Fourier Methods in Imaging (ePub)

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