Parameterization construction of integer wavelet transforms for embedded image coding

Abstract

The Integer Wavelet Transform (IWT) has proved particularly successful in the area of embedded lossy-to-lossless image coding. One of the possible methods to realize the IWT is the lifting scheme. Here we construct a new class of IWTs parameterized simply by one free parameter, which are obtained by introducing a free variable to the lifting-based factorization of a Deslauriers–Dubuc interpolating filter. The exact one-parameter expressions for this class of IWTs are deduced and different IWTs can be easily obtained by adjusting the free parameter. In particular, several IWTs with their lifting filters all having binary coefficients are constructed. Extensive experiments show that our transforms have superior compression performance for both lossless and lossy image coding than the state-of-the-art IWTs, and yet require only comparable computational complexity. In addition, a quantization method that improves the rate-distortion performance of the IWT remarkably is also discussed.

Keywords:

• Integer Wavelet Transform (IWT)
• Lossy-to-lossless image coding
• Lifting scheme
• Compression performance
• Computational complexity

Acknowledgements

This work was supported by the National Natural Science Foundation of China under grants 60021302 and 60405004.

Notes

^†Here, the normalizing factor √2 is ignored by letting [Htilde] _e (z ²)=([Htilde](z)+[Htilde](−z))/2, [Htilde] _o (z ²)=([Htilde](z)−[Htilde](−z))/(2z ⁻¹), [Gtilde] _e (z ²)=[Gtilde](z)+[Gtilde](−z), and [Gtilde] _o (z ²)=([Gtilde](z)−[Gtilde](−z))/z ⁻¹.

^†The ‘SPIHT’ codec used here was rebuilt based on the ‘Qccpack’ software package of James E. Fowler, which can be downloaded from the website: http://qccpack.sourceforge.net.