Lifting Biorthogonal B-spline Wavelets

Abstract

Multiresolution data representations provide an indispensable tool for the compression, progressive transmission, and visualization of scientific data. Wavelet transforms based on B-spline scaling functions are frequently used to obtain continuous surface- and volume representations at multiple levels of resolution. Starting with a fine-resolution data set, wavelet decomposition provides a sequence of coarser approximations based on B-spline scaling functions and a set of wavelet coefficients containing the geometric differences with respect to the finer levels. The inverse transform can be used to reconstruct the finer levels of resolution from these wavelet coefficients within linear computation time. Biorthogonal wavelet transforms facilitate local computation of decomposition and reconstruction. We survey the most relevant results regarding wavelets and present different biorthogonal wavelet constructions based on highly efficient and simple-to-use lifting operations. Our approaches are suitable for lossy and lossless compression of large-scale data sets.