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Cheney M., Borden B. Fundamentals of Radar Imaging

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Cheney M., Borden B. Fundamentals of Radar Imaging
Society for Industrial and Applied Mathematics, 2009, -164 pp.
Radar imaging is a subject of tremendous mathematical richness, with many interesting applications and many challenging open problems that are of a mathematical nature. Yet the topic is almost completely unknown in the mathematical community. This is because the field was developed within the engineering community, and the engineering literature is difficult for mathematicians to penetrate.
Mathematicians tend to like an axiomatic approach: they like to begin with one or more partial differential equations, say, the wave equation or Maxwell’s equations, and derive everything from these equations. Physicists, on the other hand, are comfortable beginning with solutions of the fundamental equations. Engineers, in contrast, are able to begin with the key part of the solution, and proceed from there. Consequently mathematicians find it difficult to read the engineering literature because they don’t understand where the first equation comes from. The goal of this monograph is to fill that gap and to show how radar imaging arises from the fundamental partial differential equations.
The focus here is on showing the connection between the physics and the mathematics, and on supplying an intuitive mathematical understanding of the basic ideas. Consequently, we ignore many issues of rigor, such as questions about the relevant function spaces and the precise conditions under which interchange of integrals is valid, because attention to these issues would only distract from the focus on the underlying ideas. We hope that this approach will provide a foundation that will enable mathematical readers to begin to read the extensive engineering literature and to start working in the field.
We have provided some references to ongoing work, but we have made no attempt at a complete literature survey or detailed history.
I Radar Basics.
Introduction.
Radar Systems.
Introduction to Scattering.
Detection of Signals in Noise.
The Radar Ambiguity Function.
II Radar Imaging.
Wave Propagation in Two and Three Dimensions.
Inverse Synthetic-Aperture Radar.
Antennas.
Synthetic-Aperture Radar.
Related Techniques.
Open Problems.
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