Uniform Scalar Quantization Research Articles

Comparison of Particle Swarm Algorithm and Ant Colony Algorithm in the Optimization of Uniform Quantizer

In this paper, we focuse on the study of parameter optimization problem of the uniform scalar dead zone quantizer (USDZQ).We used particle swarm optimization (PSO) algorithm and ant colony optimization (ACO) algorithm for the optimization. We used the two kinds of optimization algorithm for ECG signal coding test.Those ECG signals were from the MIT-BIH arrhythmia database. At the end of this paper, the results of compression are compared.

$\ell_{2}$ Optimized Predictive Image Coding With $\ell_{\infty}$ Bound

In many scientific, medical, and defense applications of image/video compression, an [Symbol: see text]∞ error bound is required. However, pure[Symbol: see text]∞-optimized image coding, colloquially known as near-lossless image coding, is prone to structured errors such as contours and speckles if the bit rate is not sufficiently high; moreover, most of the previous [Symbol: see text]∞-based image coding methods suffer from poor rate control. In contrast, the [Symbol: see text]2 error metric aims for average fidelity and hence preserves the subtlety of smooth waveforms better than the ∞ error metric and it offers fine granularity in rate control, but pure [Symbol: see text]2-based image coding methods (e.g., JPEG 2000) cannot bound individual errors as the [Symbol: see text]∞-based methods can. This paper presents a new compression approach to retain the benefits and circumvent the pitfalls of the two error metrics. A common approach of near-lossless image coding is to embed into a DPCM prediction loop a uniform scalar quantizer of residual errors. The said uniform scalar quantizer is replaced, in the proposed new approach, by a set of context-based [Symbol: see text]2-optimized quantizers. The optimization criterion is to minimize a weighted sum of the [Symbol: see text]2 distortion and the entropy while maintaining a strict [Symbol: see text]∞ error bound. The resulting method obtains good rate-distortion performance in both [Symbol: see text]2 and [Symbol: see text]∞ metrics and also increases the rate granularity. Compared with JPEG 2000, the new method not only guarantees lower [Symbol: see text]∞ error for all bit rates, but also it achieves higher PSNR for relatively high bit rates.

Design of the adaptive piecewise uniform scalar quantizer with lossless coder and Golomb-Rice code on the output, for signals with Gaussian distribution

In this paper a new compression model for signals with Gaussian distribution is presented. It consists of a piecewise uniform scalar quantizer, a lossless coder and Golomb-Rice code. Forward adaptation of this proposed model is done and constant signal-to-quantization noise ratio (SQNR) in wide range of input variances is obtained. Joined design of lossy and lossless coder is done, achieving optimal performances. Our model has small complexity since all components of the model (piecewise uniform quantizer, lossless coder and Golomb-Rice code) are very simple for realization. As an example, this model is applied on the speech signal, and it is shown that the G.712 standard is satisfied with bit-rate decrease of 1.09 bits/sample, compared to the classic uniform quantizer.

A Bit Allocation Method for Sparse Source Coding

In this paper, we develop an efficient bit allocation strategy for subband-based image coding systems. More specifically, our objective is to design a new optimization algorithm based on a rate-distortion optimality criterion. To this end, we consider the uniform scalar quantization of a class of mixed distributed sources following a Bernoulli-generalized Gaussian distribution. This model appears to be particularly well-adapted for image data, which have a sparse representation in a wavelet basis. In this paper, we propose new approximations of the entropy and the distortion functions using piecewise affine and exponential forms, respectively. Because of these approximations, bit allocation is reformulated as a convex optimization problem. Solving the resulting problem allows us to derive the optimal quantization step for each subband. Experimental results show the benefits that can be drawn from the proposed bit allocation method in a typical transform-based coding application.

