Book description
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
Professor Roger L. Easton, Jr
Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology
Professor Easton teaches undergraduate and graduate courses in linear
systems, optical imaging, and digital image processing at Rochester
Institute of Technology. He received a B. S. degree in Astronomy from
Haverford College, an M. S. in physics from the University of Maryland,
and an M. S. and Ph. D. degree in Optical Sciences from the University
of Arizona.
His research interests include the application of digital image
processing to text documents and manuscripts. He has contributed to work
on the Dead Sea Scrolls and is now part of an imaging team helping
scolars to read the original Archimiedes Palimpsest. Professor Easton
also conducts research into optical signal processing and
computer-generated holography, publishing articles on both.
