VLSI architectures of Daubechies wavelet transforms using algebraic integers

Two-Dimensional Wavelet Transforms have proven to be highly effective tools for image analysis. In this paper, we present a VLSI implementation of four- and six-coefficient Daubechies Wavelet Transforms using an algebraic integer encoding representation for the coefficients. The Daubechies filters (DAUB4 and DAUB6) provide excellent spatial and spectral locality, properties which make it useful in image compression. In our algorithm, the algebraic integer representation of the wavelet coefficients provides error-free calculations until the final reconstruction step. This also makes the VLSI architecture simple, multiplication-free and inherently parallel. Compared to other DWT algorithms found in the literature, such as embedded zero-tree, recursive or semi-recursive, linear systolic arrays and conventional fixed-point binary architectures, it has reduced hardware cost, lower power dissipation and optimized data-bus utilization. The architecture is also cascadable for computation of one- or multi-dimensional Daubechies Discrete Wavelet Transforms.