Low-Cost Lifting Architecture and Lossless Implementation of Daubechies-8 Wavelets

This paper presents three lifting structures of Daubechies-8 (also known as D8) wavelet transform using efficient factorization of the polyphase matrix. All new filter coefficients are optimally mapped with integers resulting in low cost hardware implementation. We first derive the polyphase matrices using a factorization algorithm, which forms the basis of multiple lifting structures of D8. A theoretical framework is then derived and proven experimentally to eliminate the scaling stage of the algorithm that incurs computation error in conventional integer-based wavelets. This elimination of the scaling stage makes the proposed architecture lossless. Also due to the optimum integer mapping, the 8-bit implementation of our schemes produces very similar results than that of the classical double-precision D8 filter. Finally, we compare our results with other existing lifting wavelets to demonstrate the advantage in terms of lower cost, losslessness and improved performance.