The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-IPI-600

“Optimum Restoration of Quantized Correlated Signals”

by Michael N. Huhns

August 1975

An analysis of the optimum statistical restoration of quantized signals is presented. The restoration is based upon minimizing the mean square error between the input to a quantizer and its estimate. Since a quantizer is a nonlinear device, the estimation equation which is derived achieves an optimum nonlinear restoration. Its solution requires complete statistical information usually includes the marginal distribution of each of the input variables and the correlation between them. Hence a technique is developed for generating correlated multidimensional probability density functions based on this available information. The technique is applied to Gaussian, laplacian, and Rayleigh density functions. These multidimensional density functions characterize the outputs of transform coders, DPCM coders, and PCM coders, respectively. The quantized outputs of these coders are then restored by utilizing the multidimensional densities in the estimation equation. Examples of images which have been coded and restored by these techniques are presented. The results reveal a mean square error reduction. To achieve a visually subjective improvement also, a weighted mean square error criterion is employed, where the weighting corresponds to characteristics of the human visual system.

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