Some results on two-dimensional pseudoquadrature mirror filters

One-dimensional (1-D) pseudoquadrature mirror filters (PQMF's) have been introduced as a generalization of quadrature mirror, filter (QMF) concepts. Use of such filters allows one to split directly the spectrum of an input signal into <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> equally spaced subbands which can be decimated by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N: 1</tex> , then interpolated and recombined to reproduce the original signal. In this paper, a detailed derivation of conditions specifying 2-D PQMF design constraints for a distortion-free (i.e., aliasing and amplitude distortions) reconstruction of the original signal are obtained. Potential applications for such filters include efficient subband coding of digital pictures.