Global minimum of scalar quantization errors by discrete wavelet transforms in image compression

Bing-Fei Wu*, Hung Hseng Hsu, Yi Qiang Hu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Since the histograms of the wavelet coefficients under higher frequencies have been modelled as generalized Gaussian distributed, it was the purpose of this study to apply scalar quantization followed by Discrete Wavelet Transform to image compression. The quantization error of discrete wavelet coefficients generated by scalar quantization can be globally minimized. The orthogonal principle and unbiasness property of the quantizer are sustained. It is observed that the energy of the error signal is equivalent to the difference between the input energy and output energy. Two algorithms, the secant and direct search methods, are proposed to obtain the global minimum. The convergence condition and the order of the secant method are also addressed.

Original languageEnglish
Pages (from-to)223-234
Number of pages12
JournalProceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering
Volume23
Issue number2
StatePublished - 1 Mar 1999

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