General Embedded Quantization for Wavelet-Based Lossy Image Coding

Embedded quantization is a mechanism employed by many lossy image codecs to progressively refine the distortion of a (transformed) image. Currently, the most common approach to do so in the context of wavelet-based image coding is to couple uniform scalar deadzone quantization (USDQ) with bitplane coding (BPC). USDQ+BPC is convenient for its practicality and has proved to achieve competitive coding performance. But the quantizer established by this scheme does not allow major variations. This paper introduces a multistage quantization scheme named general embedded quantization (GEQ) that provides more flexibility to the quantizer. GEQ schemes can be devised for specific decoding rates achieving optimal coding performance. Practical approaches of GEQ schemes achieve coding performance similar to that of USDQ+BPC while requiring fewer quantization stages. The performance achieved by GEQ is evaluated in this paper through experimental results carried out in the framework of modern image coding systems.

Two approaches to design of forward adaptive piecewise uniform scalar quantizers

In this paper, two forward adaptive piecewise uniform scalar quantizers are proposed for high-quality quantization of speech signals modeled by the Laplacian probability density function. In designing both forward adaptive piecewise uniform scalar quantizers an equidistant support region partition is assumed and a distribution of the number of reproduction levels per segments is optimized. The proposed models differ in the approach of determining the reproduction levels. In particular, one model defines the reproduction levels as the cell centroids and the other one as the cell midpoints. We show that, in the high-resolution case, the proposed quantizers provide approximately the same performance being close to the one of the forward adaptive nonlinear scalar compandor with equal number of quantization levels.

Vector Quantization of RF Channel Data for Ultrasound Imaging

Quantization is a necessary step in a digital beamformer that should be implemented efficiently when designing an ultrasound imaging system. Several factors should be considered, including the accuracy of both amplitude and phase in the digital representation, the quantization efficiency, and the complexity of the quantization scheme. While uniform scalar quantization (SQ) is currently used in most ultrasound imaging systems, this study used simulations and experimental data to explore vector quantization (VQ) based on the signals received by adjacent elements of the transducer array generally being strongly correlated. The signal-to-quantization-noise ratio, focusing quality, and accuracy in phase aberration correction and blood velocity estimation were assessed. The results show that using VQ instead of conventional SQ reduces the quantization noise by 10 dB with minimal degradation in the focusing quality. Similarly, the performance of correlation-based phase aberration correction was not affected at this level of quantization. Nevertheless, velocity estimation accuracy was found to be more susceptible to VQ noise when the reduction in the number of bits is limited to a factor of two. One benefit of using a more efficient quantizer is the reduced data size, which directly affects the data transfer rate and is an important design consideration for a digital imaging system.

Rate-Distortion Analysis of Dead-Zone Plus Uniform Threshold Scalar Quantization and Its Application—Part II: Two-Pass VBR Coding for H.264/AVC

In the first part of this paper, we derive a source model describing the relationship between the rate, distortion, and quantization steps of the dead-zone plus uniform threshold scalar quantizers with nearly uniform reconstruction quantizers for generalized Gaussian distribution. This source model consists of rate-quantization, distortion-quantization (D-Q), and distortion-rate (D-R) models. In this part, we first rigorously confirm the accuracy of the proposed source model by comparing the calculated results with the coding data of JM 16.0. Efficient parameter estimation strategies are then developed to better employ this source model in our two-pass rate control method for H.264 variable bit rate coding. Based on our D-Q and D-R models, the proposed method is of high stability, low complexity and is easy to implement. Extensive experiments demonstrate that the proposed method achieves: 1) average peak signal-to-noise ratio variance of only 0.0658 dB, compared to 1.8758 dB of JM 16.0's method, with an average rate control error of 1.95% and 2) significant improvement in smoothing the video quality compared with the latest two-pass rate control method.

