Adaptive spatiotemporal dictionaries offer improved reconstruction accuracy for dynamic cardiac MRI. However, most modern methods perform local encoding of image patches treating them independently. In order to increase reconstruction quality, we present a convex model that allows global control of encoding sparsity. The proposed method has a single tunable parameter and delivers 9% peak signal-to-noise ratio improvement of reconstruction compared to the state-of-the-art dictionary-based approach. Moreover, the implemented numerical scheme allowed 3-fold reconstruction time reduction.