Magnetic resonance imaging reconstruction via non‐convex total variation regularization

Abstract

Magnetic resonance imaging (MRI) reconstruction model based on total variation (TV) regularization can deal with problems such as incomplete reconstruction, blurred boundary, and residual noise. In this article, a non‐convex isotropic TV regularization reconstruction model is proposed to overcome the drawback. Moreau envelope and minmax‐concave penalty are firstly used to construct the non‐convex regularization of L2 norm, then it is applied into the TV regularization to construct the sparse reconstruction model. The proposed model can extract the edge contour of the target effectively since it can avoid the underestimation of larger nonzero elements in convex regularization. In addition, the global convexity of the cost function can be guaranteed under certain conditions. Then, an efficient algorithm such as alternating direction method of multipliers is proposed to solve the new cost function. Experimental results show that, compared with several typical image reconstruction methods, the proposed model performs better. Both the relative error and the peak signal‐to‐noise ratio are significantly improved, and the reconstructed images also show better visual effects. The competitive experimental results indicate that the proposed approach is not limited to MRI reconstruction, but it is general enough to be used in other fields with natural images.

An AtanTV Nonconvex Regularization Model for MRI Reconstruction

“…In this section, we verified the effectiveness of the proposed AtanTV method by some simulation experiments and made some numerical comparisons with TV [37] and MCTV [30,31]. The programming software was MATLAB R2015a.…”

“…Different methods using the same parameters may get diametrically opposite conclusions. In the compared TV method and MCTV method, the corresponding parameters follow the "best" parameter values provided by the authors [30,31,37].…”

“…Therefore, some excellent algorithms in convex optimization can solve it. On this basis, some researchers separately considered the MCTV model of MRI, and their simulation experiments show the effectiveness of this type of method [30][31][32].…”

Diffusion optical tomography reconstruction based on convex–nonconvex graph total variation regularization

“…CNC sparse regularization can not only overcome the shortcomings of biased estimation caused by convex sparse regularization but also avoid the local optimal solution through the global convexity of the objective function. CNC sparse regularization has shown great performance in signal denoising, 24,26 MRI image reconstruction, 27,28 fault detection, 29,30 and so on.…”

Plug-and-Play ADMM for MRI Reconstruction With Convex Nonconvex Sparse Regularization

“…Meanwhile, the convexity of the whole objective function (2) can maintain by adjusting the parameter settings. The CNC strategy is widely used in image reconstruction [18], [19], image denoising [13], [14], [20], and fault detection [21]- [23].…”