3D MR image denoising using a modified adaptive high order singular value decomposition method.

Magnetic resonance (MR) images are generally degraded by random noise governed by Rician distributions. In this study, we developed a modified adaptive high order singular value decomposition (HOSVD) method, taking consideration of the nonlocal self-similarity and weighted Schatten p-norm. We extracted 3D cubes from noise images and classified the similar cubes by the Euclidean distance between cubes to construction a fourth-order tensor. Each rank of unfolding matrices was adaptively determined by weighted Schatten p-norm regularization. The latent noise-free 3D MR images can be obtained by an adaptive HOSVD. Denoising experiments were tested on both synthetic and clinical 3D MR images, and the results showed the proposed method outperformed several existing methods for Rician noise removal in 3D MR images.