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

摘要

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.