  Purpose: To introduce, develop, and evaluate a novel denoising technique for
diffusion MRI that leverages non-linear redundancy in the data to boost the SNR
while preserving signal information. Methods: We exploit non-linear redundancy
of the dMRI data by means of Kernel Principal Component Analysis (KPCA), a
non-linear generalization of PCAto reproducing kernel Hilbert spaces. By
mapping the signal to a high-dimensional space, better redundancy is achieved
despite nonlinearities in the data thereby enabling better denoising than
linear PCA. We implement KPCA with a Gaussian kernel, with parameters
automatically selected from knowledge of the noise statistics, and validate it
on realistic Monte-Carlo simulations as well as with in-vivo human brain
submillimeter resolution dMRI data. We demonstrate KPCA denoising using
multi-coil dMRI data also. Results: SNR improvements up to 2.7 X were obtained
in real in-vivo datasets denoised with KPCA, in comparison to SNR gains of up
to 1.8 X when using state-of-the-art PCA denoising, e.g., Marchenko- Pastur PCA
(MPPCA). Compared to gold-standard dataset references created from averaged
data, we showed that lower normalized root mean squared error (NRMSE) was
achieved with KPCA compared to MPPCA. Statistical analysis of residuals shows
that only noise is removed. Improvements in the estimation of diffusion model
parameters such as fractional anisotropy, mean diffusivity, and fiber
orientation distribution functions (fODFs)were demonstrated.
Conclusion:Non-linear redundancy of the dMRI signal can be exploited with KPCA,
which allows superior noise reduction/ SNR improvements than state-of-the-art
PCA methods, without loss of signal information.
