MGF: An Algorithm for Compressed Sensing MRI with Gradient Domain Guided Image Filtering

In this paper, we develop an algorithm for magnetic resonance imaging (MRI) reconstruction with gradient domain guided image filtering (called MGF). We first turn a MRI reconstruction problem into two-phase objective functions: in the first phase, a latent image is generated to be a guidance image for gradient domain guided image filtering (GGF), and in the second phase, GGF is used to integrate fine structures of the latent image into the ideal solution, meanwhile, thenorm prior is simply yet effectively imposed on the GGF constraint for the error between latent and ideal images in image gradient domain. Then an efficient optimization scheme is derived to address the proposed model by iteratively alternating latent image reconstruction, GGF andnorm approximations, and ideal image reconstruction. Final experiments on real-valued and complex-valued MR images demonstrate the satisfactory performance of MGF in MRI reconstructions, and our method outperforms several well-known compressed sensing (CS) reconstruction approaches in terms of subjective results and objective assessments.