Quantization Step Size Research Articles

Psychophysical determination of boundaries and smoothness of color gradients.

Color gradients constitute an important component in the evaluation of the color quality of multicolored patterns that contain color transitions. A two-part psychophysical study was designed and employed to test the appearance of a set of hue-, chroma-, or lightness-based color gradients. The influence of several parameters on the visual determination of gradients' boundaries and perceived smoothness was tested. These parameters included gradient type, e.g.,transitions based on hue, chroma, lightness or their combination, orientation, slope, and quantization step size of color transitions. The influence of these parameters on intra- and interobserver variability in responses was calculated using the standardized residual sum of squares metric. In the first part of the experiment, the perceived boundaries of color gradient stimuli as well as observer confidence ratings in performing these visual tasks were determined. In the second part, the perceived smoothness ratings of the stimuli and visual confidence ratings in assessments were examined. Four binary color transition images, i.e.,brown-green, brown-tan, green-olive, and light sage-olive, were generated. Three different linear-gradient slopes were applied to each transition, and each stimulus was shown to observers, separately, in four orientations: horizontal, vertical, right diagonal, and left diagonal. Results indicate that the gradient slopes influence perceived boundaries and smoothness ratings. When determining smoothness ratings, observers were found to be more tolerant to changes in chroma and lightness than in hue.

Data fusion with factored quantization for stock trend prediction using neural networks

As compared to the continuous temporal distributions, discrete data representations may be desired for simplified and faster data analysis and forecasting. Data compression can introduce one of the efficient ways to reduce continuous historical stock market data and present them in discrete forms; while predicting stock trend, a primary concern is towards up and down directions of the price movement and thus, data discretization for a focused approach can be beneficial. In this article, we propose a quantization-based data fusion approach with a primary motivation to reduce data complexity and hence, enhance the prediction ability of a model. Here, the continuous time-series values are transformed into discrete quantum values prior to applying them to a prediction model. We extend the proposed approach and factorize quantization by integrating different quantization step sizes. Such fused data can reduce the data to mainly concentrate on the stock price movement direction. To empirically evaluate the proposed approach for stock trend prediction, we adopt long short-term memory, deep neural network, and backpropagation neural network models and compare our prediction results with five existing approaches on several datasets using ten performance metrics. We analyze the impact of specific quantization factors and determine the individual best as well as overall best factor sizes; the results indicate a consistent performance enhancement in stock trend prediction accuracy as compared to the considered baseline methods with an improvement up to 7%. To evaluate the impact of quantization-based data fusion, we analyze time required to execute the experiments along with percentage reduction in the number of unique numeric terms. Further, these results are statistically evaluated using Wilcoxon signed-rank test. We discuss the superiority and applicability of factored quantization-based data fusion approach and conclude our work with potential future research directions.

Vibration-Generation Mechanism and Reduction Method in Linear Iron-Cored Permanent-Magnet Synchronous Motors at Stationary State

This article presents the theoretical studies and experimental validation of the vibration-generation mechanism and reduction method in linear iron-cored permanent-magnet (PM) motors at stationary state. While motor noise and vibration during moving operations have been extensively studied, such vibration issue at stationary state has been relatively less explored even though it can be critically problematic for high-precision applications where strict standstill of a motor is demanded. We identify a discrete position feedback in a servo control loop as a major culprit of the stationary-state motor vibration, and investigate the vibration-generation mechanism analytically and experimentally. Closed-loop dynamics related to such undesired vibration is analyzed by modeling a position-controlled linear iron-cored PM motor with a discrete encoder feedback. The analyzed model suggests that the dominant vibration frequency is determined by the control parameters regardless of the encoder quantization, while the corresponding vibration amplitude increases solely by the encoder quantization step size. Giving a standstill command to the linear motor stage testbed position controlled with different quantization step sizes, we have confirmed that the analyzed model consists of the experimental results as well as the simulated results. Understanding the vibration-generation mechanism of linear iron-cored PM motors, we also present a reduction method of such stationary-state motor vibration by a programmable-resolution incremental encoder. Using our method, we can reduce the motor vibration significantly while overcoming the speed limit of general quadrature encoders, providing a practicalsolution to various industrial applications that require both high-throughput and high-precision performance.

