Compressed Sensing (CS) has heralded a new era in cardiac and body Magnetic Resonance (MR) imaging due to the unprecedented acceleration factors achieved within the ambit of existing scanning hardware, by exploiting the inherent sparsity of MR images in a known basis. Latter works have adopted dictionary learning strategies on vectorized image patches to enforce higher degrees of sparsity. However, the enormous computational complexity has confined them to learning from small patches, thereby foregoing any consideration of the expected structure of the MR images from prior knowledge. In order to efficiently exploit the multi-dimensional characteristic of MR data, this work learns 2D separable dictionaries possessing Kronecker structure at low computational costs by adapting the CANDECOMP/PARAFAC (CP) tensor decomposition method on stacked 2D under-sampled MR slices of similar scan type. The proposed method has been observed to obtain superior reconstruction quality in noiseless and noisy acquisition scenarios over the state-of-art. Furthermore, the learned dictionary can jointly reconstruct a stack of distinct 2D under-sampled slices of similar scan type, in significantly reduced running time. © Springer Nature Singapore Pte Ltd 2020.