Spatiotemporal dictionary learning for undersampled dynamic MRI reconstruction via joint frame-based and dictionary-based sparsity

Image reconstruction using compressed sensing relies on sparse representations of signals in some dictionary. Current state-of-the-art dictionary-learning methods are designed for spatial images and fail to systematically generalize to dynamic imaging scenarios where the spatiotemporal data, and thereby the spatiotemporal dictionary atoms, exhibit joint coherence in space and time leading to low rank. This paper proposes a novel method for learning low-rank spatiotemporal dictionaries. While leading compressed-sensing reconstruction methods employ either l₁ analysis or synthesis approaches using mathematical frames (e.g. overcomplete wavelets), approaches using dictionary learning (very recent) ignore the frame-based l₁-sparsity constraints. This paper proposes a novel method combining frame-based l₁ analysis with spatiotemporal-dictionary based sparsity (related to l₁ synthesis). The results demonstrate improved reconstructions, on simulated and clinical highly-undersampled dynamic images, using the combined approach.