标题： 带有$L^1$保真度的分数全变分去噪模型 显示英文标题

标题： Fractional total variation denoising model with $L^1$ fidelity

摘要： 我们研究了基于总变分的图像去噪模型的非局部版本，其中$L^1-$保真度项被分数阶$s$-总变分代替。我们讨论了水平集的正则性和解的唯一性，适用于保真度参数的高值和低值。我们详细分析了由凸集特征函数给出的二值数据情况。 显示英文摘要

摘要： We study a nonlocal version of the total variation-based model with $L^1-$fidelity for image denoising, where the regularizing term is replaced with the fractional $s$-total variation. We discuss regularity of the level sets and uniqueness of solutions, both for high and low values of the fidelity parameter. We analyse in detail the case of binary data given by the characteristic functions of convex sets.