论文标题
学习非本地正规化操作员
Learning nonlocal regularization operators
论文作者
论文摘要
研究了从一类非本地运算符中确定哪种操作员的学习方法对于逆问题的正则化是最佳的。被考虑的非局部运算符的类别是使用平方分数Sobolev seinorms作为正规化操作员的动机。与本地运营商正规化理论理论的第一个基本结果扩展到非局部情况。然后，开发了基于双重优化策略的框架，该框架允许从给定类中选择非局部正规化操作员，i）对于训练集的合适性能度量，以及ii）享受特别有利的属性。还提供了数值实验的结果。
A learning approach for determining which operator from a class of nonlocal operators is optimal for the regularization of an inverse problem is investigated. The considered class of nonlocal operators is motivated by the use of squared fractional order Sobolev seminorms as regularization operators. First fundamental results from the theory of regularization with local operators are extended to the nonlocal case. Then a framework based on a bilevel optimization strategy is developed which allows to choose nonlocal regularization operators from a given class which i) are optimal with respect to a suitable performance measure on a training set, and ii) enjoy particularly favorable properties. Results from numerical experiments are also provided.
