Optimal variable-rate mean-gain-shape vector quantization for image coding

A method for rate-distortion optimal variable rate mean-gain-shape vector quantization (MGSVQ) is presented with application to image compression. Conditions are derived within an entropy-constrained product code framework that result in an optimal bit allocation between mean, gain, and shape vectors at all rates. An extension to MGSVQ called hierarchical mean-gain-shape vector quantization (HMGSVQ) is similarly introduced. By considering the statistical dependence between adjacent means, this method is able to provide an improvement in the rate-distortion performance over traditional MGSVQ, especially at low bit rates. Simulation results are provided to demonstrate the rate-distortion performance of MGSVQ and HMGSVQ for image data.