基于Kantorovich-Rubinstein偏差的成像
Imaging with Kantorovich-Rubinstein discrepancy
AI总结：
本文提出将最优传输中的Kantorovich-Rubinstein范数应用于成像问题，提出了一种变分正则化模型，结合Kantorovich-Rubinstein偏差项和总变分正则化，用于图像去噪和卡通-纹理分解，并与其他方法建立联系，证明优化问题可转化为凸-凹鞍点问题并用标准工具求解。
摘要：
我们提出将最优传输中的Kantorovich-Rubinstein范数应用于成像问题。特别是，我们讨论了一种变分正则化模型，该模型包含Kantorovich-Rubinstein偏差项和总变分正则化，用于图像去噪和卡通-纹理分解。我们指出这种方法与其他最近提出的方法如总广义变分和捕捉振荡模式的范数之间的联系。我们还表明，相应的优化问题可以转化为带有简单约束的凸-凹鞍点问题，因此可以用标准工具求解。数值示例展示了有趣的特点和有利的去噪和卡通-纹理分解性能。
英文摘要：
We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems. In particular, we discuss a variational regularisation model endowed with a Kantorovich-Rubinstein discrepancy term and total variation regularization in the context of image denoising and cartoon-texture decomposition. We point out connections of this approach to several other recently proposed methods such as total generalized variation and norms capturing oscillating patterns. We also show that the respective optimization problem can be turned into a convex-concave saddle point problem with simple constraints and hence, can be solved by standard tools. Numerical examples exhibit interesting features and favourable performance for denoising and cartoon-texture decomposition.
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