Aleksandra Ž. Jovanović

Low Complex Forward Adaptive Loss Compression Algorithm and Its Application in Speech Coding

Low Complex Forward Adaptive Loss Compression Algorithm and Its Application in Speech Coding This paper proposes a low complex forward adaptive loss compression algorithm that works on the frame by frame basis. Particularly, the algorithm we propose performs frame by frame analysis of the input speech signal, estimates and quantizes the gain within the frames in order to enable the quantization by the forward adaptive piecewise linear optimal compandor. In comparison to the solution designed according to the G.711 standard, our algorithm provides not only higher level of the average signal to quantization noise ratio, but also performs a reduction of the PCM bit rate for about 1 bits/sample. Moreover, the algorithm we propose completely satisfies the G.712 standard, since it provides overreaching the curve defined by the G.712 standard in the whole of variance range. Accordingly, we can reasonably believe that our algorithm will find its practical implementation in the high quality coding of signals, represented with less than 8 bits/sample, which as well as speech signals follow Laplacian distribution and have the time varying variances.

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.

Geometric piecewise uniform lattice vector quantization of the memoryless Gaussian source

The aim of this paper is to find a quantization technique that has low implementation complexity and asymptotic performance arbitrarily close to the optimum. More specifically, it is of interest to develop a new vector quantizer design procedure for a memoryless Gaussian source that yields vector quantizers with excellent performance and the structure required for fast quantization. To achieve this, we combined a fast lattice-encoding algorithm with a geometric approach to generate a model of a geometric piecewise-uniform lattice vector quantizer. Expressions for granular distortion and the optimal number of outputs points in each region were derived. Both exact and approximative asymptotic analyses were carried out. During this process, the constant probability density function of the input signal vector was kept inside the whole region. The analysis demonstrated the existence of piecewise-constant approximations to the input-vector probability density function, which is optimal for the proposed geometric piecewise-uniform vector quantizer. The considered quantization technique is near optimal for a memoryless Gaussian source. In other words, this paper proposes a method for a near-optimum, low-complex vector quantizer design based on probability density function discretization. The presented methodology gives a signal-to-quantization noise ratio that in some cases differs from the optimum by 0.1dB or less. Improvements of the considered model in performance and complexity over some of the existing techniques are also demonstrated.

Switched nonuniform polar quantization of sources with a wide dynamic range of power

In this paper, the switched nonuniform polar quantization is asymptotically analyzed for the case when the power of an input signal varies in a wide range. We observed two compression functions: logarithmic and optimum. For the suggested quantizer model we optimized the granular distortion in order to obtain the manner of the total distribution of points, i.e., we evaluated the expressions for the amplitude-level number and the phase-level number for on one amplitude level. In addition, we found the expression for granular distortion, which we used to estimate the suggested model. We compared the numerically obtained results with the G711 and G712 standards, and on these bases, we derived conclusions about the possibilities of this switched quantization application in speech processing. The suggested quantizer can be used for data compression where the saving can reach 1.5 bits/sample. This circumstance means that the technique that we presented in the paper can be applied for voice transmission over the Internet (VoIP) and in public switched telephone networks (PSTN).

Radial compression function for vector quantizer of Laplacian source with high dynamic variance range

In this paper, our aim is to define a high dynamic range vector quantization model for an i.i.d. Laplacian source. In order to do this we use a geometric approach and lattice quantization. As a result, we achieve symmetry in distribution of code vectors and introduce the radial scalar compression function for lattice cell side determination. This enables derivation of a sophisticated creation for a condition which the radial compression function should satisfy in order to make the SQNR non-dependent on variance. It is interesting that the obtained solution represents the generalisation of solution in the case of high dynamic range scalar quantization. Because of that, in the second part of the paper, the well-known semilogarithmic A-law compression characteristic is utilized as radial scalar compression function of geometric vector quantizer. It is shown that such a model has very good performances over a very wide variance range. The proper choice of compression parameter A and dimension n enables the constant SQNR to sustain over much wider variance range than in case of log-scalar quantization. Particularly, the high dimension makes it possible to broaden the variance range over which SQNR remains constant by increasing the A value simultaneously holding the SQNR level unchanged. In comparison with the widely used log-scalar quantization, the presented solution for dimensions from 10 to 140 gives a quality improvement of 7–9 dB, while comparison of maximal SQNR value to that of optimal scalar quantization shows the SQNR growth of 3–5 dB. Furthermore, for dimension 40 the SQNR maximum is only for 0.5 dB lower than that of optimal vector quantization, while dynamic range characteristic broadening is considerable. The cited benefits of high dynamic range vector quantization make it possible to realize a high quality signal compression. Besides, in comparison with the adaptive quantization, our proposal has a smaller implementation complexity. Copyright