Rate-Distortion Analysis of Dead-Zone Plus Uniform Threshold Scalar Quantization and Its Application—Part I: Fundamental Theory

This paper provides a systematic rate-distortion (R-D) analysis of the dead-zone plus uniform threshold scalar quantization (DZ+UTSQ) with nearly uniform reconstruction quantization (NURQ) for generalized Gaussian distribution (GGD), which consists of two aspects: R-D performance analysis and R-D modeling. In R-D performance analysis, we first derive the preliminary constraint of optimum entropy-constrained DZ+UTSQ/NURQ for GGD, under which the property of the GGD distortion-rate (D-R) function is elucidated. Then for the GGD source of actual transform coefficients, the refined constraint and precise conditions of optimum DZ+UTSQ/NURQ are rigorously deduced in the real coding bit rate range, and efficient DZ+UTSQ/NURQ design criteria are proposed to reasonably simplify the utilization of effective quantizers in practice. In R-D modeling, inspired by R-D performance analysis, the D-R function is first developed, followed by the novel rate-quantization (R-Q) and distortion-quantization (D-Q) models derived using analytical and heuristic methods. The D-R, R-Q, and D-Q models form the source model describing the relationship between the rate, distortion, and quantization steps. One application of the proposed source model is the effective two-pass VBR coding algorithm design on an encoder of H.264/AVC reference software, which achieves constant video quality and desirable rate control accuracy.

Optimal entropy-constrained non-uniform scalar quantizer design for low bit-rate pixel domain DVC

In this paper, an optimal entropy-constrained non-uniform scalar quantizer is proposed for the pixel domain DVC. The uniform quantizer is efficient for the hybrid video coding since the residual signals conforming to a single-variance Laplacian distribution. However, the uniform quantizer is not optimal for pixel domain distributed video coding (DVC). This is because the uniform quantizer is not adaptive to the joint distribution of the source and the SI, especially for low level quantization. The signal distribution of pixel domain DVC conforms to the mixture model with multi-variance. The optimal non-uniform quantizer is designed according to the joint distribution, the error between the source and the SI can be decreased. As a result, the bit rate can be saved and the video quality won't sacrifice too much. Accordingly, a better R-D trade-off can be achieved. First, the quantization level is fixed and the optimal RD trade-off is achieved by using a Lagrangian function J(Q). The rate and distortion components is designed based on P(Y|Q). The conditional probability density function of SI Y depend on quantization partitions Q, P(Y|Q), is approximated by a Guassian mixture model at encocder. Since the SI can not be accessed at encoder, an estimation of P(Y|Q) based on the distribution of the source is proposed. Next, J(Q) is optimized by an iterative Lloyd-Max algorithm with a novel quantization partition updating algorithm. To guarantee the convergence of J(Q), the monotonicity of the interval in which the endpoints of the quantizer lie must be satisfied. Then, a quantizer partition updating algorithm which considers the extreme points of the histogram of the source is proposed. Consequently, the entropy-constrained optimal non-uniform quantization partitions are derived and a better RD trade-off is achieved by applying them. Experiment results show that the proposed scheme can improve the performance by 0.5 dB averagely compared to the uniform scalar quantization.

Asymptotic Characteristics of MSE-Optimal Scalar Quantizers for Generalized Gamma Sources

Characteristics, such as the support limit and distortions, of minimum mean-squared error (MSE) N-level uniform and nonuniform scalar quantizers are studied for the family of the generalized gamma density functions as N increases. For the study, MSE-optimal scalar quantizers are designed at integer rates from 1 to 16 bits/sample, and their characteristics are compared with corresponding asymptotic formulas. The results show that the support limit formulas are generally accurate. They also show that the distortion of nonuniform quantizers is observed to converge to the Panter-Dite asymptotic constant, whereas the distortion of uniform quantizers exhibits slow or even stagnant convergence to its corresponding Hui-Neuhoff asymptotic constant at the studied rate range, though it may stay at a close proximity to the asymptotic constant for the Rayleigh and Laplacian pdfs. Additional terms in the asymptote result in quite considerable accuracy improvement, making the formulas useful especially when rate is 8 or greater.

