"Fourier Methods in Imaging" introduces the mathematical tools for
modeling linear imaging systems to predict the action of the system
or for solving for the input. The chapters are grouped into five
sections, the first introduces the imaging "tasks" (direct,
inverse, and system analysis), the basic concepts of linear algebra
for vectors and functions, including complex-valued vectors, and
inner products of vectors and functions. The second section defines
"special" functions, mathematical operations, and transformations
that are useful for describing imaging systems. Among these are the
Fourier transforms of 1-D and 2-D function, and the Hankel and
Radon transforms. This section also considers approximations of the
Fourier transform. The third and fourth sections examine the
discrete Fourier transform and the description of imaging systems
as linear "filters," including the inverse, matched, Wiener and
Wiener-Helstrom filters. The final section examines applications of
linear system models to optical imaging systems, including
holography.Provides a unified mathematical description of imaging
systems. Develops a consistent mathematical formalism for
characterizing imaging systems. Helps the reader develop an
intuitive grasp of the most common mathematical methods, useful for
describing the action of general linear systems on signals of one
or more spatial dimensions. Offers parallel descriptions of
continuous and discrete cases. Includes many graphical and
pictorial examples to illustrate the concepts.
This book helps students develop an understanding of
mathematical tools for describing general one- and two-dimensional
linear imaging systems, and will also serve as a reference for
engineers and scientists
General
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