Prototype Verification of Self-Interference Suppression for Constant-Amplitude Full-Duplex Phased Array with Finite Phase Shift

In view of the strong self-interference problem when the practical phased array system is simultaneously applied for transmission and reception, under the constraints including limited quantization number, constant envelope amplitude, scanning mode, wideband signal mode, etc., this work studies it and proposes the amplitude-phase joint adjustment method and the phase-only method for beamforming optimization. Through digital simulation design, electromagnetic simulation evaluation and principle test verification, under the actual array system conditions, including 6-bit phase quantization or phase step size of 5.625° and amplitude 0.5 dB quantization step, when the transmitting beam is pointing (0°, 0°), the research has achieved a performance of 11.9~14.4 dB for self-interference suppression; at the same time, the optimized beam shape is maintained well, and the ratio of the main lobe to the side lobes does not change significantly, but the beam gain has a loss of about 2~3 dB. In addition, we studied the interference suppression performance and beam feature retention performance of the optimized beamforming weights in the case of array scanning and broadband signals, and analyzed the influence of the changes in the mutual coupling characteristics between elements caused by scanning and frequency changes on the cancellation performance. This provides a reference for the application research of the simultaneous transmitting and receiving self-interference suppression technology in the actual array system state.

Quantization Analysis and Robust Design for Distributed Graph Filters

Distributed graph filters have recently found applications in wireless sensor networks (WSNs) to solve distributed tasks such as reaching consensus, signal denoising, and reconstruction. However, when implemented over WSNs, the graph filters should deal with network limited energy constraints as well as processing and communication capabilities. Quantization plays a fundamental role to improve the latter but its effects on distributed graph filtering are little understood. WSNs are also prone to random link losses due to noise and interference. In this instance, the filter output is affected by both the quantization error and the topological randomness error, which, if it is not properly accounted in the filter design phase, may lead to an accumulated error through the filtering iterations and significantly degrade the performance. In this paper, we analyze how quantization affects distributed graph filtering over both time-invariant and time-varying graphs. We bring insights on the quantization effects for the two most common graph filters: the finite impulse response (FIR) and autoregressive moving average (ARMA) graph filter. Besides providing a comprehensive analysis, we devise theoretical performance guarantees on the filter performance when the quantization stepsize is fixed or changes dynamically over the filtering iterations. For FIR filters, we show that a dynamic quantization stepsize leads to more reduction of the quantization noise than in the fixed-stepsize quantization. For ARMA graph filters, we show that decreasing the quantization stepsize over the iterations reduces the quantization noise to zero at the steady-state. In addition, we propose robust filter design strategies that minimize the quantization noise for both time-invariant and time-varying networks. Numerical experiments on synthetic and two real data sets corroborate our findings and show the different trade-offs between quantization bits, filter order, and robustness to topological randomness.

Suppressing Shot Noise Using Quadratic Variable Step-Size Quantization for the Initial Acquisition of Camera-Raw Image Data.

Digital images from today's premium digital cameras have a higher dynamic range than what humans can perceive. Maximumly keeping the image information captured by sensors while reducing the file size of the output raw image data is highly desirable. In this paper, we show that the extractable image information contained in high-quality HDR images taken by premium cameras can be preserved using a bit-depth of only 8 to 9 bits/pixel when the shot-noise-introduced extra entropy is suppressed. The quadratic variable step-size quantization is used to suppress the shot-noise-introduced entropy. The ratio of the quantization step-size of the quadratic quantizer over the shot noise amplitude is introduced as a parameter to measure the relative quantization noise level, and is used to design the quadratic quantizers that maximally suppress the shot noise. Finally, quadratically quantized real CFA camera-raw image data are losslessly compressed. Compared with the lossless compression on linearly quantized data, at least more than 50% bitrate savings are achieved. Such high bitrate savings without loss of extractable image information are very attractive. Thus, it is highly worthwhile to explore, in the future, hardware implementations of quadratic quantization in image sensors.

