MRI Reconstruction using Minimax-Concave Total Variation Regularization based on p-norm

Magnetic resonance imaging (MRI) reconstruction model based on total variation (TV) regularization can solve some problems, e.g., incomplete reconstruction, blurred imaging, and denoising. However, it has problems such as sensitivity to outliers, poor ability to induce the sparsity of the gradient domain of MR image. In this paper, minimax-concave total variation regularization based on L_{p}-norm (MCTV-Lp) is proposed to overcome these drawbacks. Specifically, the TV-Lp regularization is constructed using the exponent {p}(0lt{p}lt 1), which is defined as the L_{p}-norm of the gradient. Then TV-Lp is combined with the minimax-concave penalty of the L_{p}-norm to construct the MCTV-Lp. Finally, the sparse reconstruction model based on minimax-concave total variation (MCTV-SRM) is proposed, where the objective function is formulated as the sum of the regularization of MCTV-Lp and the data-fitting term of L_{2}-norm. Moreover, an optimization algorithm based on the alternating direction method of multipliers (ADMM) is given to solve the related optimization problems iteratively. Results on different datasets with different experimental settings show that the proposed method is better adapted to MRI reconstruction and the relative error and PSNR are significantly improved than several typical methods, while can reconstruct MR images with clear details and textures.