MMSE design of modulated and tree-structured filter banks for efficient tradeoffs between rate, distortion, and decoder complexity

Designing filter banks for source coding purposes classically relies on perfect reconstruction filters. However, several studies have shown recently that taking the quantization noise into account in the design could yield noticeable reduction of the reconstruction distortion. In particular, a joint optimization of the synthesis filters and quantizers with respect to the output mean squared error (MSE) was proposed, and the resulting scheme was called an minimum MSE (MMSE) filter bank. However, this approach was dedicated to parallel uniform filter banks, which require a very large computational complexity. This paper is concerned with the possibility of providing MMSE filters under the constraint that the filter bank is either of a modulated or a tree-structured kind and thus of low implementation cost. Various approaches for the optimization of the synthesis bank are presented, taking into account the structural constraint. Depending on the number of parameters to be optimized, we obtain various tradeoffs between decoder complexity, transmitted bit rate, and reconstruction distortion.