An Introduction to the Mathematical Theory of Inverse Problems

Focusing on the field of inverse problems, this graduate-level textbook addresses critical applications in geophysical exploration and nondestructive testing. It delves into the challenges of ill-posed problems and explores regularization methods through analytical and numerical examples. Detailed discussions on three specific nonlinear inverse problems—inverse spectral problem, electrical impedance tomography (EIT), and inverse scattering problem—are included, alongside examinations of direct problems regarding existence and uniqueness. The text is enriched with theoretical insights, numerical procedures, exercises, and illustrations for mathematics and engineering students.