Milan R. Dincic

Optimal polar image sampling

In this paper, a problem of efficient image sampling (deployment of image sensors) is considered. This problem is solved using techniques of two-dimensional quantization in polar coordinates, taking into account human visual system (HVS) and eye sensitivity function. The optimal radial compression function for polar quantization is derived. Optimization of the number of the phase levels for each amplitude level is done. Using optimal radial compression function and optimal number of phase levels for each amplitude level, optimal polar quantization is defined. Using deployment of quantization cells for the optimal polar quantization, deployment of image sensors is done, and therefore optimal polar image sampling is obtained. It is shown that our solution (the optimal polar sampling) has many advantages compared to presently used solutions, based on the log-polar sampling. The optimal polar sampling gives higher SNR (signal-to-noise ratio), compared to the log-polar sampling, for the same number of sensors. Also, the optimal polar sampling needs smaller number of sensors, to achieve the same SNR, compared to the log-polar sampling. Furthermore, with the optimal polar sampling, points in the image middle can be sampled, which is not valid for the log-polar sampling. This is very important since human eye is the most sensitive to these points, and therefore the optimal polar sampling gives better subjective quality.

The general design of asymptotic unrestricted polar quantizers with square cells

The aim of this paper is the presentation of the designing of asymptotic unrestricted polar quantizers with square cells, since it is known that square cells give minimal moment of inertia, which leads to minimization of distortion. Until now, polar quantizers with square cells have been designed only for the optimal companding function and their performances have been analyzed only for the stationary variance. In this paper, the design is done in a general manner, i.e. it is valid for any companding function and performances are analyzed in the wide range of variances. After that, this general design is applied for the logarithmic @m-law companding function. It is important that expressions for the numbers of magnitude and phase levels are obtained in the closed form, which simplifies the design. It is shown that the proposed polar quantizer has better performances (more than 3 dB higher the maximal and the average SQNR (signal-to-quantization noise ratio)) than the corresponding scalar quantizer with @m-law. Simulation is performed, and it is shown that theoretical and simulation results are matched very well. It is shown that the proposed polar quantizer can be used both for stationary and non-stationary signals, choosing the appropriate value of @m. This quantizer can be widely used, for all signals with Gaussian distribution.

Asymptotic analysis and design of restricted uniform polar quantizer for Gaussian sources

In this paper, an asymptotically optimal restricted uniform polar quantizer (RUPQ) is designed for a Gaussian source subject to the mean-squared error (MSE) criterion. The asymptotic analysis of the RUPQ, provided in the paper, for the first time includes the overload distortion. This enables derivation of the closed-form formulas for the straightforward design of the asymptotically optimal RUPQ. In particular, the closed-form formulas are derived for the asymptotically optimal support limit of the magnitude quantizer and asymptotically optimal rate allocation between the magnitude and phase quantizers. Moreover, our analysis shows that the overload distortion of the asymptotically optimal RUPQ cannot be neglected for rates R ? 5.5 ? bit/sample in cases when the relative error in calculating signal to quantization noise ratio (SQNR) due to overload distortion neglecting ranges up to 1%. Further, it is shown that the closed-form SQNR formula derived for the asymptotically optimal RUPQ, useful for performance assessment, is reasonably accurate for rates R 3.5 ? bit/sample . Results obtained analytically and verified through simulations show that the proposed RUPQ outperforms existing RUPQs in terms of SQNR. The performances near the optimum along with the simple design of the proposed RUPQ model provide its application in various systems such as cellular systems and ultrasound medical systems, in digital spectrum analyzer and in digital processing of orthogonal frequency division multiplexing (OFDM) modulated signals.

Design of a Hybrid Quantizer with Variable Length Code

In this paper a new model for compression of Laplacian source is given. This model consists of hybrid quantizer whose output levels are coded with Golomb-Rice code. Hybrid quantizer is combination of uniform and nonuniform quantizer, and it can be considered as generalized quantizer, whose special cases are uniform and nonuniformquantizers. We propose new generalized optimal compression function for companding quantizers. Hybrid quantizer has better performances (smaller bit-rate and complexity for the same quality) than both uniform and nonuniformquantizers, because it joins their good characteristics. Also, hybrid quantizer allows great flexibility, because there are many combinations of number of levels in uniform part and in nonuniformpart, which give similar quality. Each of these combinations has different bit-rate and complexity, so we have freedom to choose combination which is the most appropriate for our application, in regard to quality, bit-rate and complexity. We do not have such freedom of choice when we use uniform or nonuniform quantizers. Until now, it has been thought that uniform quantizer is the most appropriate to use with lossless code, but in this paper we show that combination of hybrid quantizer and lossless code gives better performances. As lossless code we use Golomb-Rice code because it is especially suitable for Laplacian source since it gives average bit-rate very close to the entropy and it is easier for implementation than Huffman code. Golomb-Rice code is used in many modern compression standards. Our model can be used for compression of all signals with Laplacian distribution.

