Hybrid regularization for compressed sensing MRI: Exploiting shearlet transform and group-sparsity total variation

Magnetic resonance imaging (MRI) has been extensively used in clinical practice but suffers from long data acquisition time. Following the success of compressed sensing (CS) theory, many efforts have been made to accurately reconstruct MR images from undersampled k-space measurements and therefore dramatically reduce MRI scan time. To further improve image quality, we formulate undersampled MRI reconstruction as a least-squares optimization problem regularized by shearlet transform and overlapping-group sparsity-promoting total variation (OSTV). Shearlet transform, a directional representation system, is capable of capturing the optimal sparse representation for images with plentiful geometrical information. OSTV performs well in suppressing staircase-like artifacts often arising in traditional TV-based reconstructed images. To guarantee solution stability and efficiency, the resulting optimization problem is solved using an alternating direction methods of multipliers (ADMM)-based numerical algorithm. Extensive experimental results on both phantom and in vivo MRI datasets have demonstrated the superior performance of our proposed method in terms of both quantitative evaluation and visual quality.