Mathematical Foundations of Imaging, Tomography and Wavefield Inversion by Anthony J. Devaney – A Cambridge University P

Introduction

In the rapidly advancing fields of medical imaging, geophysics, and wave physics, the ability to reconstruct hidden structures from measured data is a cornerstone of modern science. Mathematical Foundations of Imaging, Tomography and Wavefield Inversion by Anthony J. Devaney offers a rigorous yet accessible journey into the mathematics that power these technologies. Published by Cambridge University Press, this hardcover edition is an indispensable resource for Indian graduate students, researchers, and professionals who seek a deep understanding of inverse problems and wave-based imaging.

Book Overview

This book systematically builds the theoretical framework required to tackle imaging and inversion problems. Starting from the simplest wave equation models, it progresses through scalar and vector wave theories, always connecting abstract mathematics to practical computation. The inclusion of MATLAB-based examples ensures that readers can immediately apply concepts to real-world scenarios, making it ideal for both self-study and classroom use in Indian universities.

Key Highlights

• Comprehensive coverage of inverse scattering, diffraction tomography, and wavefield inversion
• Step-by-step derivation of solutions using Green function techniques
• MATLAB code examples integrated throughout the text for hands-on learning
• Bridges theory and practice with applications in medical imaging, radar, and seismology
• Clear explanations of field time reversal and propagation in inhomogeneous media

Inside the Book

The content is structured to guide the reader from fundamental principles to advanced topics. Early chapters establish the mathematics of wave propagation and scattering. Later chapters delve into computational methods for solving inverse problems, including regularization and optimization. Each concept is illustrated with diagrams and MATLAB scripts, allowing readers to experiment and verify results. The final sections explore vector wave models, preparing readers for cutting-edge research in electromagnetics and elastodynamics.

Key Topics

• Inhomogeneous and homogeneous Helmholtz equations
• Green function techniques for wave propagation
• Scattering in homogeneous and inhomogeneous backgrounds
• Diffraction tomography and filtered backpropagation
• Field time reversal and its imaging applications
• Vector wave inversion for electromagnetic and elastic waves

Reader Benefits

Indian students and researchers will find this book particularly valuable because it:

• Provides a strong mathematical foundation without assuming prior knowledge of inverse theory
• Offers MATLAB code that can be adapted for local research projects
• Connects abstract theory to real-world applications such as ultrasound imaging and ground-penetrating radar
• Serves as a reliable reference for PhD coursework and competitive exams like GATE and CSIR-NET

Learning Outcomes

By studying this book, readers will be able to:

• Derive and solve the Helmholtz equation for various source configurations
• Implement Green function methods for wavefield modeling
• Understand the mathematical basis of computed tomography (CT) and magnetic resonance imaging (MRI)
• Apply time reversal techniques to locate sources and scatterers
• Develop algorithms for inverse scattering in inhomogeneous media

Who Should Read

This book is tailored for graduate students in physics, electrical engineering, applied mathematics, and biomedical engineering. It is also highly suitable for researchers in medical imaging, geophysics, acoustics, and remote sensing. Professionals working in Indian defence laboratories, oil exploration, and healthcare technology will find the content directly applicable to their work.

About the Author

Anthony J. Devaney is a distinguished physicist and educator with decades of experience in wave propagation and inverse scattering. He has contributed significantly to the development of diffraction tomography and has taught at leading institutions worldwide. His clear teaching style and deep insight into the subject make this book a classic in the field.

About the Publisher

Cambridge University Press is one of the world's oldest and most respected academic publishers. Known for rigorous peer review and high-quality production, Cambridge books are trusted by scholars and students across India. This hardcover edition is built to last, with crisp typesetting and durable binding.

Conclusion

Mathematical Foundations of Imaging, Tomography and Wavefield Inversion is more than a textbook—it is a gateway to mastering the mathematics behind modern imaging. Whether you are a student beginning your research journey or a professional seeking to deepen your expertise, this book offers the clarity and depth you need. Order your copy from Bookshops.in today and add this essential volume to your library.