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.
Taehoon Shin, Jon F. Nielsen, Krishna S. Nayak