Mathematical Foundations of Imaging, Tomography and Wavefield Inversion

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.

Spis treści:
1. Radiation and initial value problems for the wave equation
2. Radiation and boundary value problems in the frequency domain
3. Eigenfunction expansions of solutions to the Helmholtz equation
4. Angular spectrum and multipole expansions
5. The inverse source problem
6. Scattering theory
7. Surface scattering and diffraction
8. Classical inverse scattering and diffraction tomography
9. Waves in inhomogeneous media
10. Time reversal imaging for systems of discrete scatterers
11. The electromagnetic field
Appendices
Index.