Reconstruction of undersampled dynamic spiral MR images

The temporal resolution of dynamic MRI can be increased by sampling a fraction of k-space in an interleaved fashion, which causes spatial and temporal aliasing. We describe algebraically the aliasing process caused by spiral undersampling to formulate unaliasing as a set of independent inverse problems. Since each linear system is severely ill-conditioned, zeros are assumed in the solution. Specifically the size and the location of assumed zeros necessary for obtaining a unique solution is inspected. To overcome the problems of excessive memory and computation time needed for direct inverse computation, a fast implementation of the conjugate gradient (CG) method is proposed. Simulation using dynamic spiral cardiac images demonstrates improved temporal resolution of the proposed method.