Fast approximations of the orthogonal dual-tree wavelet bases

Recently, there has been a significant interest in the design of iterated filter banks in which the resulting wavelet bases form an approximate Hilbert transform pair. In this work, we propose three approximations of such dual-tree wavelet bases that satisfy Hilbert transform conditions. Our designs are derived from Selesnick´s and Kingsbury´s orthogonal wavelet filter solutions, and meet other desirable properties such as high coding gain, reduced computational complexity and sufficient regularity. The quantization is performed in the lattice domain using sum-of-power-of-two (SOPOT) coefficients. Several performance comparisons are presented. Furthermore, this paper introduces a proposition that lattice coefficients of filters that are time-reversals of each other are closely related.