Asymptotic MSE Distortion of Mismatched Uniform Scalar Quantization

Asymptotic formulas are derived for the mean-squared error (MSE) distortion of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -level uniform scalar quantizers designed to be MSE optimal for one density function, but applied to another, as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> → ∞. These formulas, which are based on the Euler-Maclaurin formula, are then applied with generalized gamma, Bucklew-Gallagher, and Hui-Neuhoff density functions as the designed-for and applied-to densities. It is found that the mismatch between the designed-for and applied-to densities can disturb the delicate balance between granular and overload distortions in optimal quantization, with the result that, generally speaking, the granular or overload distortion dominates, respectively, depending on whether the applied-to density function has a lighter or heavier tail than the designed-for density. Specifically, in the case of generalized gamma densities, a variance mismatch makes overload distortion dominate for an applied-to source with a slightly larger variance, whereas a shape mismatch can tolerate a wider variance difference while retaining the dominance of the granular distortion. In addition, for the studied density functions, the Euler-Maclaurin approach is used to derive asymptotic formulas for the optimal quantizer step size in a simpler, more direct, way than previous approaches.

Design of novel piecewise uniform scalar quantizer for Gaussian memoryless source

In this paper we propose a novel piecewise uniform scalar quantizer model designed for a Gaussian memoryless source. The segment thresholds of this quantizer model are equidistant while the number of reproduction levels inside segments is determined by optimizing the inner distortion and under the constraint of total number of reproduction levels. For the proposed quantizer model the quantization efficiency and signal to quantization noise ratio (SQNR) is studied. On the basis of the comparison with the efficiency and SQNR of uniform quantizer advantages of the proposed quantizer model are shown. Particularly, it is shown that with the proposed quantizer the correlation between the input signal and the quantization error can be eliminated more than by using the uniform quantizer as well as that the proposed quantizer provides higher level of SQNR.

Design of Forward Adaptive Piecewise Uniform Scalar Quantizer with Optimized Reproduction Level Distribution per Segments

The problem we address in this paper is the design of nearly optimal scalar quantizer in a wide variance range of the Laplacian input signals, using the piecewise uniform quantizers while restricting the class of quantizers to be forward adaptive. Particularly, the design procedure of the piecewise uniform quantizer with an equidistant support region partion and the optimized reproduction level distribution per segments is presented along with the design procedure of its forward adaptive version. Reproduction level optimization is performed by optimizing the granular distortion of the proposed quantizer using the method of the Lagrange multipliers. For the proposed model we study the influence of the segment number on the SQNR, as well as the SQNR robustness in a wide variance range. Since the results obtained for the assumed Laplacian distribution indicate the SQNR improvement over the G.711 standard, one can expect that the proposed quantizer will be effective in the quantization of signals having the same distribution and the time varying characteristics. Ill. 4, bibl. 10 (in English; abstracts in English and Lithuanian).DOI: http://dx.doi.org/10.5755/j01.eee.119.3.1356

Switched Nonuniform and Piecewise Uniform Scalar Quantization of Laplacian Source

In this paper switched nonuniform and piecewise uniform scalar quantization of Laplacian source are analyzed. This scalar quantization techniques are used in order to obtain higher signal quality by increasing signal-to-quantization noise ratio (SNRQ) with respect to it’s necessary robustness over a broad range of input variances in a wide range of signal volumes. We observe μ-law compandor implementation to achieve compromise between high-rate digitalization and variance adaptation. The main contribution of this model is kipping almost the same quality as the nonuniform compandor model, with simpler realization structure and the possibility of it’s applying for digitalization of wide range continuous signals.

Power Constrained Linear Estimation in Wireless Sensor Networks With Correlated Data and Digital Modulation

We study the problem of joint quantization and power allocation in wireless sensor networks where spatially distributed sensors observe a Gaussian random source, quantize the resulting noisy observations, and transmit over orthogonal fading channels to a remote fusion center (FC). The role of the FC is to reconstruct the source with minimal distortion using linear minimum mean square error estimation rule. In this paper, we undertake the design of joint quantization and power allocation based on the following optimization problem: minimize the reconstruction distortion for a given total network power consumption. To address this problem, at each sensor node uniform scalar quantization is assumed. Moreover, assuming pseudo-quantization noise model we show that the problem can be solved using a block-coordinate descent type algorithm which iteratively optimizes the quantization bits and the power allocations. The algorithm takes into account the spatial correlation, the observation noise, and the channel quality of the sensors. Numerical and simulation examples corroborate the analytical results. The examples illustrate that the proposed design holds a considerable performance gain compared to a quantization scheme based on uniform power allocation to the sensors.

