论文标题
分析涉及不连续运算符的不足问题解决方案的正则化方法
Analysis of regularization methods for the solution of ill-posed problems involving discontinuous operators
论文作者
论文摘要
我们考虑了解决不合适的操作员方程的解决方案的正则化概念，该方程是由连续和不连续的操作员组成的。特定的应用程序是级别设置正则化，我们在其中开发了一种新颖的最小化概念。拟议的水平设置正规化能够处理不断变化的拓扑结构。给出了解释拓扑分裂的功能分析框架。水平集正规化方法的渐近极限是一个进化过程，该过程是在数值上实现的，并且通过解决逆源问题来证明所提出的算法的质量。
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a novel concept of minimizers. The proposed level set regularization is capable of handling changing topologies. A functional analytic framework explaining the splitting of topologies is given. The asymptotic limit of the level set regularization method is an evolution process, which is implemented numerically and the quality of the proposed algorithm is demonstrated by solving an inverse source problem.
