Adaptive Transform Learning and Joint Sparsity Based PLORAKS Parallel Magnetic Resonance Image Reconstruction

Parallel magnetic resonance (MR) imaging is an important acceleration technique based on the spatial sensitivities of array receivers. The recently proposed Parallel low-rank modeling of local k-space neighborhoods (PLORAKS) approach uses the low-rank matrix model based on local neighborhoods of undersampled multichannel k-space data for reconstruction purposes. The joint total variation (JTV) regularization term was then combined with the PLORAKS model to improve the quality of reconstructed images. To further improve the quality of parallel MR imaging, we propose combining adaptive transform learning and joint sparsity with the PLORAKS model to obtain two algorithms, and reconstruction problems are solved by using the alternating direction method of multipliers (ADMM) and conjugate gradient techniques. The experimental results show that the two proposed algorithms can achieve higher performance than the PLORAKS algorithm and the PLORAKS-JTV algorithm with the JTV regularization term in terms of the signal-to-noise ratio (SNR), normalized root mean square error (NRMSE), high-frequency error norm (HFEN), and structural similarity index measure (SSIM).