Image Reconstruction From Highly Undersampled $( {\bf k}, {t})$ -Space Data With Joint Partial Separability and Sparsity Constraints

Partial separability (PS) and sparsity have been previously used to enable reconstruction of dynamic images from undersampled ( k,t)-space data. This paper presents a new method to use PS and sparsity constraints jointly for enhanced performance in this context. The proposed method combines the complementary advantages of PS and sparsity constraints using a unified formulation, achieving significantly better reconstruction performance than using either of these constraints individually. A globally convergent computational algorithm is described to efficiently solve the underlying optimization problem. Reconstruction results from simulated and in vivo cardiac MRI data are also shown to illustrate the performance of the proposed method.