Compressed Sensing Reconstruction Based on Combination of Group Sparse Total Variation and Non-Convex Regularization

Reducing the long data acquisition time has always been the challenge of magnetic resonance imaging (MRI). The theory of compressed sensing makes it possible to reconstruct magnetic resonance (MR) images from undersampled k-space data, which inevitably results in the degradation of images. Therefore, it's desirable to find ways to make improvements on the reconstruction quality. A new method based on combination of group sparse total variation and non-convex regularization (GSTVNR) is proposed in this paper. First, to suppress the staircase artifacts and enhance the group sparsity in the finite difference domain of MR images, the group sparse total variation (GSTV) is exploited in our model. Second, non-convex regularization term is combined with GSTV to promote group sparsity more strongly. We choose three different non-convex penalty functions and limit the range of related parameter to guarantee the strict convexity of total cost function. An alternating direction method of multipliers (ADMM) is utilized to solve our model. The effectiveness of GSTV and non-convex regularization are respectively verified in our experiments. Besides, both in visual inspection and quantitative evaluations, our method is demonstrated to achieve higher-quality images compared with some state-of-the-art methods.