Solution paths of variational regularization methods for inverse problems

Variable-smoothing Regularization Methods for Inverse Problems

Many inverse problems of practical interest are ill-posed in the sense that solutions do not depend continuously on data. To eeectively solve such problems, regularization methods are typically used. One problem associated with classical regularization methods is that the solution may be oversmoothed in the process. We present an alternative \local regularization" approach in which a decomposit...

Iterated Regularization Methods for Solving Inverse Problems

Computational and Variational Methods for Inverse Problems

A Survey of Direct Methods for Solving Variational Problems

This study presents a comparative survey of direct methods for solving Variational Problems. Thisproblems can be used to solve various differential equations in physics and chemistry like RateEquation for a chemical reaction. There are procedures that any type of a differential equation isconvertible to a variational problem. Therefore finding the solution of a differential equation isequivalen...

Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by Neubauer [5]. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in t...