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Synopsis

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

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