Accelerating dynamic magnetic resonance imaging by nonlinear sparse coding

Although being high-dimensional, dynamic magnetic resonance images usually lie on low-dimensional manifolds. Nonlinear models have been shown to capture well that latent low-dimensional nature of data, and can thus lead to improvements in the quality of constrained recovery algorithms. This paper advocates a novel reconstruction algorithm for dynamic magnetic resonance imaging (dMRI) based on nonlinear dictionary learned from low-spatial but high-temporal resolution images. The nonlinear dictionary is initially learned using kernel dictionary learning, and the proposed algorithm subsequently alternates between sparsity enforcement in the feature space and the data-consistency constraint in the original input space. Extensive numerical tests demonstrate that the proposed scheme is superior to popular methods that use linear dictionaries learned from the same set of training data.