Compressed sensing magnetic resonance imaging based on shearlet sparsity and nonlocal total variation.

Compressed sensing (CS) has been utilized for acceleration of data acquisition in magnetic resonance imaging (MRI). MR images can then be reconstructed with an undersampling rate significantly lower than that required by the Nyquist sampling criterion. However, the CS usually produces images with artifacts, especially at high reduction rates. We propose a CS MRI method called shearlet sparsity and nonlocal total variation (SS-NLTV) that exploits SS-NLTV regularization. The shearlet transform is an optimal sparsifying transform with excellent directional sensitivity compared with that by wavelet transform. The NLTV, on the other hand, extends the TV regularizer to a nonlocal variant that can preserve both textures and structures and produce sharper images. We have explored an approach of combining alternating direction method of multipliers (ADMM), splitting variables technique, and adaptive weighting to solve the formulated optimization problem. The proposed SS-NLTV method is evaluated experimentally and compared with the previously reported high-performance methods. Results demonstrate a significant improvement of compressed MR image reconstruction on four medical MRI datasets.