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

Abstract

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-L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> ) is proposed to overcome these drawbacks. Specifically, the TV-L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> regularization is constructed using the exponent ${p}(0\lt{p}\lt 1)$, which is defined as the $L_{p}-$norm of the gradient. Then TV-L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> is combined with the minimax-concave penalty of the $L_{p}-$norm to construct the MCTV-L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> . 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-L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> 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.