Inverse Problems

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography.

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography.

This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering.

This will be the first book on the topic of new methods in inverse problems in electromagnetics. The inverse problems such as optimization, synthesis, diagnostics, and identification are becoming one of the most important subjects in the field because of the significant practical applications to electric circuits and electromagnetics. This book introduces the recent achievements in mathematics and computing. The information on how to use the modern theoretical ideas and methods to solve inverse problems will help both students and specialists. The book systematically treats modern mathematic methods of inverse problems solution by providing descriptions of the most important practical inverse problems and the methods to solve them. Included also are descriptions of the properties of inverse problems and known methods of their solution as well as the practical implementation of these methods in electric circuits theory and electromagnetic fields theory.

This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications.