Denoising of 3D magnetic resonance images by using higher-order singular value decomposition

• The Wiener filter-augmented HOSVD is extended to denoise 3D MR data.
• The Wiener filter-augmented HOSVD achieves comparable performance to that of BM4D.
• A novel recursive HOSVD method is proposed to exploit filtering residual for better performance.
• The recursive HOSVD outperforms current state-of-the-art 3D denoising algorithms.

The denoising of magnetic resonance (MR) images is important to improve the inspection quality and reliability of quantitative image analysis. Nonlocal filters by exploiting similarity and/or sparseness among patches or cubes achieve excellent performance in denoising MR images. Recently, higher-order singular value decomposition (HOSVD) has been demonstrated to be a simple and effective method for exploiting redundancy in the 3D stack of similar patches during denoising 2D natural image. This work aims to investigate the application and improvement of HOSVD to denoising MR volume data. The wiener-augmented HOSVD method achieves comparable performance to that of BM4D. For further improvement, we propose to augment the standard HOSVD stage by a second recursive stage, which is a repeated HOSVD filtering of the weighted summation of the residual and denoised image in the first stage. The appropriate weights have been investigated by experiments with different image types and noise levels. Experimental results over synthetic and real 3D MR data demonstrate that the proposed method outperforms current state-of-the-art denoising methods.

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