Denoising Using Marchenko-Pastur Principal Component Analysis

State-of-the-art denoising for diffusion and functional imaging applications.

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.

Comparison of original diffusion MRI data (show on the left) to MPPCA denoised counterpart. From the top: a diffusion-weighted (DW) image, signal-to-noise ratio (SNR), and fractional anisotropy (FA).

Reduction of thermal noise is an essential step in the pre-processing 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.


Veraart J, Novikov DS, Christiaens D, Ades-Aron B, Sijbers J, Fieremans E.
Denoising of diffusion MRI using random matrix theory.
Neuroimage. 2016 Nov 15;142:394-406. doi: 10.1016/j.neuroimage.2016.08.016

Veraart J, Fieremans E, Novikov DS.
Diffusion MRI noise mapping using random matrix theory.
Magn Reson Med. 2016 Nov;76(5):1582-1593. doi: 10.1002/mrm.26059

Ades-Aron B, Lemberskiy G, Veraart J, Golfinos J, Fieremans E, Novikov DS, Shepherd T.
Improved Task-based Functional MRI Language Mapping in Patients with Brain Tumors through Marchenko-Pastur Principal Component Analysis Denoising.
Radiology. 2021 Feb;298(2):365-373. doi: 10.1148/radiol.2020200822

Ades-Aron B, Veraart J, Kochunov P, McGuire S, Sherman P, Kellner E, Novikov DS, Fieremans E.
Evaluation of the accuracy and precision of the diffusion parameter EStImation with Gibbs and NoisE removal pipeline.
Neuroimage. 2018 Dec;183:532-543. doi: 10.1016/j.neuroimage.2018.07.066

Novikov D, Veraart J, Fieremans E, inventors. Universiteit Antwerpen, New York University, assignees.
System, method and computer accessible medium for noise estimation, noise removal and Gibbs ringing removal.
US patent 10,698,065 B2. June 30, 2020.


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