Obtain the Best Estimate of a Strongly Scattering Object from Limited Scattered Field Data
Introduction to Imaging from Scattered Fields presents an overview of the challenging problem of determining information about an object from measurements of the field scattered from that object. It covers widely used approaches to recover information about the objects and examines the assumptions made a priori about the object and the consequences of recovering object information from limited numbers of noisy measurements of the scattered fields.
The book explores the strengths and weaknesses of using inverse methods for weak scattering. These methods, including Fourier-based signal and image processing techniques, allow more straightforward inverse algorithms to be exploited based on a simple mapping of scattered field data.
The authors also discuss their recent approach based on a nonlinear filtering step in the inverse algorithm. They illustrate how to use this algorithm through numerous two-dimensional electromagnetic scattering examples. MATLAB® code is provided to help readers quickly apply the approach to a wide variety of inverse scattering problems.
In later chapters of the book, the authors focus on important and often forgotten overarching constraints associated with exploiting inverse scattering algorithms. They explain how the number of degrees of freedom associated with any given scattering experiment can be found and how this allows one to specify a minimum number of data that should be measured. They also describe how the prior discrete Fourier transform (PDFT) algorithm helps in estimating the properties of an object from scattered field measurements. The PDFT restores stability and improves estimates of the object even with severely limited data (provided it is sufficient to meet a criterion based on the number of degrees of freedom).
Suitable for graduate students and researchers working on medical, geophysical, defense, and industrial inspection inverse problems, this self-contained book provides the necessary details for readers to design improved experiments and process measured data more effectively. It shows how to obtain the best estimate of a strongly scattering object from limited scattered field data.
"It has gone straight to the top of my recommended reading list for students interested in the fundamental theory of waves and inverse scattering."
—Optics & Photonics News, April 2015
"Introduction to Imaging from Scattered Fields is an essential guide to diffraction tomography and inverse methods. The text combines theoretical analysis of scattering models with practical numerical analysis in a highly accessible narrative."
—David J. Brady, Professor of Electrical and Computer Engineering and Michael J. Fitzpatrick Professor of Photonics, Duke University
"This excellent text provides a clear and systematic treatment of the fundamental theory of waves and inverse scattering whilst remaining accessible to practitioners in remote sensing and imaging. It includes a range of examples and MATLAB code, and it should prove a valuable reference and textbook …"
—Dr. Mark Spivack, Department of Applied Mathematics and Theoretical Physics, University of Cambridge
"… bring[s] the practitioner or student of imaging up to the necessary level for understanding the physical and mathematical underpinnings of scattered fields and inverse scattering problems, with an ultimate eye on practical implementation to real problems in a variety of real-world imaging applications."
—Dr. Michael Kotlarchyk, Professor and Head of School of Physics and Astronomy, Rochester Institute of Technology
PART I - FUNDAMENTALS
Inverse Scattering Problem Overview
Theoretical Issues and Concerns
Evanescent and Propagating Waves
Material Properties and Modeling
Scattering from Compact Structures
Inverse Scattering Fundamentals
Categorization of Inverse Scattering Problems
Inverse Scattering in Two Dimensions
First Born Approximation
PART II – INVERSION METHODS
Data Inversion in "k" Space: A Fourier Perspective
Target Modeling and Data Generation
Target Modeling Environment
Imaging Algorithm Implementations: Example Reconstructions
Born Approximation Observations
Degrees of Freedom
Requirements for Degrees of Freedom for Sources
Requirement for Degrees of Freedom for Receivers
Relationship Between Born Approximation and Mie Q Factor
Alternate Inverse Methods
Born Iterative Method
Distorted Born Iterative Method
Conjugate Gradient Method
Prior Discrete Fourier Transform
Homomorphic (Cepstral) Filtering
Cepstral Filtering with Minimum Phase
Generating the Minimum Phase Function
Two Dimensional Filter Methods
Removing the Reference
PART III - APPLICATIONS
Applications to Real Measured Data
Ipswich Data Results
Institut Fresnel Data Results
Comparison of Reconstruction Methods
Final Observations and Summary
Advanced Cepstral Filtering
Processing Source Data Independently
Effects of Modified Filters in Cepstral Domain
Effects of Random Under-Sampling
Advanced Topics in Inverse Imaging
Practical Steps for Imaging Strong Scatterers
An Overall Approach to Degrees of Freedom in Imaging
PART IV – APPENDECIES
Appendix A – Fourier Analysis Review
Appendix B – The Phase Retrieval Problem
Appendix C – Prior Discrete Fourier Transform
Appendix D – The Poynting Vector
Appendix E – Resolution and Degrees of Freedom
Appendix F – MATLAB® Exercises with COMSOL® Data