Alternating total variation and non-local total variation for fast compressed sensing magnetic resonance imaging

Total variance-(TV) based compressed sensing MRI (CS-MRI) reconstruction methods are effective in restoring a magnetic resonance (MR) image structure from undersampled k-space data. However, the local details of MR images are usually oversmoothed such that block effects are easily caused. Fortunately, the problem can be overcome by the non-local total variation (NLTV), which is highly effective in keeping fine details and sharping image edges. Nevertheless, NLTV is not good at finding similar patches. Considering TV and NLTV are complementary, it is proposed to use them alternatively instead of combining them in one objective function for CS-MRI. In one alternation, the objective function containing the TV and the wavelet regularisations is firstly used to build the structure of the reconstructed MR image through running several iterations of the optimisation method and then the objective function including the NLTV and the wavelet constraints is used to remove the blocking effects and to preserve the image details through running only one iteration of the optimisation method. A number of alternations are run to find the final reconstruction image. Experimental results validate the effectiveness of the method regarding both reconstruction accuracy and computation complexity.