3D Magnetic resonance image denoising using nonlocal and nonconvex tensor train regularization.

Magnetic resonance images (MRI) denoising aims to obtain clean image for further treatment by doctors. Recently, low-rank tensor methods have achieved amazing results in MRI denoising. Nevertheless, imbalanced matricization from Tucker decomposition and nuclear norm penalty mechanism are incapable of fully characterizing the internal structure information of 3D MR image. To mitigate these matters, a novel framework, which combines non-local self-similarity technique and low-rank tensor regularization from tensor train decomposition with balanced matricization, is proposed to noise removal. The constructed fourth-order tensor from non-local self-similarity technique is conducted by tensor train regularization with weighted Schatten-p norm function. The designed method not only considers structural correlation across different dimensions for 3D MR images, but also takes the importance of various singular values into account. Experimental results over synthetic and real images demonstrate that our proposal achieves competitive performance with respect to the state-of-the-art MR images denoising filters (ANLM3D, BM4D, WNNM3D, NLM-tSVD and HOSVD-R) both visually and quantitatively.