A new approach to constructing the noncommutative scalar field theory is presented. Not only between x̂i and p̂j, we impose commutation relations between x̂is as well as p̂js, and give a new representation of x̂i, p̂js. We carry out both firstand second-quantization explicitly. The second-quantization is performed in both the operator formalism and the functional integral one. e-mail: [email protected]...

OF THE DISSERTATION Quantization Over Noisy Channels and Bit Allocation by Benjamin Farber Doctor of Philosophy in Electrical Engineering (Communication Theory and Systems) University of California, San Diego, 2005 Professor Kenneth Zeger, Chair In this dissertation we study two problems related to scalar quantization, namely quantization over a noisy channel and bit allocation. Scalar quantize...

We perform the stochastic quantization of scalar QED based on a generalization of the stochastic gauge fixing scheme and its geometric interpretation. It is shown that the stochastic quantization scheme exactly agrees with the usual path integral formulation. *) Email: [email protected]

Source coding based on Gaussian Mixture Models (GMM) has been recently proposed for LPC quantization. We address in this paper the related problem of designing efficient codebooks for Gaussian vector sources. A new technique of ellipsoidal lattice vector quantization (VQ) is described, based on 1) scalar companding optimized for Gaussian random variables and 2) rectangular lattice codebooks wit...

Wavelet image decompositions generate a tree-structured set of coeecients, providing an hierarchical data-structure for representing images. While early wavelet-based algorithms for image compression concentrated on optimal quantization of wavelet coee-cients, several recent researchers have proposed approaches which couple coeecient quantization (either scalar or vector-based) with various str...

Image and video compression has become an increasingly important and active area. Many techniques have been developed in this area. Any compression technique can be modeled as a threestage process. The jirst stage can be generally called a signal processing stage where an image or video signal is converted into a direrent domain. Usually, there is no or little loss of information in this stage....

In an effort to efficiently code the spectral envelope of speech signals for wideband speech coding based on sinusoidal models, a robust computation of discrete cepstrum coefficients and their quantization is investigated. A parameterization of the spectral envelope has been proposed which is based on discrete cepstral coefficients using regularization techniques. This paper presents an efficie...

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance b...

We present a fully constructive method for quantization of the solution X of a scalar SDE in the path space Lp[0, 1] or C[0, 1]. The construction relies on a refinement strategy, which takes into account the local regularity of X and uses Brownian motion (bridge) quantization as a building block. Our algorithm is easy to implement, its computational cost is close to the size of the quantization...

We study the potential merits of vector quantization and show that there can be an arbitrary discrepancy between the worst-case rates required for scalar and vector quantization. Specifically, we describe a random variable and a distortion measure where quantization of a single instance to within a given distortion requires an arbitrarily large number of bits in the worst case, but quantization...