Global denoising for 3D MRI

BACKGROUND: Denoising is the primary preprocessing step for subsequent application of MRI. However, most commonly-used patch-based denoising methods are heavily dependent on the degree of patch matching. Due to the large number of voxels in the 3D MRI dataset, the procedure of searching sufficient similarity patches was limited by the empirical compromising between computational efficiency and estimation accuracy, and cannot fulfill the application in multimodal MRI dataset with different SNR and resolutions. METHODS: In this study, we propose a modified global filtering framework for 3D MRI. For each denoising voxel, the similarity weighting matrix is computed using the reference patch and other patches from the whole dataset. This large weighting matrix is then approximated using the k-means clustering Nyström method to achieve computational viability. RESULTS: Experiments on both synthetic and in vivo MRI datasets demonstrated that the proposed adaptive Nyström low-rank approximation could achieve competitive estimation compared with exact global filter while reducing the sampling rate by four orders of magnitude. In addition, the corresponding global filter improved patches-based method in both spatial and transform domain. CONCLUSION: We propose a global denoising framework for 3D MRI which extracts information from the entire dataset to restore each voxel. This large weighting matrix of the global filter is approximated using Nyström low-rank approximation with an adaptive k-means clustering sampling scheme, which significantly reduce the sampling rate as well as the running time. The proposed method is capable of denoising in multimodal MRI dataset and can be used to improve currently used patch-based methods.