Tangent vector-based gradient method with l₁₂-regularization: Iterative half thresholding algorithm for CS-MRI

This paper presents a new method using tangent vector-based l₁₂-regularization for compressed sensing MR image reconstruction.

The proposed method with l₁₂-regularization is tested on four datasets: (i) 1-D sparse signal (ii) numerical cardiac phantom, (iii & iv) two sets of in-vivo cardiac MRI datasets acquired using 30 receiver coil elements with Cartesian and radial trajectories on 3T scanner. The results are compared with standard CS reconstruction, which utilizes l₁-regularization. The experiments were also conducted for two different types of samplings: (i) cartesian sub-sampling and (ii) 2D random Gaussian sub-sampling.

The quality of the reconstructed images is validated through Root Mean Square Error (RMSE) and Peak Signal-to-Noise Ratio (PSNR). The results show that the proposed method outperforms the standard CS reconstructions in our experiments with an improvement of 54.8% in RMSE and 14.3% in terms of PSNR. Moreover, the Gaussian random sub-sampling-based image reconstruction results are better than the Cartesian sub-sampling-based reconstruction results.

The results show that the proposed method yields a good sparse signal approximation and superior convergence behavior, which implies a promising technique for the reconstruction of cardiac MR images as compared to the conventional CS algorithm.