Denoise Functional Magnetic Resonance Imaging With Random Matrix Theory Based Principal Component Analysis

High-resolution functional MRI (fMRI) is largely hindered by random thermal noise. Random matrix theory (RMT)-based principal component analysis (PCA) is promising to reduce such noise in fMRI data. However, there is no consensus about the optimal strategy and practice in implementation. In this work, we propose a comprehensive RMT-based denoising method that consists of 1) rank and noise estimation based on a set of newly derived multiple criteria, and 2) optimal singular value shrinkage, with each module explained and implemented based on the RMT. By incorporating the variance stabilizing approach, the denoising method can deal with low signal-to-noise ratio (SNR) (such as <5) magnitude fMRI data with favorable performance compared to other state-of-the-art methods. Results from both simulation and
in-vivo
high-resolution fMRI data show that the proposed denoising method dramatically improves image restoration quality, promoting functional sensitivity at the same level of functional mapping blurring compared to existing denoising methods. Moreover, the denoising method can serve as a drop-in step in data preprocessing pipelines along with other procedures aimed at removal of structured physiological noises. We expect that the proposed denoising method will play an important role in leveraging high-quality, high-resolution task fMRI, which is desirable in many neuroscience and clinical applications.