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Fourier Methods in Imaging

Roger L. Easton Jr.

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John Wiley & Sons img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Elektronik, Elektrotechnik, Nachrichtentechnik


Fourier Methods in Imaging introduces the mathematical toolsfor modeling linear imaging systems to predict the action of thesystem or for solving for the input. The chapters are grouped intofive sections, the first introduces the imaging "tasks"(direct, inverse, and system analysis), the basic concepts oflinear algebra for vectors and functions, including complex-valuedvectors, and inner products of vectors and functions. The secondsection defines "special" functions, mathematical operations, andtransformations that are useful for describing imaging systems.Among these are the Fourier transforms of 1-D and 2-D function, andthe Hankel and Radon transforms. This section also considersapproximations of the Fourier transform. The third and fourthsections examine the discrete Fourier transform and the descriptionof imaging systems as linear "filters", including the inverse,matched, Wiener and Wiener-Helstrom filters. The final sectionexamines applications of linear system models to optical imagingsystems, including holography. * Provides a unified mathematical description of imagingsystems. * Develops a consistent mathematical formalism for characterizingimaging systems. * Helps the reader develop an intuitive grasp of the most commonmathematical methods, useful for describing the action of generallinear systems on signals of one or more spatial dimensions. * Offers parallel descriptions of continuous and discretecases. * Includes many graphical and pictorial examples to illustratethe concepts. This book helps students develop an understanding ofmathematical tools for describing general one- and two-dimensionallinear imaging systems, and will also serve as a reference forengineers and scientists


(Journal of Electronic Imaging, 1 April 2011)
"Overall, this is an excellent text, appropriate for the graduate student approaching this material for the first time, and for the seasoned professional looking for an up-to-date reference."
(Zentralblatt Math, 2010)
"This comprehensive textbook represents a practical review of Fourier techniques in imaging methods. It will be very useful for graduate students (in engineering, science, computer science, and applied mathematics) as well as engineers interested in linear imaging systems."
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