Image coding using wavelets based on perfect reconstruction IIR filter banks

This paper re-examines modulated polyphase filter banks which use reverse-time subfilters to achieve perfect reconstruction and studies their performance for image coding when used to form a wavelet decomposition. To code the wavelet coefficients, we use the embedded zerotree wavelet (EZW) algorithm developed by Shapiro (1993) which is reasonably simple and yet achieves very good rate-distortion performance. The problem of eliminating filter transients is thoroughly studied and optimal results are derived in both the absence and presence of subband coefficient quantization. Using this analysis as a starting point, we develop a new method of coding the filter states (required to eliminate edge transients) for transmission to the receiver which efficiently exploits interscale redundancy and is easily incorporated into the zerotree algorithm. Comparing this direct transmission method to circular convolution, we find that it achieves superior rate-distortion performance in a wide range of cases. Coding comparisons between two infinite impulse response (IIR) wavelets and a number of biorthogonal wavelets are presented. These comparisons indicate that the performance of the polyphase allpass wavelet is comparable to that of the best finite impulse response (FIR) biorthogonal wavelets with considerably reduced computational complexity.