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Reconstruction from highly accelerated dynamic magnetic resonance imaging (MRI) is of great significance for medical diagnosis. The application of low-rank and sparse matrix decomposition to MRI can improve imaging speed and efficiency. However, the consistence of the learned low-rank and sparse structures for similar input samples is not well addressed in literature. In this paper, we propose a manifold constrained low-rank and joint sparse learning model that embeds the manifold priors into low-rank and joint sparse decomposition. It is noted that the joint sparsity is investigated to exploit the shared information. Further, the manifold constraints for low-rank and joint sparse parts are forced the optimization process to satisfy the structure preservation requirement. To solve the above manifold learning problem, a manifold constrained alternating direction method of multipliers (McADMM) approach is designed. It is proved theoretically that the sequence generated by McADMM converges to a stationary point. Numerical comparisons on simulation data and real-world dynamic cardiac MRI data are presented to demonstrate its efficiency.