Adaptive nonuniform polar quantization application to high quality speech compression

The logarithmic companding technique has shown to be extremely useful in speech quantization with rate of 8 bits/sample. However, for lower bit rates it is not the ideal solution for high quality speech coding. Because of that, in this paper we establish source coding scheme which enables better spectrum efficiency for input that has a large dynamic range. Since our wish is also to improve signal quality in comparison with quality defined with standards G.711 and G.712, we opt for adaptive technique application to the speech coding. Our research shows that proper design of forward gain-adaptive polar quantization can enable compression of about 1 bit/sample as well as significantly better quality than in case of using coder designed according to standard G.711. Furthermore, performances can be sustained over the whole speech dynamic range. Also, if the requisite speech quality is not supposed to be lower than G.712 standard quality, the achieved compression can be almost 1.5 bits/sample. Besides, we propose knew simple encoding rule which can additionally reduce bit rate for 0.1 bit/sample.

Optimal log-polar image sampling

In order to achieve better image compression simultaneously maintaining the high signal quality, the image sampling has become very important. Also, since the human eye sensitivity has circularly symmetric distribution, in recent years it is usual to apply log-polar image sampling. In this paper, we perform optimization of log-polar image sampling and show the significant improvement in comparison with the product log-polar sampling. Namely, for equal numbers of sensors optimal model gives higher signal-to-noise ratio (SNR) up to 2.5 dB, i.e., it is possible to decrease the number of required sensors by 45% for the same SNR. Furthermore, research shows that in optimal log-polar image sampling, the middle region of image, which is not sampled, can be made to be smaller than in the case of product sampling.

Linearization of the product polar quantizer for A/D conversion of measurement signals

In this paper, the linearization of product polar quantizers is presented. Product polar quantizers are very important in A/D (analogue-to-digital) conversion and compression of measurement signals with Gaussian distribution, as they have much better performances than scalar quantizers and can be widely used in many modern measurement systems such as telemetry, telemedicine, wireless sensor networks, distributed measurement systems and remote control systems. The key limiting factor in the realization of product polar quantizers is the fact that the companding function for the magnitude quantization is non-linear. To decrease complexity of realization of product polar quantizers, we suggest the linearization of the companding function. Two methods of linearization are proposed. Although both methods are good, we highlight the second method, which achieves high performances with a small number of linear segments, due to optimization of the last linear segment. The convergence of expressions for the distortion before and after linearization is proved. The analysis is developed in the general manner (for any companding function) and applied on a µ-law companding function. The influence of linearization on the robustness of product polar quantizers is analysed. The best solutions for the design of the linearized product polar quantizers, considering complexity and quality, are proposed. The linearization of product polar quantizers compatible with the widely used G.711 standard is performed. It is shown that linearized product polar quantizers, although much simpler, can achieve performances very close to those of the corresponding non-linearized quantizers. Theory is proved by the simulation and experiment.

Switched Quasi-Logarithmic Quantizer with Golomb–Rice Coding

This paper proposes a model of switched quasi-logarithmic quantizer for speech signal based on G.711 standard with usage of Golomb-Rice (GR) coding. In order to achieve better performances a method with switched quantizer is applied. Variance range is split into quantizers and for each of them a separate quantizer is designed, i.e. the support region is determined. Optimization of the support region and choice of the parameter μ is done in order to obtain a quantizer that obeys G.712 standard and gives minimal average bit rate. Every quantizer within the variance range has own model with a two-stage coder. Two stages are introduced with purpose to reduce the bit rate, whereby GR code plays its role as Variable Length Code (VLC). The first stage uses a GR coder for coding segments of the quantizer’s support region, whereas the second stage applies the coding method with fixed code lengths for coding cells within a segment. GR has simpler and cheaper hardware realization than other VLC codes, Huffman’s for instance, with very satisfying results regarding quality of quantized signal. DOI: http://dx.doi.org/10.5755/j01.eie.23.4.18727

A contribution to the design of fast code converters for position encoders

ABSTRACT Pseudorandom binary sequences (PRBS) are very useful in many areas of applications. Absolute position encoders based on PRBS have many advantages. However, the pseudorandom code is not directly applicable to the digital electronic systems, hence a converter from pseudorandom to natural binary code is needed. Recently, a fast pseudorandom/natural code converter based on Galois PRBS generator (much faster than previously used converter based on Fibonacci PRBS generator) was proposed. One of the main parts of the Galois code converter is an initial logic. The problem of the design of the initial logic has been solved only for some single values of resolution, but it is still not solved for any value of resolution, which significantly limits the applicability of the fast Galois code converter. This paper solves this problem presenting the solution for the design of the initial logic of the fast Galois pseudorandom/natural code converters used in the pseudorandom position encoders, in general manner, that is for any value of the resolution, allowing for a wide applicability of the fast Galois pseudorandom position encoders. Rigorous mathematical derivation of the formula for the designing of the initial logic is presented. Simulation of the proposed converter is performed in NI MultiSim software. The proposed solution, although developed for pseudorandom position encoders, can be used in many other fields where PRBS are used.

Designing quantizers for coding signals with fixed and variable codeword length

This paper presents various methods for improvements of quantizers design. Both scalar and vector quantizers are considered. Also, design of lossless codes for quantization levels coding is considered. This subject is very current, since quantizers are very important in digital telecommunication systems as a main part of analog-to-digital (A/D) converters.