Lazar Velimirovic

Multi-criteria Influence Diagrams – A Tool for the Sequential Group Risk Assessment

This chapter describes the use of influence diagrams in the risk assessment and proposes their extension to the group decision making using fuzzy logic, sequential approach and multi-criteria evaluation. Instead of classical Bayesian networks using conditional probability tables that are often difficult or impossible to obtain, a verbal expression of probabilistic uncertainty, represented by fuzzy sets is used in this approach. Influence diagrams are modeling the multistage decision processes and the interrelations among different chance and value nodes as well, enabling the iterative approach to the risk assessment. After the first, independent assessment of the group of experts, this preliminary risk grade is the input in the second step where the adapted risk grade has been adopted based on known evaluations, and interaction among decision makers. The different risk components and decision maker’s attitudes are considered by ordered weighted averages (OWA) operators. This inference engine is illustrated through the assessment of risk caused by improper drug storage in pharmaceutical cold chain by the group of experts in the iterative assessment process.

Design of piecewise uniform scalar quantizer for the backward adaptive algorithm

This paper proposes a novel piecewise uniform scalar quantizer model built on the bases of the Jayants quantizer model. The novel model utilizes the Jayants manner of maximum amplitude adaptation, which means according to the one word memory and with the use of the backward adaptive technique. Particularly, the proposed model is equal to the Jayants quantizer model when the step size multiplier, introduced by the novel model, has the unit value. Therefore, we actually propose more general model of a quantizer that, as we will demonstrate, provides overreaching of the Jayants average signal to quantization noise ratio for about 9 dB.

Analysis of switched quantizer based on the quadratic spline functions

ABSTRACT In this paper, an approximation of the optimal compressor function using the quadratic spline functions with 2L = 8 segments is described. Since the quadratic spline with 2L = 8 segments provides better approximation of the optimal compression function than quadratic spline with 2L = 4 segments, capitalizing on the benefits of the obtained spline approximation, quantizer designing process is firstly performed for the so assumed number of segments and the Laplacian source of a unit variance. Then, to enhance the usability of the proposed model, the switched quantization technique is applied and a beneficial analysis is derived, providing insight in the robustness of the proposed quantizer performances with respect to the mismatch in designed for and applied to variances. Reached quality has been compared to another model from the literature, and it has been shown that the proposed model outperforms the previous model by almost 1.3 dB.

Design of compandor quantizer using spline approximations

In this paper, the approximation of the optimal compressor function using spline functions of the first and second degree is done. Coefficients on which we form approximative spline functions are determined in two ways: by solving equation systems that are formed from treshold condition and by minimization mean square error (MSE). On the basis of the obtained approximate spline functions, a quantizer designing is done. In order to reduce realization complexity of the designed model, in this paper it is proposed that the optimal compressor function in different segments is approximated by different spline functions. Also, the optimization of quantizers segment threshold is done. For the quantizer designed on the basis of approximative spline functions, segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). It is shown that by quantizer models proposed in this paper the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved.

Approximation of the optimal compressor function combining different spline functions in segments

In this paper the companding quantizer design using the approximative spline functions of the first and the second degree is done. The spline function of the first degree and the second degree is used for the approximation of the optimal compressor function. In order to reduce realization complexity of the designed model, in this paper it is proposed that the optimal compressor function in different segments is approximated by different spline functions, which means that the approximation of the optimal compressor function is done by combining the spline function of the first degree and the second degree. Comprehensive analysis of the results obtained for the proposed companding quantizer for the number of segments 2L = 4 i 2L = 8 is done.

Numerical Determination of the Optimal Value of Quantizer’s Segment Threshold Using Quadratic Spline Functions

In this paper, an approximation of the optimal compressor function using the quadratic spline functions has been presented. The coefficients of the quadratic spline functions are determined by minimizing the mean-square error (MSE). Based on the obtained approximative quadratic spline functions, the design for companding quantizer for Gaussian source is done. The support region of proposed companding quantizer is divided on segments of unequal size, where the optimal value of segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). It is shown that by the companding quantizer proposed in this paper, the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved.

Asymmetrical Two-Level Scalar Quantizer with Extended Huffman Coding for Compression of Laplacian Source

This paper proposes a novel model of the two-level scalar quantizer with extended Huffman coding. It is designed for the average bit rate to approach the source entropy as close as possible provided that the signal to quantization noise ratio (SQNR) value does not decrease more than 1 dB from the optimal SQNR value. Assuming the asymmetry of representation levels for the symmetric Laplacian probability density function, the unequal probabilities of representation levels are obtained, i.e. the proper basis for further implementation of lossless compression techniques is provided. In this paper, we are concerned with extended Huffman coding technique that provides the shortest length of codewords for blocks of two or more symbols. For the proposed quantizer with extended Huffman coding the convergence of the average bit rate to the source entropy is examined in the case of two to five symbol blocks. It is shown that the higher SQNR is achieved by the proposed asymmetrical quantizer with extended Huffman coding when compared with the symmetrical quantizers with extended Huffman coding having equal average bit rates.

Design of quantizer for Laplacian source based on the probability density function approximation

In this paper, piecewise linear approximation of the probability density function is done. On the basis of the obtained approximated probability density function, a companding quantizer is designed. The signal at the entrance of the companding quantizer is modeled by Laplacian probability density function. Performances of the proposed companding quantizer are estimated on the basis of comparison of calculated values of signal to quantization noise ratio and approximation error, with the calculated values that correspond to the model of piecewise uniform scalar quantizer, that is also proposed in this paper.