Accelerating MR Parameter Mapping Using Nonlinear Compressive Manifold Learning and Regularized Pre-Imaging

In this study, we present a novel method to reconstruct the MR parametric maps from highly undersampled k-space data. Specifically, we utilize a nonlinear model to sparsely represent the unknown MR parameter-weighted images in high-dimensional feature space. Each image at a specific time point is assumed to belong to a low-dimensional manifold which is learned from training images created based on the parametric model. The final reconstruction is carried out by venturing the sparse representation of the images in the feature space back to the input space, using the pre-imaging technique. Particularly, among an infinite number of solutions that satisfy the data consistency, the one that is closest to the manifold is selected as the desired solution. The underlying optimization problem is solved using kernel trick, sparse coding, and split Bregman iteration algorithm. In addition, both spatial and temporal regularizations are utilized to further improve the reconstruction quality. The proposed method is validated on both phantom and in vivo human brain T2 mapping data. Results suggest that the proposed method is superior to the conventional linear model-based reconstruction methods, in terms of artifact removal and quantitative estimation accuracy. The proposed method could be potentially beneficial for quantitative MR applications.