This task involves mathematical study, design, and development of a wavelet system in Matlab. The system generates the filters of any possible symmetric (i.e., biorthogonal) or orthogonal wavelet. It also has some nice features such as the plotting of the corresponding wavelets and the frequency response of the generated filters so as to visually evaluate the quality and effectiveness of the filters for data compression.
The system is serving as a test bed of various ideas and concepts related to image/video compression and wavelet applications in general. We have used it to examine thousands of wavelets. The result was that only about 20 wavelets are useful in practice for data compression.
Wavelets have been the focus of intensive research in recent years, and have found applications in many areas such as data compression, signal processing, image processing, pattern recognition, graphics, and numerical analysis. Considering the variety and importance of those applications, and taking into account the fact that different wavelets have different characteristics and thus offer different capabilities, it is highly useful to have wavelet system that performs fundamental wavelet operations. The system developed in this project serves that purpose.
The technical accomplishments of this Task this year are the following. First, the wavelet system is now complete in Matlab. Second, with the help of the system, thousands of wavelets were evaluated for data compression use, and only about 20 wavelets proved to be useful in image compression. Those 20 wavelets will be made publically available.
Future direction of the project: First, a version of the wavelet system in C is being developed by another member of the Compression Algorithms Group, to be put on the WEB individually and as part of the GAMS system. A preliminary version of it has already been put on the Web. Second, further experimentation will be conducted for determining automated methods to evaluate wavelets for various applications. Third, several publications are expected from the research being conducted on the system.