3D magnetic resonance image denoising using low-rank tensor approximation

The Magnetic Resonance (MR) Imaging technique has important applications in clinical diagnosis and scientific research. However, in practice the MR images are often corrupted by noise. Existing image denoising methods, mostly designed for natural image denoising do not take into account the multiple dimensionality of the 3D MR images, and are thus not suitable for 3D MR images denoising. In this paper, we present a novel noise reduction method for 3D MR images based on low-rank tensor approximation, considering both the non-local spatial self-similarity and the correlation across the slices of the 3D MR images. Specifically, for each exemplar 3D patch, similar 3D patches are first grouped to form a 4th order tensor. As the similar patches contain similar structures, the latent clear MR images can be recovered by a low-rank tensor approximation. To this end, an adaptive higher order singular value thresholding method is proposed. Experimental results on 3D MR images show that the proposed method can provide substantial improvements over the current state-of-the-art image denoising methods in terms of both objective metric and subjective visual quality.