Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale. The associated inverse scale space flow can be obtained using the classical Bregman iteration applied to a convex, absolutely one-homogeneous regularizer. In order to extend these approaches to general energies with non-convex data term, we apply the Bregman iteration to a lifted version of the functional with sublabel-accurate discretization. We provide a condition for the subgradients of the regularizer under which this lifted iteration reduces to the standard Bregman iteration. We show experimental results for the convex and non-convex case.

中文翻译：

---

使用函数提升的非凸变分问题的尺度空间逆迭代

非线性滤波方法允许获得有关非经典比例尺概念的图像分解。可以使用经典的Bregman迭代来获得相关的逆尺度空间流，该经典Bregman迭代应用于凸的，绝对一齐的正则化器。为了将这些方法扩展为具有非凸数据项的一般能量，我们将Bregman迭代应用于具有次标签精确离散化的函数的提升版本。我们为正则化器的次梯度提供了条件，在这种条件下，这种提升的迭代减少为标准的Bregman迭代。我们显示了凸和非凸情况的实验结果。