CF-HOSVD: a two-stage denoising method based on higher-order singular value decomposition for 3D magnetic resonance images

Magnetic Resonance Imaging (MRI) is a crucial medical imaging technique, but MR images are often corrupted by noise. To address this issue, the higher-order singular value decomposition (HOSVD) denoising method is one of the mainstream approaches to remove noise in MR images. Notably, the Iterative Low-Rank HOSVD (ILR-HOSVD) algorithm has demonstrated its supremacy in terms of peak signal-to-noise ratio (PSNR). However, ILR-HOSVD overlooks the potential impact of the orthogonal bases under high noise conditions. Moreover, the reliance on multiple iterative optimizations in ILR-HOSVD results in considerable computational overhead, leading to prolonged denoising times. In this study, we propose the Coarse-Fine HOSVD (CF-HOSVD) denoising algorithm, which consists of two stages: a coarse HOSVD (C-HOSVD) denoising stage for pre-filtering and a fine HOSVD (F-HOSVD) denoising stage based on low-rank tensor approximation theory. Specifically, the conventional HOSVD denoising algorithm is first applied to pre-filter the MR images, representing the C-HOSVD, and then the orthogonal bases generated by the prefiltered images with a lower noise level are used to assist the F-HOSVD denoising. The proposed CF-HOSVD algorithm was evaluated on simulated noise-free datasets from the BrainWeb and MRXCAT, and compared with state-of-the-art traditional denoising methods. The experimental results demonstrate the superiority of CF-HOSVD, as it consistently outperforms other methods in terms of PSNR, structure similarity index metric (SSIM), and visual effect.