Denoising Using Marchenko-Pastur Principal Component Analysis

We are sharing a novel denoising algorithm called Marchenko-Pastur principal component analysis (MPPCA). MPPCA outperforms other state-of-the-art denoising methods in preserving the underlying signal at the level of diffusion-sensitized and/or functional MR images and parameters of interest while boosting the signal-to-noise ratio (SNR) by a factor of 2 to 4.

Reduction of thermal noise is an essential step in the preprocessing of MR image series. Thermal noise corrupts MRI measurements and propagates to the parameters of interest, affecting statistical analysis of functional MRI or the visual inspection and quantification of potential biomarkers that may be derived from diffusion MRI. MPPCA addresses this problem, which cannot be solved on the hardware side due to physical limitations inherent in MR imaging.

Principal component analysis (PCA) has been previously applied to diffusion or functional MRI data to transform them into a principal components basis and preserve only the signal-carrying principal components. This approach has shown promise because such imaging series exhibit sufficient redundancy. However, the number of principal components that significantly contribute to the actual noise-free signal is unknown and is expected to depend on imaging factors such as SNR. Commonly used criteria include thresholding of the eigenvalues associated with the principal components by an empirically set value. 

The MPPCA method adopts an objective criterion to identify noise-only eigenvalues in PCA. The method is based on a result from random matrix theory, which shows that the Marchenko-Pastur distribution constitutes a distinct fingerprint of noise-only principal components. Because the noise-only eigenvalues are expected to obey this universal Marchenko-Pastur law, we now have an objective criterion to distinguish between signal and noise in our data that promotes the preservation of signal during PCA denoising.

Contact

Questions about this resource may be directed to Jelle Veraart, PhD.