Dynamic MR imaging reconstruction by three-dimensional dictionary learning

Magnetic Resonance Imaging (MRI) has been widely used in medical diagnosis due to its excellent discernibility to soft tissues and no radiation damage. Recent years, compressed sensing (CS) based reconstruction method for dynamic MRI is a hot topic for it enables accurate reconstruction from undersampled k-space data, which can significantly reduce the data-acquisition time. In this paper, we proposed a novel method for three-dimensional dynamic MRI reconstruction with higher undersampling rates and better imaging quality by extending the atoms in dictionary learning from two dimensions to three dimensions. In this way, spatial correlation among slices is fully exploited implicitly with no artificial interference. The proposed algorithm is simply composed of two steps: adaptive dictionary learning in one step, then restoring and filling in the three dimensional k-space in another step. Numerical experiments were carried out on three-dimensional MR images of anatomies with a variety of undersampling schemes and ratios. The results show that, by only 30 iterations, the proposed method improves the reconstruction quality over the state-of-the-art three-dimensional reconstruction methods with a reduction of more than 95% in normalized mean square error (NMSE). Besides, the influence of parameter variations to the reconstruction quality is also analyzed. The parameter variation ranging from 20% to 200% can only bias the image quality within 0.001 in NMSE.