Noise Propagation and MP-PCA Image Denoising for High-Resolution Quantitative $R_2^{\rm{*}}$, $T_2^{\rm{*}}$, and Magnetic Susceptibility Mapping (QSM)

Objective: Quantitative Susceptibility Mapping (QSM) measures magnetic susceptibility of tissues, aiding in the detection of pathologies like traumatic brain injury, cerebral microbleeds, Parkinson's disease, and multiple sclerosis, through analysis of variations in substances such as iron and calcium. Despite its clinical value, using high-resolution QSM (voxel sizes < 1 mm³) reduces signal-to-noise ratio (SNR), which compromises diagnostic quality. Methods: Denoising of T₂^*-weighted (T₂^*w) data was implemented using Marchenko-Pastur Principal Component Analysis (MP-PCA), allowing to enhance the quality of R₂^*, T₂^*, and QSM maps. Proof of concept of the denoising technique was demonstrated on a numerical phantom, healthy subjects, and patients with brain metastases and sickle cell anemia. Results: Effective and robust denoising was observed across different scan settings, offering higher SNR and improved accuracy. Noise propagation was analyzed between T₂^*w, R₂^*, and T₂^* values, revealing augmentation of noise in T₂^*w compared to R₂^* values. Conclusions: The use of MP-PCA denoising allows the collection of high resolution (∼0.5 mm³) QSM data at clinical scan times, without compromising SNR. Significance: The presented pipeline could enhance the diagnosis of various neurological diseases by providing higher-definition mapping of small vessels and of variations in iron or calcium.