Optimal subband coders of quantized multidimensional signals

A new general method is presented for the analysis of the effects of quantization and transmission noise in subband filter-bank multidimensional signal and image coders. Using general statistical noise characterization, the filter banks are obtained, which are optimal in the sense of minimizing the variance of the difference of the reconstructed signal from the original. It is shown that these are not identical to those achieving perfect reconstruction in lossless coding. A general method is described for the optimal selection of the synthesis filters if the analysis filters and quantizers are given. Assuming the use of these optimal synthesis filters, a method is then developed for the determination of the optimal analysis filters and the optimal bit-allocation to the subbands. The effects of quantization on perfect reconstruction filter-banks are analyzed next, and an explicit expression is determined for the quantizer noise-to-signal ratio for such banks. Given arbitrary quantizers, the analysis filters which are optimal in the sense of minimizing the output noise power are obtained. Finally, the jointly optimal selection is determined for the analysis filters and the bit allocations of the subbands. It is seen that this selection is identical to that determined for the theoretically optimal filter-banks.