Non-local MRI denoising using random sampling

In this paper, we propose a random sampling non-local mean (SNLM) algorithm to eliminate noise in 3D MRI datasets. Non-local means (NLM) algorithms have been implemented efficiently for MRI denoising, but are always limited by high computational complexity. Compared to conventional methods, which raster through the entire search window when computing similarity weights, the proposed SNLM algorithm randomly selects a small subset of voxels which dramatically decreases the computational burden, together with competitive denoising result. Moreover, structure tensor which encapsulates high-order information was introduced as an optimal sampling pattern for further improvement. Numerical experiments demonstrated that the proposed SNLM method can get a good balance between denoising quality and computation efficiency. At a relative sampling ratio (i.e. ξ = 0.05), SNLM can remove noise as effectively as full NLM, meanwhile the running time can be reduced to 1/20 of NLM's.