Voxel-Matching NORDIC: Non-local patch formation by time-series similarity increases tSNR in high-resolution BOLD fMRI.

Submillimeter functional magnetic resonance imaging (fMRI) based on blood-oxygenation-level-dependent (BOLD) signal enables the study of brain function at the submillimeter level, uncovering insights into fine-scale organisations like cortical layers and columns. However, its inherently low contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR) often limit its reliability and applicability. Noise Reduction with Distribution Corrected Principal Components Analysis (NORDIC PCA) is a locally low-rank denoising algorithm that reduces thermal noise levels in BOLD fMRI in a local patch manner. However, local patches often contain a mixture of signals from multiple tissues that negatively affect the low-rank structure of the patches, which limits the denoising capabilities of the algorithm. We propose an alternative approach for patch formation by gathering similar non-local voxels, dubbed voxel-matching (VM) NORDIC. The results on submillimeter-resolution BOLD fMRI data indicate that VM-NORDIC effectively promotes the low rank of the patches by boosting signal redundancy, allowing for more efficient noise attenuation. Moreover, the method barely affects spatial smoothness due to the non-local voxel selection based on time-series similarity. In particular, VM-NORDIC outperforms standard NORDIC with default local patching (Standard-NORDIC) in terms of temporal SNR (tSNR) (~9-90% larger than Standard-NORDIC; ~23-250% larger than the original) and spatial smoothness estimates (~20% of the smoothness induced by Standard-NORDIC). These improvements are fundamental to improving the validity and precision of fMRI studies at submillimeter resolutions.