Based on transformed $\ell_1$ regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its performance, we propose a TTV-regularized Mumford--Shah model with fuzzy membership function for image segmentation. To solve it, we design an alternating direction method of multipliers (ADMM) algorithm that utilizes the transformed $\ell_1$ proximal operator. Numerical experiments demonstrate that using TTV is more effective than classical TV and other nonconvex TV variants in image segmentation.

翻译：基于变换$\ell_1$正则化，变换总变分（TTV）具有鲁棒的图像恢复能力，其性能可与TV$^p$（$0<p<1$）等其他非凸总变分（TV）正则化方法相竞争。受其性能启发，我们提出了一种结合模糊隶属度函数的TTV正则化Mumford-Shah模型用于图像分割。为求解该模型，我们设计了一种利用变换$\ell_1$近端算子的交替方向乘子法（ADMM）算法。数值实验表明，在图像分割任务中，使用TTV比经典TV及其他非凸TV变体更为有效。