## Wavelet Transforms That Map Integers to Integers

Publication
, Journal Article

Calderbank, AR; Daubechies, I; Sweldens, W; Yeo, BL

Published in: Applied and Computational Harmonic Analysis

January 1, 1998

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 socalled 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. © 1998 Academic Press.

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## Published In

Applied and Computational Harmonic Analysis

## DOI

## ISSN

1063-5203

## Publication Date

January 1, 1998

## Volume

5

## Issue

3

## Start / End Page

332 / 369

## Related Subject Headings

- Numerical & Computational Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

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MLA

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Calderbank, A. R., Daubechies, I., Sweldens, W., & Yeo, B. L. (1998). Wavelet Transforms That Map Integers to Integers.

*Applied and Computational Harmonic Analysis*,*5*(3), 332–369. https://doi.org/10.1006/acha.1997.0238Calderbank, A. R., I. Daubechies, W. Sweldens, and B. L. Yeo. “Wavelet Transforms That Map Integers to Integers.”

*Applied and Computational Harmonic Analysis*5, no. 3 (January 1, 1998): 332–69. https://doi.org/10.1006/acha.1997.0238.Calderbank AR, Daubechies I, Sweldens W, Yeo BL. Wavelet Transforms That Map Integers to Integers. Applied and Computational Harmonic Analysis. 1998 Jan 1;5(3):332–69.

Calderbank, A. R., et al. “Wavelet Transforms That Map Integers to Integers.”

*Applied and Computational Harmonic Analysis*, vol. 5, no. 3, Jan. 1998, pp. 332–69.*Scopus*, doi:10.1006/acha.1997.0238.Calderbank AR, Daubechies I, Sweldens W, Yeo BL. Wavelet Transforms That Map Integers to Integers. Applied and Computational Harmonic Analysis. 1998 Jan 1;5(3):332–369.

## Published In

Applied and Computational Harmonic Analysis

## DOI

## ISSN

1063-5203

## Publication Date

January 1, 1998

## Volume

5

## Issue

3

## Start / End Page

332 / 369

## Related Subject Headings

- Numerical & Computational Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics