Jn. Bradley et V. Faber, PERFECT RECONSTRUCTION WITH CRITICALLY SAMPLED FILTER BANKS AND LINEAR BOUNDARY-CONDITIONS, IEEE transactions on signal processing, 43(4), 1995, pp. 994-997
This work is concerned with the boundary conditions involved in proces
sing a finite discrete-time signal with a critically sampled perfect r
econstruction filter bank. It is desirable that the boundary condition
s reduce edge effects and define a transformation into a space having
the same dimensionality as the original signal, The complication that
arises is in the computation of the inverse transform: Although it is
straightforward to reconstruct the signal values that were not influen
ced by the boundary conditions, recovering those values on the boundar
ies is nontrivial. The solution of this problem is discussed for gener
al linear boundary conditions, No symmetry assumptions are made on the
boundary conditions or on the impulse responses of the analysis filte
rs, A low-rank linear transform is derived that expresses the boundary
values in terms of the transform coefficients, which in turn provides
a method for inverting the subband decomposition, The application of
the results in the case of two-channel orthonormal wavelet filters is
discussed, and the effects of the filter support on the conditioning o
f the inverse problem are investigated.