论文标题
通过无界域中的变异曲率来降级的水平集合的收敛
Convergence of level sets in total variation denoising through variational curvatures in unbounded domains
论文作者
论文摘要
我们提供了一些液位集合的几何融合的结果，用于降级的总变异溶液，因为正则化参数趋于零。其中的共同特征是，它们利用有限周长集的变异平均曲率的显式结构。因此，没有假定理想数据的级别集的额外规律性，尤其是其总差异的亚级别可能是空的。作为交换，需要对数据或噪声的其他限制。我们考虑两种情况：具有参数选择的特征函数，具体取决于噪声水平和无声的通用数据。
We present some results of geometric convergence of level sets for solutions of total variation denoising as the regularization parameter tends to zero. The common feature among them is that they make use of explicit constructions of variational mean curvatures for general sets of finite perimeter. Consequently, no additional regularity of the level sets of the ideal data is assumed, and in particular the subgradient of the total variation at it could be empty. In exchange, other restrictions on the data or on the noise are required. We consider two cases: characteristic functions with a parameter choice depending on the noise level, and noiseless generic data.
