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 in troduced in the field of functional analysis as a method for approxima ting continuous functions at different resolutions. The aim of the wav elet decomposition is that of approximating a continuous function with smoother versions belonging to closed subspaces V(j) of L2(R): as sho wn by Mallat, the coefficients of the expansion of these approximation s in suitable bases of V(j) 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/synthe sis filter banks relative to the piecewise polynomial wavelet decompos ition (the same used by Mallat) is presented: using IIR filters yields great computational saving with respect to FIR implementation. Some e xperimental results of the application of the IIR banks to digital ima ge coding are also given at the end of the paper.