Noise removal from MR images via iterative regularization based on higher-order singular value decomposition

Abstract

Despite the success of magnetic resonance imaging techniques in many applications, acquisition noise is still a limiting factor for the quality and hence the usefulness of the techniques. In this paper, a new algorithm for denoising magnetic resonance images based on higher-order singular value decomposition is proposed. The proposed algorithm first forms a single tensor from the noisy data. Next, higher-order singular value decomposition is applied on this tensor with respect to a set of learned orthogonal directional matrices over the corresponding tensor mode. Finally, soft thresholding is iteratively applied to the calculated coefficients, thereby suppressing the noise. The new algorithm is further enhanced with a post-process Wiener filtering. The proposed algorithm has two advantages over existing tensor denoising approaches: (1) It combines the noisy image slices into a single tensor, thereby exploiting non-local image similarity across slices and (2) it uses an iterative regularization framework to suppress the noise. Experiments are conducted on synthetic and real magnetic resonance images to compare the performance of the proposed algorithm to state-of-the-art denoising approaches. The comparison is made quantitatively in terms of peak of signal-to-noise ratio, structural similarity index and mean absolute difference, and qualitatively through visual comparisons. The results demonstrate the competitive performance of the proposed algorithm.