M-MRI: A manifold-based framework to highly accelerated dynamic magnetic resonance imaging

High-dimensional signals, including dynamic magnetic resonance (dMR) images, often lie on low dimensional manifold. While many current dynamic magnetic resonance imaging (dMRI) reconstruction methods rely on priors which promote low-rank and sparsity, this paper proposes a novel manifold-based framework, we term M-MRI, for dMRI reconstruction from highly undersampled k-space data. Images in dMRI are modeled as points on or close to a smooth manifold, and the underlying manifold geometry is learned through training data, called 'navigator' signals. Moreover, low-dimensional embeddings which preserve the learned manifold geometry and effect concise data representations are computed. Capitalizing on the learned manifold geometry, two regularization loss functions are proposed to reconstruct dMR images from highly undersampled k-space data. The advocated framework is validated using extensive numerical tests on phantom and in-vivo data sets.