Author: Alexander Petukhov (University of South Carolina)

Title: Wavelet bases, associated with recursive filters, and their applications to image and video compression.

Abstract: For the last 10 years the theory of compactly supported wavelet bases became a powerful tool for many theoretical and applied problems, relating to signal processing. The algorithms of expansion of functions in such bases are implemented as a collection of discrete convolutions with numerical sequences, which has only finite number of non-zero coefficients, i.e., finite impulse response (FIR) filters. The frequency characteristic of FIR filter is a trigonometric polynomial. We consider wavelet bases, such that expansion in them is implemented with filters with a rational frequency response. The new types of wavelet bases give new opportunities for image and video compression. Despite the fact, that this types of filters has infinite impulse response (IIR-filters), there is an effective numerical realization in the form of a composition of well known in a radio engineering, so-called, recursive filters. The computional complexity for realization of filters with a rational frequency response are proportional to a sum of degrees of the numerator and the denominator, that is comparable to complexity of expansions in compactly supported bases.