Optimally smooth symmetric quadrature mirror lters for image coding

Symmetric quadrature mirror lters (QMF's) ooer several advantages for wavelet-based image coding. Symmetry and odd-length contribute to eecient boundary handling and preservation of edge detail. Symmetric QMF's can be obtained by mildly relaxing the lter bank orthogonality conditions. We describe a computational algorithm for these lter banks which is also symmetric in the sense that the analysis and synthesis operations have identical implementations, up to a delay. The essence of a wavelet transform is its multiresolution decomposition , obtained by iterating the lowpass lter. This allows one to introduce a new design criterion, smoothness (good behavior) of the lowpass lter under iteration. This design constraint can be expressed solely in terms of the lowpass lter tap values (via the eigenvalue decomposition of a certain nite-dimensional matrix). Our innovation is to design near-orthogonal QMF's with linear-phase symmetry which are optimized for smoothness under iteration, not for stopband rejection. The new class of optimally smooth QMF lter banks yields high performance in a practical image compression system.