Optimal companding vector quantization for circularly symmetric sources

In this paper, it is shown that optimal Z_2 lattice vector quantization can be implemented using radial companding technique. We derive the optimal vector compressor function for radial compander of memoryless Gaussian source. This result is obtained by taking into consideration the source geometry and by establishing the relation between the volumes and the point densities at the compressor input and compressor output. We also derive the linearized model - the piecewise linear compander. Its performance closely approaches that of optimal vector quantization. For example, for R=8bits/dimension and L=16 regions, the difference between corresponding distortions is about 0.037dB, while the asymptotic performances are identical.

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.

DPCM quantizer adaptation method for efficient ECG signal compression

This paper addresses the problem of electrocardiogram (ECG) signal compression with the goal to provide a simple compression method that outperforms previously proposed methods. Starting with the study of the ECG signal nature, the manner has been found to optimize rate-quality ratio of the ECG signal by means of differential pulse code modulation (DPCM) and subframe after subframe procession. Particularly, the proposed method includes two kinds of adaptations, short-time and long-time adaptations. The switched quantization i.e. the short-time DPCM quantizer range adaptation is performed according to the statistics of the ECG signal within particular subframes. It is ascertained that the short-time adaptation enables a sophisticated compression control as well as a constant quality of the ECG signal in both segments of low amplitude and high amplitude dynamics. In addition, by grouping the subframes of a particular frame into two groups according to their dynamics and performing the long-time DPCM quantizer range adaptation, based on the statistics of the groups, it has been revealed that an important quality gain is achieved with an insignificant rate increase. Moreover, the two iterative approaches proposed in the paper, mainly differ in the fact whether the long-time range adaptations of the used DPCM quantizers are performed according to the maximum amplitudes or according to the average powers of the signal difference determined in all subframes within a certain group. The benefits of both approaches to the above proposed method are shown and discussed in the paper.

Optimal piecewise linear radial compression function for Laplacian source

In order to achieve a quantisation technique that has low implementation complexity and performance arbitrarily close to that of Laplacian source optimal vector quantisation, a model of optimal geometric piecewise uniform cubic lattice vector quantiser will be proposed. It will be shown that the presented design procedure is not only much easier for realisation than the procedure of optimal vector quantiser design, but also gives the signal to quantisation noise ratio which in some cases differs from that of the optimal vector quantisation for 0.05 dB and less. It will also be demonstrated that the optimal geometric piecewise uniform vector quantiser model can be described with the optimal piecewise linear radial compression function. Further, since the optimal geometric piecewise uniform lattice vector quantisation in the case of large enough subregions number has performances identical to those of optimal vector quantisation, the optimal nonlinear radial compression function for Laplacian source will also be derived. Copyright

An iterative method for optimal resolution‐constrained polar quantizer design

Purpose – The purpose of this paper is to address the problem of polar quantization optimization. Particularly, the aim is to find the method for the optimal resolution‐constrained polar quantizer design.Design/methodology/approach – The new iterative algorithm for determination of the optimal decision and representation magnitude levels and algorithm for optimization of number of phase cells within each magnitude level, is proposed.Findings – At high rates, the new optimal polar quantizer outperforms the optimal polar compander for 0.2 dB, while the more significant gain should be expected at lower rates. In this paper, in order to enable practical implementation of quantizer model, algorithm which transforms real values for the optimal numbers of phase cells within magnitude levels into integer ones is also proposed. Moreover, the approximate closed form of signal‐to‐quantization ratio is derived.Practical implications – Since circularly symmetric sources and complex presentation of signals arise in num...