An approach to expose dithering-based JPEG anti-forensics

A forensic analyst needs to exploit various kinds of artefacts for developing a powerful forensic technique. Among those, the JPEG compression artefacts such as blocking artefacts & DCT histogram artefacts are the most widely used. JPEG anti-forensic techniques aim to disguise forensic detectors by removing these artefacts. Hence, a technique for the detection of dithering-based JPEG anti-forensic methods is the need of an hour. An approach proposed in this paper exploits the spread of discrete cosine transform (DCT) coefficients around integer multiple of quantization step size with repeated application of dithering-based JPEG anti-forensics. The paper first briefly explains dithering-based state-of-the-art JPEG anti-forensic techniques. Then the proposed method is illustrated thoroughly, and finally, experimental results are reported to demonstrate the accuracy of the proposed method.

Synchronization of Transmission Systems with ANS-DM Codecs

Adaptive Delta Modulation with Non-uniform Sampling (ANS-DM) is one of the waveform coding techniques, where a sampling instant and a quantization step size are adapted to the signal. The ANS-DM modulator produces an output binary stream, that carries information about the signal and includes necessary data of coder parameters (sampling instant and quantization step). In the demodulator, these values are recovered for proper signal reconstruction. The paper reports the problem of synchronizing clocks (transmitting and receiving) in the (ANS-DM) delta codecs systems. The original synchronization method, valuable in systems dedicated to the transmission of the bits with variable time duration was projected and experimentally verified. Performed measurements and observations have shown the elimination of the synchronization loss phenomenon.

Viewport-Based Omnidirectional Video Quality Assessment: Database, Modeling and Inference

This article first provides a new Viewport-based OmniDirectional Video Quality Assessment (VOD-VQA) database, which includes eighteen salient viewport videos extracted from the original OmniDirectional Videos (ODVs), and corresponding 774 impaired samples generated by compressing the raw viewports using a variety of combinations of its Spatial (frame size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula> ), Temporal (frame rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> ), and Amplitude (quantization stepsize <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> ) Resolutions (STAR). Total 160 subjects have assessed the processed viewport videos rendered on the head mounted display (HMD) when they stabilize their fixations. We then have formulated an analytical model to connect the perceptual quality of a compressed viewport video with its STAR variables, noted as the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q^{{\mathsf {VP}}}_{\tt {STAR}}$ </tex-math></inline-formula> index. All four model parameters can be predicted using linearly weighted content features, making the proposed metric generalized to various contents. This model correlates well with the mean opinion scores (MOSs) collected for processed viewport videos, having both the Pearson Correlation Coefficient and Spearman’s Rank Correlation Coefficient (SRCC) at 0.95 according to an independent validation test, yielding the state-of-the-art performance in comparison to those popular objective metrics (e.g., Weighted to Spherically uniform (WS)-Peak Signal to Noise Ratio (PSNR), WMS-SSIM, Video Multimethod Assessment Fusion (VMAF), Feature SIMilarity Index (FSIM), and Visual Saliency based IQA Index (VSI)). Furthermore, this viewport-based quality index <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q^{{\mathsf {VP}}}_{\tt {STAR}}$ </tex-math></inline-formula> is extended to infer the overall ODV quality, a.k.a., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q^{{\mathsf {ODV}}}_{\tt {STAR}}$ </tex-math></inline-formula> , by linearly weighing the saliency-aggregated qualities of salient viewports and the quality of quick-scanning (or non-salient) area. Experiments have shown that inferred <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q^{{\mathsf {ODV}}}_{\tt {STAR}}$ </tex-math></inline-formula> can accurately predict the MOS with competitive performance to the state-of-the-art algorithm using another four independent and third-party ODV assessment datasets. All related materials are made publicly accessible at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://vision.nju.edu.cn/20/86/c29466a467078/page.htm</uri> for reproducible research.

