Regularization Methods to Solve Various Inverse Problems

The area of mathematical inverse problems is quite broad and involves the qualitative and quantitative analysis of a wide variety of physical models. Applications include, for example, The problem of inverse heat conduction, image reconstruction, tomography, the inverse scattering problem, and the determination of unknown coefficients or boundary parameters appearing in partial differential equation models of physical phenomena. We will survey some recent developments in the area of regularization methods for mathematical inverse problems and indicate where further contributions are needed. Finally we will discuss current work in the area of iterative solution methods, regularization schemes which have been successfully applied to a number of important non linear inverse problems.