A Novel Reconstruction Approach Combining Global and Local Low-rank Constraints for Undersampled Dynamic MRI

Background: Dynamic Magnetic Resonance Imaging (MRI) can be used to diagnose organs' motion, so it is useful and has been used widely. Reconstructing dynamic MRI from undersampled measurements can accelerate the imaging speed, this has attracted the attention of many researchers. For dynamic MRI, there is much global and local correlation in spatial and temporal dimensions, and if the spatial and temporal redundancy can be utilized efficiently in the reconstruction process, higher spatial and temporal resolutions can be achieved. Methods: In this paper, we propose a novel reconstruction method which utilizes the redundancy in spatial and temporal domains jointly. In particular, a 2-D matrix is obtained by vectorizing the images of every frame of a 3-D dynamic MRI sequence, and we extract overlapping 2-D patches from this matrix. Similar patches will be searched from these 2-D patches, and a non-convex function is used to approximate the low-rank matrices formed by these similar patches. At the present stage, only local correlation in the temporal dimension is employed. Discussion: To obtain better image quality, the global correlation in the temporal dimension is utilized by a low-rank penalty which is relaxed by the nuclear norm. Conclusion: We validate the proposed algorithm by using retrospectively undersampled in vivo cardiac datasets, and the proposed algorithm shows superior reconstruction performance compared to existing state-of-the-art methods such as k-t FOCUSS, k-t SLR, and L+S.