Frame representations, which correspond to overcomplete generalizations to basis expansions, are often used in signal processing to provide robustness to errors. In this thesis robustness is provided through the use of projections to compensate for errors in the representation coefficients, with specific focus on quantization and erasure errors. The projections are implemented by modifying the ...

We consider optimal scalar quantization with rth power distortion and constrained Rényi entropy of order α. For sources with absolutely continuous distributions the high rate asymptotics of the quantizer distortion has long been known for α = 0 (fixed-rate quantization) and α = 1 (entropyconstrained quantization). These results have recently been extended to quantization with Rényi entropy cons...

This paper studies quantization error in the context of Matching Pursuit coded streams. The quantization noise is shown to depend on error on both coefficients and indexes. It is moreover influenced by the redundancy of the Matching Pursuit dictionary. A novel general formulation of the structural redundancy in overcomplete decompositions is shown to enhance the accuracy of classical redundancy...

We propose a polynomial-time algorithm for optimal scalar quantizer design on discrete-alphabet sources. Special cases of the proposed approach yield optimal design algorithms for fixed-rate and entropy-constrained scalar quantizers, multi-resolution scalar quantizers, multiple description scalar quantizers, and Wyner-Ziv scalar quantizers. The algorithm guarantees globally optimal solutions fo...

Abst rac t Experimental results of the quantization of Linear Predictive Coded (LPC) coefficients using two general approaches, scalar coefficient quantization and vector quantization, are presented. The LPC coefficients were quantized in several domains: Line Spectral Frequency (LSF), cepstral, predictor, reflection and autocorrelation. Two distortion measures were used to evaluate the quantiz...

Divergences that arise in the quantization of scalar quantum field models by means of a lattice-space functional integration may be attributed to a single integration variable, and this fact is demonstrated by showing that if the integrand for that single integration variable is appropriately changed, then a perturbation expansion becomes orderby-order finite and divergence free. The paper conc...

We investigate stochastic quantization as a method to go from a classical PDE (with stochastic time λ) to a corresponding quantum theory in the limit λ→∞. We test the method for a linear PDE satisfied by the free scalar field. We begin by giving some background about the importance of establishing the property of reflection positivity for the limit λ → ∞. We then prove that the measure determin...

We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized by H(S,R). The fuzzy sphere is included as a special case parametrized by the integer two-cohomology class H(S,Z), which has finite number of degrees of fre...