Reduced Reference Perceptual Quality Model With Application to Rate Control for Video-Based Point Cloud Compression.

In rate-distortion optimization, the encoder settings are determined by maximizing a reconstruction quality measure subject to a constraint on the bitrate. One of the main challenges of this approach is to define a quality measure that can be computed with low computational cost and which correlates well with the perceptual quality. While several quality measures that fulfil these two criteria have been developed for images and videos, no such one exists for point clouds. We address this limitation for the video-based point cloud compression (V-PCC) standard by proposing a linear perceptual quality model whose variables are the V-PCC geometry and color quantization step sizes and whose coefficients can easily be computed from two features extracted from the original point cloud. Subjective quality tests with 400 compressed point clouds show that the proposed model correlates well with the mean opinion score, outperforming state-of-the-art full reference objective measures in terms of Spearman rank-order and Pearson linear correlation coefficient. Moreover, we show that for the same target bitrate, rate-distortion optimization based on the proposed model offers higher perceptual quality than rate-distortion optimization based on exhaustive search with a point-to-point objective quality metric. Our datasets are publicly available at https://github.com/qdushl/Waterloo-Point-Cloud-Database-2.0.

Training of Mixed-Signal Optical Convolutional Neural Networks With Reduced Quantization Levels

Mixed-signal artificial neural networks (ANNs) that employ analog matrix-multiplication accelerators can achieve higher speed and improved power efficiency. Though analog computing is known to be susceptible to noise and device imperfections, various analog computing paradigms have been considered as promising solutions to address the growing computing demand in machine learning applications, thanks to the robustness of ANNs. This robustness has been explored in low-precision, fixed-point ANN models, which have proven successful on compressing ANN model size on digital computers. However, these promising results and network training algorithms cannot be easily migrated to analog accelerators. The reason is that digital computers typically carry intermediate results with higher bit width, though the inputs and weights of each ANN layers are of low bit width; while the analog intermediate results have low precision, analogous to digital signals with a reduced quantization level. Here we report a training method for mixed-signal ANN with two types of errors in its analog signals, random noise, and deterministic errors (distortions). The results showed that mixed-signal ANNs trained with our proposed method can achieve an equivalent classification accuracy with noise level up to 50% of the ideal quantization step size. We have demonstrated this training method on a mixed-signal optical convolutional neural network based on diffractive optics.

Limit Cycles in High-Resolution Quantized Feedback Systems

In this paper, the existence of limit cycles in high-resolution quantized feedback systems is examined. It is well known that the relay and the quantized feedback systems exhibit self-oscillations, due to their switching nature. However, the quantizer is a more general nonlinearity as compared to the relay, due to its switching at multiple discrete levels. An extension of periodic switching conditions uncovers the existence of self-oscillations in some systems under high quantization resolution. Multiple limit cycle solutions of switching instants and periods have been found, depending on the initial states of the system. Further analysis on the stability of the limit cycle via the Jacobian of the Poincare map reveals numerical bounds on the quantization step size for a stable limit cycle. Analytical results on the existence of limit cycles in first and second order systems are also presented.

Temporal quantization deteriorates the discrimination of interaural time differences.

Cochlear implants (CIs) often replace acoustic temporal fine structure by a fixed-rate pulse train. If the pulse timing is arbitrary (that is, not based on the phase information of the acoustic signal), temporal information is quantized by the pulse period. This temporal quantization is probably imperceptible with current clinical devices. However, it could result in large temporal jitter for strategies that aim to improve bilateral and bimodal CI users' perception of interaural time differences (ITDs), such as envelope enhancement. In an experiment with 16 normal-hearing listeners, it is shown that such jitter could deteriorate ITD perception for temporal quantization that corresponds to the often-used stimulation rate of 900 pulses per second (pps): the just-noticeable difference in ITD with quantization was 177 μs as compared to 129 μs without quantization. For smaller quantization step sizes, no significant deterioration of ITD perception was found. In conclusion, the binaural system can only average out the effect of temporal quantization to some extent, such that pulse timing should be well-considered. As this psychophysical procedure was somewhat unconventional, different procedural parameters were compared by simulating a number of commonly used two-down one-up adaptive procedures in Appendix B.

