We determine the asymptotically optimal compressor function for a multidimen-sional compander when the source is memoryless. Under certain technical assumptions on the compressor function, it is shown that the best k-dimensional compressor function consists of the best scalar compressor functions for each component of the source vector. The mean-squared error of optimal multidimensional compand...

The generalized Fényes–Nelson model of quantum mechanics is applied to the free scalar field. The resulting Markov field is equivalent to the Euclidean Markov field with the times scaled by a common factor which depends on the diffusion parameter. This result is consistent between Guerra’s earlier work on stochastic quantization of scalar fields. It suggests a deep connection between Euclidean ...

High-rate (or asymptotic) quantization theory has found formulas for the average squared length (more generally, the q-th moment of the length) of the error produced by various scalar and vector quantizers with many quantization points. In contrast, this paper finds an asymptotic formula for the probability density of the length of the error and, in certain special cases, for the probability de...

Transform coding consists of a scalar quantization of the features of an image representation. These features should be independent enough to justify the scalar approach. The coefficients of the commonly used DCT representation still show some dependence that may reduce its efficiency. In this work, a perceptually inspired non-linear transform is used to map the DCT into a new representation th...

The goal of this paper is finding an asymptotic equation which determines the amplitude range of asymptotically optimal scalar quantizers for Laplacian input signals with an unrestricted amplitude range. It is very important to show how the amplitude range depends on the number of quantization levels. The approximation method for determining the amplitude range is suggested. This method can be ...

In his famous paper [7] Gersho stressed that the codecells of optimal quantizers asymptotically make an equal contribution to the distortion of the quantizer. Motivated by this fact, we investigate in this paper quantizers in the scalar case, where each codecell contributes with exactly the same portion to the quantization error. We show that such quantizers of Gersho type or Gersho quantizers ...