Mathematical Foundations of Imaging, Tomography and Wavefield Inversion

by Anthony J. Devaney

• ISBN13: 9780521119740
• ISBN10: 052111974X
• Format: Hardcover
• Copyright: 2012-07-30
• Publisher: Cambridge University Press

Summary

Inverse problems are of interest and importance across many branches of physics, mathematics, engineering and medical imaging. In this text, the foundations of imaging and wavefield inversion are presented in a clear and systematic way. The necessary theory is gradually developed throughout the book, progressing from simple wave equation based models to vector wave models. By combining theory with numerous MATLAB based examples, the author promotes a complete understanding of the material and establishes a basis for real world applications. Key topics of discussion include the derivation of solutions to the inhomogeneous and homogeneous Helmholtz equations using Green function techniques; the propagation and scattering of waves in homogeneous and inhomogeneous backgrounds; and the concept of field time reversal. Bridging the gap between mathematics and physics, this multidisciplinary book will appeal to graduate students and researchers alike. Additional resources including MATLAB codes and solutions are available online at www.cambridge.org/9780521119740.

Table of Contents

Radiation and initial value problems for the wave equation

Radiation and boundary value problems in the frequency domain

Eigenfunction expansions of solutions to the Helmholtz equation

Angular spectrum and multipole expansions

The inverse source problem

Scattering theory

Surface scattering and diffraction

Classical inverse scattering and diffraction tomography

Waves in inhomogeneous media

Time reversal imaging for systems of discrete scatterers

The electromagnetic field

Appendices

Index

Table of Contents provided by Publisher. All Rights Reserved.