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In this paper, we propose a new dynamic MR image reconstruction technique that combines the compressed sensing-based dynamic methods with parallel imaging techniques to achieve high accelerations. The method decouples the reconstruction process into two sequential steps. In the first step, a series of aliased dynamic images is reconstructed using a CS method from the highly undersampled £-space data. In the second step, the missing £-space data for the original image are reconstructed by the nonlinear GRAPPA technique. The sampling strategy for each step is thereby designed independently such that the incoherent undersampling requirement for CS and structured undersampling requirement for parallel imaging can be satisfied simultaneously. Experimental results demonstrate that the proposed method improves the reconstruction quality of dynamic cardiac cine MRI over the state-of-the-art method.