Improved MRI reconstruction via non-convex elastic net

This work proposes the use of an elastic-net to reconstruct Magnetic Resonance Images from their partially sampled K-space. The resulting elastic-net formulation of this problem is composed of two terms - the first term promotes sparsity and the other one promotes a grouping effect. The advantage of using an elastic-net for MRI reconstruction is that it can recover the hierarchically correlated sparse wavelet coefficients of the image. We develop two reconstruction methods via two elastic-net formulations - the synthesis prior and the analysis prior. We also impose non-convex sparsity penalties. There are no existing algorithms that solve such problems; hence we derive efficient algorithms for solving them. The experimental results show that our proposed analysis prior method outperforms state-of-the-art in MRI reconstruction.