Compressive sensing (CS) MRI have been developed to speed up data acquisition without significantly degrading image quality. This paper proposes a novel compressed sensing reconstruction method exploiting temporally complementary morphological characteristics. This method relies on some well-developed signal processing techniques: Morphological component analysis (MCA) and sparse derivatives. It also relies on well-developed MRI reconstruction techniques: Incoherent undersampling schemes and parallel imaging. Other MRI schemes were simulated to make comparsion with our MCA-based CS method. CS and parallel imaging has been merged together to highly increase acceleration rate. This work simulates this framework also. Performance of applying different temporal regularizations individually and hybrid signal models based on MCA with and without auxilary spatial regularization are all analyzed in this paper. Nonlinear conjugate gradient algorithm is applied to gain all signal components simultaneously.