Construction of optimal subband coders using optimized and optimal quantizers

A method is presented for the optimization of arbitrary quantizers by use of a compensating postfilter. It is shown that the resulting optimized quantizers fit the model of a linear time-invariant filter followed by additive noise uncorrelated with the input which also characterizes the optimal (Lloyd–Max) quantizers. On the basis of this model, an expression for the variance of the error of a subband coder using optimized quantizers is explicitly determined. Given analysis filters which statistically separate the subbands, it is shown that this variance is minimized if these synthesis filters are chosen, which would achieve perfect reconstruction in lossless coding. The globally optimum such filter bank, minimizing the coder error variance, is further obtained by proper choice of its analysis filters. A novel method for the determination of optimal bit allocation to subbands of filter banks with optimized quantizers is also developed. The results are evaluated experimentally by comparison of the optimum uniformly split subband image coding scheme to classical logarithmically-split filter bank (wavelet) coding methods.