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As Lord Kelvin said, "Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." This has remained durable knowledge for a century, and has extended its applicability to topics as diverse as medical imaging (CT scanning), the presentation of images on screens and their digital transmission, remote sensing, geophysical exploration, and many branches of engineering. Fourier Analysis and Imaging is based on years of teaching a course on the Fourier Transform at the senior or early graduate level, as well as on Prof. Bracewell's 1995 text Two-Dimensional Imaging. It is an excellent textbook and will also be a welcome addition to the reference library of those many professionals whose daily activities involve Fourier analysis in its many guises.
List of contents
1 Introduction.- 2 The Image Plane.- 3 Two-Dimensional Impulse Functions.- 4 The Two-Dimensional Fourier Transform.- 5 Two-Dimensional Convolution.- 6 The Two-Dimensional Convolution Theorem.- 7 Sampling and Interpolation in Two Dimensions.- 8 Digital Operations.- 9 Rotational Symmetry.- 10 Imaging by Convolution.- 11 Diffraction Theory of Sensors and Radiators.- 12 Aperture Synthesis and Interferometry.- 13 Restoration.- 14 The Projection-Slice Theorem.- 15 Computed Tomography.- 16 Synthetic-Aperture Radar.- 17 Two-Dimensional Noise Images.- Appendix A Solutions to Problems.
Summary
As Lord Kelvin said, "Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." This has remained durable knowledge for a century, and has extended its applicability to topics as diverse as medical imaging (CT scanning), the presentation of images on screens and their digital transmission, remote sensing, geophysical exploration, and many branches of engineering. Fourier Analysis and Imaging is based on years of teaching a course on the Fourier Transform at the senior or early graduate level, as well as on Prof. Bracewell's 1995 text Two-Dimensional Imaging. It is an excellent textbook and will also be a welcome addition to the reference library of those many professionals whose daily activities involve Fourier analysis in its many guises.
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"What is striking about the book is how much text there is and how rich that text is in supplementing the formal structure that is presented. Indeed, this is a hallmark of Bracewell's writing and why, in my opinion, he is held in such high esteem. ... I highly recommend it to anyone who has even a passing interest in the hows and whys of image creation, manipulation, or display."
(Brian H. Kolner, UC Davis, CA)
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"What is striking about the book is how much text there is and how rich that text is in supplementing the formal structure that is presented. Indeed, this is a hallmark of Bracewell's writing and why, in my opinion, he is held in such high esteem. ... I highly recommend it to anyone who has even a passing interest in the hows and whys of image creation, manipulation, or display."
(Brian H. Kolner, UC Davis, CA)
