IIR implementation of piecewise polynomial wavelet representation with application to image coding

The wavelet decomposition permits a multiresolution representation of continuous and discrete signals. Orthonormal bases of wavelets were introduced in the field of functional analysis as a method for approximating continuous functions at different resolutions. The aim of the wavelet decomposition is that of approximating a continuous function with smoother versions belonging to closed subspaces Vj of L2R: as shown by Mallat, the coefficients of the expansion of these approximations in suitable bases of Vj can be recursively calculated, by means of digital filtering operations (as in subband coding schemes), from the coefficients relative to higher resolution subspaces. In this work an infinite impulse response (IIR) implementation of the analysis/synthesis filter banks relative to the piecewise polynomial wavelet decomposition (the same used by Mallat) is presented: using IIR filters yields great computational saving with respect to FIR implementation. Some experimental results of the application of the IIR banks to digital image coding are also given at the end of the paper.