On the quantization efficiency of independent and uncorrelated random variables

The quantization efficiency of independent and uncorrelated random variables is evaluated. The uncorrelated and independent random variables are generated by Karhunen-Loeve (K-L) transform of the natural scene image and the encrypted image, respectively. As for the encrypted image samples, they are defined as the weighted sum of the natural scene image samples. After transform, optimal scalar and vector quantization is then performed on these transform coefficients. Simulation results show that the performance of scalar quantization of the independent random variables increases compared with that for the uncorrelated ones. Since the encrypted image can be easily generated by fast Fourier transform, the desirability of using vector quantization decreases. Because vector quantization is much more difficult to implement compared with scalar quantization, the performance improvement of scalar quantization by encryption is a feasible solution