Bayes-Optimal MMSE Detector for Massive MIMO Relaying With Low-Precision ADCs/DACs

In this study, we focus on the detector design for a massive multiple-input multiple-output amplify-and-forward relaying system with low-precision analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). A general relaying model with direct and relay links is considered. Several studies have been performed on the basis of simple but performance-limited linear transceivers. The optimal detector for the aforementioned setting remains unknown. To bridge this gap, we develop a minimum mean squared error detector based on the framework of variational Bayes inference. The proposed detector works similarly to the iterative turbo update, and the extrinsic information of the direct and relay links are updated through maximum ratio combining. Furthermore, our algorithm uses a partially parallel update schedule that improves the convergence compared with an intuitive method that is based on a fully parallel schedule. We then present the state evolution (SE) as an analytical framework to investigate the mean squared error and symbol error rate of the detector. By specifying the dynamics of the SE, we reveal that low-precision ADCs/DACs, that is, those using 2-4-bit quantization, realize a good tradeoff between performance and cost. Moreover, low-precision ADCs/DACs provide numerous insights into the relaying system and its design, such as the quantization step size.

Distributed Sequential Hypothesis Testing With Quantized Message-Exchange

This work considers the cooperative sequential hypothesis testing problem in a distributed network with quantized communication channels. The sensors observe independent sequences of samples and in the meantime, exchange their local information in the form of quantized statistics at every sampling interval. The communication links are represented as an undirected graph. In this distributed setup, every sensor performs its own sequential test based on the local samples and the messages from the neighbour sensors. Our goal is to devise the distributed sequential test that comprises the quantization scheme, the message-exchange protocol and the test procedure such that every sensor in the network fully exploits the network diversity and achieves the (asymptotically) optimal performance in terms of the stopping time. In particular, two distributed sequential tests are proposed based on different quantization schemes and a quantized message-exchange protocol that satisfies certain conditions. The first quantization scheme uniformly quantizes the local statistic at each sensor and at every sampling interval; the second one hinges on a modified level-triggered quantization technique, and resembles the Lebesgue sampling of the running local statistic. Our analyses show that the uniform quantization based distributed sequential test yields sub-optimal performance, while the one based on level-triggered quantization achieves the order-2 asymptotically optimal performance at every sensor for any fixed quantization step-size. Furthermore, we generalize the proposed sequential tests to the cluster-based network. Numerical results are provided to corroborate our analyses and demonstrate the effectiveness of the proposed sequential tests.

Design of high-resolution quantization scheme with exp-Golomb code applied to compression of special images

For the compression of special image, such as medical image and aerial image, the reconstructed image quality is of utmost importance in the performance analysis. In this paper, a high-resolution quantization scheme based on the exp-Golomb code is proposed, aiming at improving the reconstructed image quality and realizing high-resolution near-lossless compression. Rather than quantizing the whole image uniformly, which adopted by most popular quantization schemes, an adaptive quantizer with smaller distortion is designed. Both the quantization step size and the quantization proportion are determined adaptively. Compression algorithms based on our adaptive quantizer can provide better reconstructed image quality, and the high frequency information of the image, such as texture and edge, can be better preserved.

