Rate-Distortion-Optimal Subband Coding Without
Perfect-Reconstruction Constraints

by M. K. Mihcak, P. Moulin, M. Anitescu and K. Ramchandran


We investigate the design of subband coders without the traditional
perfect-reconstruction constraint on the filters. The coder uses scalar
quantizers, and its filters and bit allocation are designed so as to
optimize a rate-distortion criterion.
Using convexity analysis, we show that optimality can be achieved
using filter banks that are the cascade of a (paraunitary) principal component
filter bank for the input spectral process and a set of pre-- and
post--filters surrounding each quantizer.  Analytical expressions
for the pre-- and postfilters are then derived. An algorithm for computing
the globally optimal filters and bit allocation is given.
We also develop closed-form solutions for the special case of
two-channel coders under an exponential rate--distortion model.
Finally, we investigate a constrained-length version of the filter
design problem, which is applicable to practical coding scenarios.
While the optimal filter banks are nearly perfect-reconstruction
at high rates, we demonstrate an apparently surprising advantage
of optimal FIR filter banks: they significantly outperform
optimal perfect-reconstruction FIR filter banks at all bit rates.