Efficient PCA denoising of spatially correlated MRI data

Mar[c]enko-Pastur (MP) PCA denoising is emerging as an effective means for noise suppression in MRI acquisitions with redundant dimensions. However, MP-PCA performance is severely compromised by spatially correlated noise - an issue typically affecting most modern MRI acquisitions - almost to the point of returning the original images with little or no noise removal. In this study, we develop and apply two new strategies that enable efficient and robust denoising even in the presence of severe spatial correlations. This is achieved by measuring a-priori information about the noise variance and combing these estimates with PCA denoising thresholding concepts. The two denoising strategies developed here are: 1) General PCA (GPCA) denoising that uses a-priori noise variance estimates without assuming specific noise distributions; and 2) Threshold PCA (TPCA) denoising which removes noise components with a threshold computed from a-priori estimated noise variance to determine the upper bound of the MP distribution. These strategies were tested in simulations with known ground truth and applied for denoising diffusion MRI data acquired using pre-clinical (16.4T) and clinical (3T) MRI scanners. In synthetic phantoms, MP-PCA failed to denoise spatially correlated data, while GPCA and TPCA correctly classified all signal/noise components. In cases where the noise variance was not accurately estimated (as can be the case in many practical scenarios), TPCA still provides excellent denoising performance. Our experiments in pre-clinical diffusion data with highly corrupted by spatial correlated noise revealed that both GPCA and TPCA robustly denoised the data while MP-PCA denoising failed. In in vivo diffusion MRI data acquired on a clinical scanner in healthy subjects, MP-PCA weakly removed noised, while TPCA was found to have the best performance, likely due to misestimations of the noise variance. Thus, our work shows that these novel denoising approaches can strongly benefit future pre-clinical and clinical MRI applications.