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Multidimensional incremental parsing for universal source coding.

Soo Hyun Bae¹, Biing-Hwang Juang

¹Center for Signal and Image Processing, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250, USA. soohyun@ece.gatech.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|September 12, 2008

Summary

A new multidimensional incremental parsing algorithm (MDIP) generalizes Lempel-Ziv coding for discrete sources. It offers efficient image compression, with a local minimax distortion method providing superior perceptual fidelity.

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Area of Science:

Computer Science
Information Theory
Data Compression

Background:

The Lempel-Ziv (LZ) coding algorithm is a foundational method for lossless data compression.
Generalizing LZ-based approaches to multidimensional discrete sources presents challenges in data representation and transmission.
Existing methods may struggle with capturing complex structures in multidimensional data.

Purpose of the Study:

To investigate a multidimensional incremental parsing algorithm (MDIP) as a generalization of Lempel-Ziv coding.
To develop and evaluate novel distortion functions for universal lossy source coders.
To explore the application of MDIP in image compression, assessing both lossless and lossy scenarios.

Main Methods:

The study introduces a multidimensional incremental parsing algorithm (MDIP) comprising maximum decimation matching, hierarchical source coding, and dictionary augmentation.
Two classes of maximum decimation matching are analyzed as counterparts to LZ's longest match search.
Two distortion functions, local average distortion and local minimax distortion, are proposed for lossy source coding.

Main Results:

A lossless image compression algorithm based on MDIP demonstrated efficiency in capturing source structure, though not outperforming Lempel-Ziv-Welch.
Lossy compression algorithms using MDIP were implemented; the local average distortion method minimized signal distortion.
The local minimax distortion-based algorithm yielded images with superior perceptual fidelity compared to other compression methods.

Conclusions:

The MDIP framework offers a viable approach for multidimensional discrete source coding.
The local minimax distortion function is effective for achieving perceptually high-quality lossy compression.
Further research into feature extraction for multidimensional sources is inspired by these findings.