Perfect reconstruction versus MMSE filter banks in source coding

Classically, the filter banks (FBs) used in source coding schemes have been chosen to possess the perfect reconstruction (PR) property or to be maximally selective quadrature mirror filters (QMFs). This paper puts this choice back into question and solves the problem of minimizing the reconstruction distortion, which, in the most general case, is the sum of two terms: a first one due to the non-PR property of the FB and the other being due to signal quantization in the subbands. The resulting filter banks are called minimum mean square error (MMSE) filter banks. Several quantization noise models are considered. First, under the classical white noise assumption, the optimal positive bit rate allocation in any filter bank (possibly nonorthogonal) is expressed analytically, and an efficient optimization method of the MMSE filter banks is derived. Then, it is shown that while in a PR FB, the improvement brought by an accurate noise model over the classical white noise one is noticeable, it is not the case for the MMSE FB. The optimization of the synthesis filters is also performed for two measures of the bit rate: the classical one, which is defined for uniform scalar quantization, and the order-one entropy measure. Finally, the comparison of rate-distortion curves (where the distortion is minimized for a given bit rate budget) enables us to quantify the SNR improvement brought by MMSE solutions.