Correlation Model for Uniform Scalar Quantizers with Arbitrary Representation Levels

This article derives closed-form expressions for correlation values of quantization errors in a set of uniform quantizers with arbitrary representation levels, operating on a vector of Gaussian stochastic variables. The problem is relevant to subband coding of random vectors using linear filter hunks, a technique that may be useful fur lossy compression of micro-array images. The results obtained here generalize previous results in which the representation levels are constrained to be midpoints of uniform quantization intervals. In particular, a set of expressions for auto-and cross-correlation values of the quantization error vector are derived. Monte-Carlo simulations are used to verify the validity of the given expressions, which indicate a very good match between numerical results and the values predicted by the derived expressions.