PERFECT RECONSTRUCTION VERSUS MMSE FILTER BANKS IN-SOURCE CODING

Classically, the filter banks (FB's) used in source coding schemes hav e been chosen to possess the perfect reconstruction (PR) property or t o be maximally selective quadrature mirror filters (QMF's), This paper puts this choice back into question and solves the problem of minimiz ing 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 F B and the other being due to signal quantization in the subbands. The resulting filter banks are called minimum mean square error (MMSE) fil ter banks. In this paper, several quantization noise models are consid ered. First, under the classical white noise assumption, the optimal p ositive bit rate allocation in any filter bank (possibly nonorthogonal ) is expressed analytically, and an efficient optimization method of t he 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 classi cal white noise one is noticeable, it is not the case for MMSE FB, The optimization of the synthesis filters is also performed for two measu res of the bit rate: the classical one, which is defined for uniform s calar quantization, and the order-one entropy measure. Finally, the co mparison of rate-distortion curves (where the distortion is minimized for a given bit rate budget) enables us to quantify the SNR improvemen t brought by MMSE solutions.