Multichannel Weighted Schatten p -Norm Minimization and Generalized Robust PCA

Quantitative sodium (²³Na) magnetic resonance imaging (MRI) provides unique metabolic information but is hampered by inherently low signal-to-noise ratio (SNR), which compromises the accuracy and precision of tissue sodium concentration (TSC) measurements. To address this fundamental measurement challenge, we propose a novel reconstruction framework designed to enhance the reliability of TSC quantification. Our method, termed MC-WSNM-GRPCA, models the multi-dimensional ²³Na MRI data by integrating multi-channel weighted nuclear norm minimization with generalized robust principal component analysis. This model-based denoising approach leverages inter-slice noise variations and flexible low-rank approximations to robustly separate the low-energy ²³Na signal from noise components in the image domain. We evaluated the framework using simulated data corrupted by various noise types, including Gaussian, Rician, and acquisition noise, and in vivo data from glioma patients, acquired with a 32-channel ²³Na/¹H head coil. Compared to several state-of-the-art methods, our approach demonstrated superior performance in both noise suppression and preservation of underlying signal fidelity, as evaluated by quantitative metrics and visual quality. In conclusion, the proposed model-based reconstruction framework effectively improves the precision of TSC quantification from low-SNR ²³Na MRI data. This work provides a promising solution for enhancing the clinical value of quantitative sodium imaging in applications such as early diagnosis of brain tumors and stroke.