On the Information Dimension of Stochastic Processes

The authors have recently defined the R\'enyi information dimension rate $d(\{X_t\})$ of a stationary stochastic process $\{X_t,\,t\in\mathbb{Z}\}$ as the entropy rate of the uniformly-quantized process divided by minus the logarithm of the quantizer step size $1/m$ in the limit as $m\to\infty$ (B. Geiger and T. Koch, "On the information dimension rate of stochastic processes," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Aachen, Germany, June 2017). For Gaussian processes with a given spectral distribution function $F_X$, they showed that the information dimension rate equals the Lebesgue measure of the set of harmonics where the derivative of $F_X$ is positive. This paper extends this result to multivariate Gaussian processes with a given matrix-valued spectral distribution function $F_{\mathbf{X}}$. It is demonstrated that the information dimension rate equals the average rank of the derivative of $F_{\mathbf{X}}$. As a side result, it is shown that the scale and translation invariance of information dimension carries over from random variables to stochastic processes.

Gaussian Mixture Message Passing for Blind Known Interference Cancellation

This paper proposes a Gaussian mixture message passing (GMMP) scheme to implement the blind known-interference cancellation (BKIC). Being aware of interference data as a priori information, the BKIC aims at canceling the interference without estimating the interference channel. Since the target signals are represented by continuous real-valued variables, the previous BKIC scheme is constructed as a real-valued belief propagation (RBP) for implementing message passing on the factor graph that represents the corresponding signal model. To implement the RBP-BKIC, the real-valued variables are actually quantized into vectors of discrete values. As such, the quantized RBP-BKIC has some drawbacks: 1) its performance is determined by the quantization step size and 2) it can only be applied to real signaling with 1-D PAM modulations. To overcome these drawbacks, we propose a GMMP scheme for the BKIC. First, we reveal that all messages passing over the factor graph of BKIC systems can be exactly represented by the mixtures of weighted Gaussian probability density functions. Superior to the quantized RBP-BKIC, we further show that the proposed GMMP scheme is an exact and efficient solution to the BKIC. In particular, it can approach performances of point-to-point communication systems with complex QAM modulations at the cost of affordable computational complexities. Moreover, we put forth a message passing framework that combines the GMMP-BKIC and the channel decoding into an iterative message passing scheme.

Modeling the Perceptual Quality of Viewport Adaptive Omnidirectional Video Streaming

Instead of streaming the entire OmniDirectional Videos (ODVs) that are often sampled at ultra high definition and high frame rate, a viewport adaptive streaming is preferred in practice. We usually stream the High-Quality (HQ) content within current viewport, while Low-Quality (LQ) elsewhere to save the network bandwidth consumption. Such scheme would lead to a quality refinement after user adapts his/her focus to a new viewport. In this paper, we thus model the perceptual impact of the quality variations (through adjusting the Quantization Stepsize (QS or q) and Spatial Resolution (SR or s)) with respect to the Refinement Duration (RD or τ) when performing the refinement from an arbitrary LQ scale to an arbitrary HQ one. A number of quality variations are studied to cover sufficient use cases in practice, resulting in a unified analytical model, as a product of separable exponential functions that measure the QS and SR induced perceptual impacts in terms of the RD, and a perceptual index measuring the subjective quality of corresponding viewport video after refinement. This model is first validated in a managed lab environment via independent subjective assessments by constraining user's navigation to avoid unexpected noise, where both Pearson Correlation Coefficient (PCC) and Spearman's Rank Correlation Coefficient (SRCC) are around 0.97. We then extend the validations in a real-life viewport-dependent streaming system, still yielding PCC and SRCC about 0.96 when comparing collected subjective scores with model predictions.

A transform size based quantization for high efficiency video coding

Quantization is a key component in High Efficiency Video Coding (HEVC) standard. It enhances coding efficiency, and also introduces quantization distortion which causes degradation of the quality of the reconstructed video. In current framework, HEVC has adopted more transform sizes, and it is obvious that the transform unit (TU) with different transform size has different feature. A TU-level quantization technique, namely an adaptive quantization step size Q along with a fixed transform size is proposed in this paper. The proposed algorithm is implemented in HM software. Compared with HM anchor, the proposed TU-level quantization step adjustment (TUQA) method achieves an average of 0.32%, 2.34% and 2.58% BD bitrate saving for luminance and chrominance components, respectively. The largest BD bitrate saving is up to 1.0% for luminance and 3.8% for chrominance.