Symmetry-Preserving Lattice Vector Quantization for Reversible Half-Sample Symmetric FIR Filter Banks

Linear phase FIR filter banks form an integral part of the ISO/IEC JPEG 2000 image coding standard. One feature they enable is lossless subband coding based on reversible filter bank implementations. While this meshes well with symmetric boundary-handling techniques for whole-sample symmetric (odd- length) linear phase filters, there are obstructions with half- sample symmetric (even-length) filters, a fact that influenced the JPEG 2000 standard. We show how these obstructions can be overcome for a class of half-sample symmetric filter banks by employing lattice vector quantization to ensure symmetry- preserving rounding in reversible implementations.