Lossless integer wavelet transform

TLDR

Wavelet transformation of integer input data enables signal compression, but conventional quantization is lossy, making the overall compression/decompression scheme lossy. The authors define a critical wavelet coefficient quantization that is the coarsest level permitting perfect reconstruction. They demonstrate this quantization for the Haar transform and for arbitrarily smooth wavelet transforms derived from it. The resulting integer wavelet transform supports multiresolution subband compression schemes that allow gradual refinement of decompressed data while preserving the option for perfect reconstruction.

Abstract

Signal compression can be obtained by wavelet transformation of integer input data followed by quantification and coding. As the quantification is usually lossy, the whole compression/decompression scheme is lossy too. We define a critical wavelet coefficient quantification, i.e., the coarsest quantification that allows perfect reconstruction. This is demonstrated for the Haar transform and for arbitrarily smooth wavelet transforms derived from it. The new integer wavelet transform allows implementation of multiresolution subband compression schemes, in which the decompressed data are gradually refined, retaining the option of perfect reconstruction.