Low-rank regularized implicit neural representation for k-space completion in fast MRI reconstruction

Motivation: The highly reduced k-space measurements would induce noises and artifacts in the reconstructed image in parallel imaging. Goal(s): To effectively complete the undersampled k-space points for MRI acceleration and provide high-quality images. Approach: We developed a novel k-space completion framework based on implicit neural representation. The inherent low-rankness of k-space is incorporated into the model to capture the continuous representation in k-space. The proposed method was evaluated on the public dataset and compared with the image and k-space domain reconstruction methods. Results: The results show that our method can effectively complete the undersampled k-space points without any priors in the image domain. Impact: The proposed method leverages implicit neural representation in the k-space reconstruction, demonstrating the ability to complete the undersampled k-space points at high acceleration factor. This result implies our method can further reduce the measured k-space points and accelerate MRI acquisition.