### Abstract

Image compression systems commonly operate by transforming the input signal into a new representation whose elements are independently quantized. The success of such a system depends on two properties of the representation. First, the coding rate is minimized only if the elements of the representation are statistically independent. Second, the perceived coding distortion is minimized only if the errors in a reconstructed image arising from quantization of the different elements of the representation are perceptually independent. We argue that linear transforms cannot achieve either of these goals and propose, instead, an adaptive nonlinear image representation in which each coefficient of a linear transform is divided by a weighted sum of coefficient amplitudes in a generalized neighborhood. We then show that the divisive operation greatly reduces both the statistical and the perceptual redundancy amongst representation elements. We develop an efficient method of inverting this transformation, and we demonstrate through simulations that the dual reduction in dependency can greatly improve the visual quality of compressed images.

Original language | English (US) |
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Pages (from-to) | 68-80 |

Number of pages | 13 |

Journal | IEEE Transactions on Image Processing |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2006 |

### Keywords

- Independent components
- JPEG
- Nonlinear response
- Perceptual independence
- Perceptual metric
- Scalar quantization
- Statistical independence
- Transform coding

### ASJC Scopus subject areas

- Software
- Computer Graphics and Computer-Aided Design

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## Cite this

*IEEE Transactions on Image Processing*,

*15*(1), 68-80. https://doi.org/10.1109/TIP.2005.860325