Daubechies Wavelet Based Compression and Denoising Techniques for Biometric Images

Finger print readers and retinal eye scanners have been an integral aspect of research and space organisations, forensic tests and so on. But to use it on a daily basis, Image compression is a necessary aspect considering the huge population of our country. Wavelet transform provides a platform for this process. In this paper, a novel idea to implement wavelet transform based on Daubechies wavelets has been discussed. The paper also discusses the concepts of linear transform, quantization, dequantization and image denoising. The image is first transformed using discrete wavelet transform to obtain the wavelet coefficients. The process of image compression is achieved by quantizing and encoding the coefficients. Uniform scalar quantization is done on the basis function coefficients in order to reduce their precision by reducing the number of bits required to store the transformed coefficients. The resulting quantized coefficients are then encoded using Huffman entropy encoding. In order to ensure that the image is free from disturbances like noise signals, denoising technique has been implemented using the wavelet coefficients. A paper of such an application has been proposed to tackle the global phenomenon of terrorism through the use of biometric devices including finger print reader and retinal eye scanner.

Compression of 3D Integral Images Using 3D Wavelet Transform

Integral imaging is a technique capable of displaying 3D images with continuous parallax in full natural color. It has been reported by many research groups and is becoming a viable alternative for 3D television. With the development of 3D integral imaging, image compression becomes mandatory for the storage and transmission of 3D integral images. In this paper, the use of the lifting scheme in the application of a 3D Wavelet Transform for the compression of 3D Integral Images is proposed. The method requires the extraction of different viewpoint images from an integral image. The 3D wavelet decomposition is computed by applying three separate 1D transforms along the coordinate axes of the given sequence of Viewpoint Images. The spatial wavelet decompositions on a single viewpoint and on the inter-viewpoint images are performed using the biorthogonal Cohen-Debauchies-Feauveau 9/7 and 5/3 filter banks, respectively. All the resulting wavelet coefficients from application of the 3D wavelet decomposition are arithmetic encoded. Simulations are performed on a set of different grey level 3D Integral Images using a uniform scalar quantizer with deadzone. The results for the average of the four intensity distributions are presented and compared with previous use of 2D DWT and 3D-DCT based schemes. It was found that the algorithm achieves better rate-distortion performance and reconstructs the images with much better image quality at very low bit rates.

Design of Piecewise Uniform Scalar Quantizer with Geometric Progression of Segment Width

In this paper, the design procedure of the piecewise uniform scalar quantizer having segments with widths that form a geometric progression is presented. The proposed quantizer design ...

Entropy of Highly Correlated Quantized Data

This paper considers the entropy of highly correlated quantized samples. Two results are shown. The first concerns sampling and identically scalar quantizing a stationary continuous-time random process over a finite interval. It is shown that if the process crosses a quantization threshold with positive probability, then the joint entropy of the quantized samples tends to infinity as the sampling rate goes to infinity. The second result provides an upper bound to the rate at which the joint entropy tends to infinity, in the case of an infinite-level uniform threshold scalar quantizer and a stationary Gaussian random process. Specifically, an asymptotic formula for the conditional entropy of one quantized sample conditioned on the previous quantized sample is derived. At high sampling rates, these results indicate a sharp contrast between the large encoding rate (in bits/sec) required by a lossy source code consisting of a fixed scalar quantizer and an ideal, sampling-rate-adapted lossless code, and the bounded encoding rate required by an ideal lossy source code operating at the same distortion.