The answer is image compression. Modern mathematics (developed
in the last 20 years), electrical engineering (DSP) and computer science
have been responsible for the development of good image compression algorithms.
The course will cover the mathematical basis of many of the ideas behind
image processing such as filtering, filter banks, the discrete Fourier
and cosine transforms and the discrete wavelet transform. All of this will
be balanced by concrete applications of these ideas to various image
processing problems with a special emphasis on image compression. The images
help make the mathematics more concrete, as the two pictorial illustrations of
Discrete Cosine Transform (DCT) based JPEG compression and Discrete
Wavelet Transform (DWT) based JPEG compression below show.
The course is aimed at juniors and seniors, though any mathematically well-prepared student will benefit from the course. The basic mathematical ideas can be built upon matrix algebra and some Fourier series. The course work will consist of homework assignments, exams and one or two projects. The primary computational tool will be Matlab. It is not necessary to know Matlab beforehand, though some computational expertise is expected (e.g. one of MATLAB, MAPLE, or C++).
This course has now been offered (at least) eight times and includes materials developed by Allen Broughton and Ed Doering several years ago, additions by Roger Lautzenheiser in Winter 01-02, and much material developed by Kurt Bryan. I have TOTALLY REVISED and REWRITTEN the notes. They are now of textbook quality and come with Matlab scripts, projects, and exercises. Our main goal will be to understand the mathematics behind the current DCT-based JPEG (see picture above) compression method and the new wavelet-based JPEG 2000 compression method (see picture above). By learning the mathematical foundations as well as their application, we expect that students will gain background to further their learning of image processing methods.
I particularly welcome any student who wants to do a related Imaging Certificate project after taking the course.
Any questions? Send me email: kurt.bryan@rose-hulman.edu
Return to the The MA 439 Page.