Celebratio Mathematica — Daubechies

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A. R. Calderbank, I. Daubechies, W. Sweldens, and B.-L. Yeo: “Lossless image compression using integer to integer wavelet transforms,” pp. 596–599 in 1st international conference on image processing (Santa Barbara, CA, 26–29 October 1997), vol. 1. IEEE (Piscataway, NJ), 1997. incollection

Wim Sweldens	Related
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A. R. Calderbank, I. Daubechies, W. Sweldens, and B.-L. Yeo: “Wavelet transforms that map integers to integers,” Appl. Comput. Harmon. Anal. 5 : 3 (July 1998), pp. 332–369. MR 1632537 Zbl 0941.42017 article

Invertible wavelet transforms that map integers to integers have important applications in lossless coding. In this paper we present two approaches to build integer to integer wavelet transforms. The first approach is to adapt the precoder of Laroia et al., which is used in information transmission; we combine it with expansion factors for the high and low pass band in subband filtering. The second approach builds upon the idea of factoring wavelet transforms into so-called lifting steps. This allows the construction of an integer version of every wavelet transform. Finally, we use these approaches in a lossless image coder and compare the results to those given in the literature.

Wim Sweldens	Related
A. Robert Calderbank	Related
Boon-Lock Yeo	Related