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We introduce a novel algorithm to recover real time dynamic MR images from highly under-sampled k- t space measurements. The proposed scheme models the images in the dynamic dataset as points on a smooth, low dimensional manifold in high dimensional space. We propose to exploit the non-linear and non-local redundancies in the dataset by posing its recovery as a manifold smoothness regularized optimization problem. A navigator acquisition scheme is used to determine the structure of the manifold, or equivalently the associated graph Laplacian matrix. The estimated Laplacian matrix is used to recover the dataset from undersampled measurements. The utility of the proposed scheme is demonstrated by comparisons with state of the art methods in multi-slice real-time cardiac and speech imaging applications. [ABSTRACT FROM AUTHOR]

We introduce a kernel low-rank algorithm to recover free-breathing and ungated dynamic MRI from spiral acquisitions without explicit k-space navigators. It is often challenging for low-rank methods to recover free-breathing and ungated images from undersampled measurements; extensive cardiac and respiratory motion often results in the Casorati matrix not being sufficiently low-rank. Therefore, we exploit the non-linear structure of the dynamic data, which gives the low-rank kernel matrix. Unlike prior work that rely on navigators to estimate the manifold structure, we propose a kernel low-rank matrix completion method to directly fill in the missing k-space data from variable density spiral acquisitions. We validate the proposed scheme using simulated data and in-vivo data. Our results show that the proposed scheme provides improved reconstructions compared to the classical methods such as low-rank and XD-GRASP. The comparison with breath-held cine data shows that the quantitative metrics agree, whereas the image quality is marginally lower. [ABSTRACT FROM AUTHOR]