Regularisation of Inverse Problems

Driven by the needs of applications in both sciences and industry, the field of inverse problems has become one of the fastest-growing areas in applied mathematics recently. This book starts with an overview of some classes of inverse problems of practical interest. Inverse problems typically lead to mathematical models that are ill-posed in the sense of Hadamard. Their solutions are especially unstable under data perturbations, necessitating the development of special numerical methods, known as regularization methods, to cope with these instabilities. This book is devoted to the mathematical theory of regularization methods and aims to provide an up-to-date account of the currently available results regarding regularization methods for both linear and nonlinear ill-posed problems. Both continuous and iterative regularization methods are considered in detail.