SNR-enhanced diffusion MRI with structure-preserving low-rank denoising in reproducing kernel Hilbert spaces

Purpose: To introduce, develop, and evaluate a novel denoising technique for diffusion MRI that leverages nonlinear redundancy in the data to boost the SNR while preserving signal information.

Methods: We exploit nonlinear redundancy of the dMRI data by means of kernel principal component analysis (KPCA), a nonlinear generalization of PCA to reproducing kernel Hilbert spaces. By mapping the signal to a high-dimensional space, a higher level of redundant information is exploited, 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 and low-resolution dMRI data. We also demonstrate KPCA denoising on multi-coil dMRI data.

Results: SNR improvements up to 2.7 $\times$ were obtained in real in vivo datasets denoised with KPCA, in comparison to SNR gains of up to 1.8 $\times$ using a linear PCA denoising technique called Marchenko-Pastur PCA (MPPCA). Compared to gold-standard dataset references created from averaged data, we showed that lower normalized root mean squared error was achieved with KPCA compared to MPPCA. Statistical analysis of residuals shows that anatomical information is preserved and only noise is removed. Improvements in the estimation of diffusion model parameters such as fractional anisotropy, mean diffusivity, and fiber orientation distribution functions were also demonstrated.

Conclusion: Nonlinear redundancy of the dMRI signal can be exploited with KPCA, which allows superior noise reduction/SNR improvements than the MPPCA method, without loss of signal information.