Parametric deslauriers-dubuc interpolating wavelets: Construction and performance analysis for image coding

This paper mainly focuses on how to construct new parametric Deslauriers-Dubuc (D-D) biorthogonal in- terpolating wavelets which have arbitrary vanishing moments, symmetry, and depend on one free parameter via lifting scheme. We first derive their existence conditions necessary for the wavelets with the polyphase matrix theory. Then, we demonstrate the detailed algorithm for constructing their associated wavelet filter bank and interpolating wavelet trans- forms. With the algorithm, four classes of parametric D-D wavelets with vanishing moment pairs of (4, 2), (4, 4), (6, 2) and (6, 4), respectively are constructed. Finally, according to the coding gain criterion, we design four new interpolating wavelets for image coding by adjusting the free parameter; they all have dyadic-fraction filter coefficients and can realize a multiplication-free DWT. Extensive simulations show that the two interpolating wavelets exhibit performances superior to the CDF-9/7 wavelet, especially with a gain of up to 0.44 dB in PSNR over the latter for rich-textured image and a lower computational cost by 17%. In addition, significant improvement in subjectively visual quality is also observed.