Wavelet decomposition of wide-sense stationary Markov processes with application to image coding

Abstract

The discrete wavelet decomposition of wide-sense stationary Markov processes is investigated with application to image coding. It is shown that the wavelet coefficients of the decomposition are a set wide-sense stationary time series. Their means and correlation functions are derived with properties and relationships established at every resolution. These results are then used to develop an optimal bit allocation scheme for image coding using wavelet transforms, which enables high compression ratio while maintaining good visual quality. The proposed method is well adapted to progressive image transmission as well as very low bit rate compression.