A novel method and fast algorithm for MR image reconstruction with significantly under-sampled data

The aim of this work is to improve the accuracy, robustness andefficiency of the compressed sensing reconstruction technique inmagnetic resonance imaging. We propose a novel variational modelthat enforces the sparsity of the underlying image in terms of itsspatial finite differences and representation with respect to adictionary. The dictionary is trained using prior information toimprove accuracy in reconstruction. In the meantime the proposedmodel enforces the consistency of the underlying image with acquireddata by using the maximum likelihood estimator of the reconstructionerror in partial k-space to improve the robustness to parameterselection. Moreover, a simple and fast numerical scheme is providedto solve this model. The experimental results on both synthetic andin vivo data indicate the improvement of the proposed model inpreservation of fine structures, flexibility of parameter decision, and reduction of computational cost.