Optimal subband coding with Lloyd-Max quantization

A new method is presented for the analysis of the effects of Lloyd-Max quantization in subband filter banks and for the optimal design of such filter banks. A rigorous statistical model of a vector Lloyd-Max quantizer is established first, consisting of a linear time-invariant filter followed by additive noise uncorrelated with the input. On the basis of this model, an expression for this variance of the error of a subband coder using Lloyd-Max quantizers is explicitly determined. Given analysis filters which statistically separate the subbands, it is shown that this variance is minimized if the synthesis filters are chosen, which would achieve perfect reconstruction in lossless coding. The globally optimum filter bank, minimizing the coder error variance, is further obtained by proper choice of its analysis filters. The results are evaluated experimentally in the realistic setting of a logarithmically split subband image coding scheme