Entropy-constrained scalar quantization and minimum entropy with error bound by discrete wavelet transforms in image compression

The global maximum of an entropy function with different decision levels fo r a three-level scaler quantizer performed after a discrete wavelet transfo rm was derived. Herein, we considered the case of entropy-constrained scala r quantization capable of avoiding many compression ratio reductions as the mean squared error was minimized. We also dealt with the problem of minimu m entropy with an error bound, which was referred to as the rate distortion function, For generalized Gaussian distributed input signals, the Shannon bound would decrease monotonically when the parameter of distribution gamma was to leave from 2. That is, the Gaussian distributions would contain the highest Shannon bound among the generalized Gaussian distributions. Additi onally, we proposed two numerical approaches of the secant and false positi on methods implemented in real cases to solve the problems of entropy-const rained scalar quantization and minimum entropy with an error bound, The con vergence condition of the secant method was also addressed.