Denoise ultra-low-field 3D magnetic resonance images using a joint signal-image domain filter

Ultra-low-field magnetic resonance imaging (MRI) could suffer from heavy uncorrelated noise, and its removal could be a critical post-processing task. As a primary source of interference, Gaussian noise could corrupt the sampled MR signal (k-space data), especially at lower B₀ field strength. For this reason, we consider both signal and image domains by proposing a new joint filter characterized by a Kalman filter with linear prediction and a nonlocal mean filter with higher-order singular value decomposition (HOSVD) for denoising 3D MR data. The Kalman filter first attenuates the noise in k-space, and then its reconstruction images are used to guide HOSVD denoising process with exploring self-similarity among 3D structures. The clearer prefiltered images could also generate improved HOSVD learned bases used to transform the noise corrupted patch groups in the original MR data. The flexibility of proposed method is also demonstrated by integrating other k-space filters into the algorithm scheme. Experimental data includes simulated MR images with the varying noise level and real MR images obtained from our 50 mT MRI scanner. The results reveal that our method has a better noise-removal ability and introduces lesser unexpected artifacts than other related MRI denoising approaches.