Denoising complex-valued diffusion MR images using a two-step, nonlocal principal component analysis approach

Purpose: To propose a two-step, nonlocal principal component analysis (PCA) method and demonstrate its utility for denoising complex diffusion MR images with a few diffusion directions. Methods: A two-step denoising pipeline was implemented to ensure accurate patch selection even with high noise levels and was coupled with data preprocessing for g-factor normalization and phase stabilization before data denoising with a nonlocal PCA algorithm. At the heart of our proposed pipeline was the use of a data-driven optimal shrinkage algorithm to manipulate the singular values in a way that would optimally estimate the noise-free signal. Our approach's denoising performances were evaluated using simulation and in vivo human data experiments. The results were compared with those obtained with existing local PCA-based methods. Results: In both simulation and human data experiments, our approach substantially enhanced image quality relative to the noisy counterpart, yielding improved performances for estimation of relevant diffusion tensor imaging metrics. It also outperformed existing local PCA-based methods in reducing noise while preserving anatomic details. It also led to improved whole-brain tractography relative to the noisy counterpart. Conclusion: The proposed denoising method has the utility for improving image quality for diffusion MRI with a few diffusion directions and is believed to benefit many applications, especially those aiming to achieve high-quality parametric mapping using only a few image volumes.