Basic Theory and Examples
Presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. This volume discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects, and presents diverse real-world applications, important test cases, and possible pitfalls.
Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data.

This book presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles.

A Taste of Inverse Problems: Basic Theory and Examples

• rigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations;
• presents diverse real-world applications, important test cases, and possible pitfalls; and
• treats these applications with the same rigor and depth as the theory.