The successes of these algorithms reflect the fact that the space-frequency localization of the wavelet transform is well matched to the class of typical images that are compressed. This project is directed at better understanding the relationship between characterization of general classes of images and the compression efficiency that is achievable over each class. Our goal is to refine our classifications in order to identify practically useful classes of images for which significant improvements in compression efficiency can be achieved and to extend these ideas to higher dimensional data. The primary focus of this subteam is research on lossy compression, which naturally must then address fundamental approximation and information theoretic issues. Lossy encoder algorithms which are compatible with progressive transmission provide lossless compression or may be terminated when sufficiently accurate detail has been obtained.
Similar ideas apply to signals and other data formats.
Much of our understanding of image compression has been developed from the study of rate-distortion relationships for either discrete gaussian random processes or samples of bandlimited continuous gaussian random processes. The successes of these algorithms reflect the fact that the space-frequency localization of the wavelet transform is well matched to the class of typical images that are compressed. Current research is directed at understanding the interplay between classification and rate-distortion analysis in order to achieve optimal performance over general classes of images. Mathematically, there are several important theorems which give understanding of the interplay between classification and rate distortion analysis. Approximation theory is very useful since it gives precise characterizations of functions with a given approximation rate.