Efficient 1D and 2D Daubechies Wavelet Transforms with Application to Signal Processing

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Abstract

In this paper we have introduced new, efficient algorithms for computing one- and two-dimensional Daubechies wavelet transforms of any order, with application to signal processing. These algorithms has been constructed by transforming Daubechies wavelet filters into weighted sum of trivial filters. The theoretical computational complexity of the algorithms has been evaluated and compared to pyramidal and ladder ones. In order to prove the correctness of the theoretical estimation of computational complexity of the algorithms, sample implementations has been supplied. We have proved that the algorithms introduced here are the most robust of all class of Daubechies transforms in terms of computational complexity, especially in two dimensional case.