Learning Joint-Sparse Codes for Calibration-Free Parallel MR Imaging
The integration of compressed sensing and parallel imaging (CS-PI) has shown an increased popularity in recent years to accelerate magnetic resonance (MR) imaging. Among them, calibration-free techniques have presented encouraging performances due to its capability in robustly handling the sensitivity information. Unfortunately, existing calibration-free methods have only explored joint-sparsity with direct analysis transform projections. To further exploit joint-sparsity and improve reconstruction accuracy, this paper proposes to Learn joINt-sparse coDes for caliBration-free parallEl mR imaGing (LINDBERG) by modeling the parallel MR imaging problem as an <inline-formula> <tex-math notation="LaTeX">$\ell _{\textsf {2}}$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$\ell _{F}$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$\ell _{\textsf {2},\textsf {1}}$ </tex-math></inline-formula> minimization objective with an <inline-formula> <tex-math notation="LaTeX">$\ell _{\textsf {2}}$ </tex-math></inline-formula> norm constraining data fidelity, Frobenius norm enforcing sparse representation error and the <inline-formula> <tex-math notation="LaTeX">$\ell _{\textsf {2},\textsf {1}}$ </tex-math></inline-formula> mixed norm triggering joint sparsity across multichannels. A corresponding algorithm has been developed to alternatively update the sparse representation, sensitivity encoded images and K-space data. Then, the final image is produced as the square root of sum of squares of all channel images. Experimental results on both physical phantom and in vivo data sets show that the proposed method is comparable and even superior to state-of-the-art CS-PI reconstruction approaches. Specifically, LINDBERG has presented strong capability in suppressing noise and artifacts while reconstructing MR images from highly undersampled multichannel measurements.