### Abstract

We propose a new transform coding algorithm that integrates all optimization steps into a coherent and consistent framework. Each iteration of the algorithm is designed to minimize coding distortion as a function of both the transform and quantizer designs. Our algorithm is a constrained version of the LBG algorithm for vector quantizer design. The reproduction vectors are constrained to lie at the vertices of a rectangular grid. A significant result of our approach is a new transform basis specifically designed to minimize mean-squared quantization distortion for both fixed-rate and entropy-constrained coding. For Gaussian distributed data, this transform reduces to the Karhunen-Loeve transform (KLT). However, in general the coding optimal transform (COT) differs from the KLT enough to provide up to 1 dB improvement in compressed signal-to-noise ratio (SNR) on images. We describe a practical algorithm that finds the COT for a given signal. In addition, we present image compression results demonstrating the SNR improvement achieved with our algorithm relative to KLT based transform coding.

Original language | English (US) |
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Title of host publication | Data Compression Conference Proceedings |

Editors | J.A. Storer, M. Cohn |

Pages | 381-390 |

Number of pages | 10 |

State | Published - 2001 |

Event | Data Compression Conference - Snowbird, UT, United States Duration: Mar 27 2001 → Mar 29 2001 |

### Other

Other | Data Compression Conference |
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Country | United States |

City | Snowbird, UT |

Period | 3/27/01 → 3/29/01 |

### Fingerprint

### ASJC Scopus subject areas

- Hardware and Architecture
- Electrical and Electronic Engineering

### Cite this

*Data Compression Conference Proceedings*(pp. 381-390)

**The coding-optimal transform.** / Archer, C.; Leen, T. K.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Data Compression Conference Proceedings.*pp. 381-390, Data Compression Conference, Snowbird, UT, United States, 3/27/01.

}

TY - GEN

T1 - The coding-optimal transform

AU - Archer, C.

AU - Leen, T. K.

PY - 2001

Y1 - 2001

N2 - We propose a new transform coding algorithm that integrates all optimization steps into a coherent and consistent framework. Each iteration of the algorithm is designed to minimize coding distortion as a function of both the transform and quantizer designs. Our algorithm is a constrained version of the LBG algorithm for vector quantizer design. The reproduction vectors are constrained to lie at the vertices of a rectangular grid. A significant result of our approach is a new transform basis specifically designed to minimize mean-squared quantization distortion for both fixed-rate and entropy-constrained coding. For Gaussian distributed data, this transform reduces to the Karhunen-Loeve transform (KLT). However, in general the coding optimal transform (COT) differs from the KLT enough to provide up to 1 dB improvement in compressed signal-to-noise ratio (SNR) on images. We describe a practical algorithm that finds the COT for a given signal. In addition, we present image compression results demonstrating the SNR improvement achieved with our algorithm relative to KLT based transform coding.

AB - We propose a new transform coding algorithm that integrates all optimization steps into a coherent and consistent framework. Each iteration of the algorithm is designed to minimize coding distortion as a function of both the transform and quantizer designs. Our algorithm is a constrained version of the LBG algorithm for vector quantizer design. The reproduction vectors are constrained to lie at the vertices of a rectangular grid. A significant result of our approach is a new transform basis specifically designed to minimize mean-squared quantization distortion for both fixed-rate and entropy-constrained coding. For Gaussian distributed data, this transform reduces to the Karhunen-Loeve transform (KLT). However, in general the coding optimal transform (COT) differs from the KLT enough to provide up to 1 dB improvement in compressed signal-to-noise ratio (SNR) on images. We describe a practical algorithm that finds the COT for a given signal. In addition, we present image compression results demonstrating the SNR improvement achieved with our algorithm relative to KLT based transform coding.

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M3 - Conference contribution

SP - 381

EP - 390

BT - Data Compression Conference Proceedings

A2 - Storer, J.A.

A2 - Cohn, M.

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