Introduction to Imaging from Scattered Fields
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).
INTRODUCTION. THEORETICAL BACKGROUND. SYSTEMATIC METHOD FOR PRODUCING SIMULATED SCATTERED FIELD DATA FROM KNOWN STRUCTURES. WELL-KNOWN INVERSION METHODS. DATA ACQUISITION CONSIDERATIONS. RECENT SIGNAL PROCESSING-BASED APPROACHES. APPLICATION OF SIGNAL PROCESSING-BASED METHODS. EFFECTS OF FILTERING AND SAMPLING. UNIFIED INVERSE IMAGING APPROACH AND CONSTRAINTS. REFERENCES. APPENDICES.
"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