Optimal Quantization Research Articles

Multi‐bit quantisation for similarity‐preserving hashing

As a promising alternative to traditional search techniques, hashing‐based approximate nearest neighbour search provides an applicable solution for big data. Most existing efforts are devoted to finding better projections to preserve the neighbouring structure of original data points in Hamming space, but ignore the quantisation procedure which may lead to the breakdown of the neighbouring structure maintained in the projection stage. To address this issue, the authors propose a novel multi‐bit quantisation (MBQ) method using a Matthews correlation coefficient (MCC) term and a regularisation term. The authors' method utilises the neighbouring relationship and the distribution information of original data points instead of the projection dimension usually used in the previous MBQ methods to adaptively learn optimal quantisation thresholds, and allocates multiple bits per projection dimension in terms of the learned thresholds. Experiments on two typical image data sets demonstrate that the proposed method effectively preserves the similarity between data points in the original feature space and outperforms state‐of‐the‐art quantisation methods.

Quantization and training of object detection networks with low-precision weights and activations

As convolutional neural networks have demonstrated state-of-the-art performance in object recognition and detection, there is a growing need for deploying these systems on resource-constrained mobile platforms. However, the computational burden and energy consumption of inference for these networks are significantly higher than what most low-power devices can afford. To address these limitations, this paper proposes a method to train object detection networks with low-precision weights and activations. The probability density functions of weights and activations of each layer are first directly estimated using piecewise Gaussian models. Then, the optimal quantization intervals and step sizes for each convolution layer are adaptively determined according to the distribution of weights and activations. As the most computationally expensive convolutions can be replaced by effective fixed point operations, the proposed method can drastically reduce computation complexity and memory footprint. Performing on the tiny you only look once (YOLO) and YOLO architectures, the proposed method achieves comparable accuracy to their 32-bit counterparts. As an illustration, the proposed 4-bit and 8-bit quantized versions of the YOLO model achieve a mean average precision of 62.6% and 63.9%, respectively, on the Pascal visual object classes 2012 test dataset. The mAP of the 32-bit full-precision baseline model is 64.0%.

Least upper bound of the exact formula for optimal quantization of some uniform Cantor distributions

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. Let $P$ be a Borel probability measure on $\mathbb R$ such that $P = \frac 12 P\circ S_1^{-1}+\frac 12 P\circ S_2^{-1},$ where $S_1$ and $S_2$ are two contractive similarity mappings given by $S_1(x) = rx$ and $S_2(x) = rx+1-r$ for $0<r<\frac 12$ and $x∈ \mathbb R$. Then, $P$ is supported on the Cantor set generated by $S_1$ and $S_2$. The case $r = \frac 13$ was treated by Graf and Luschgy who gave an exact formula for the unique optimal quantization of the Cantor distribution $P$ (Math. Nachr., 183 (1997), 113-133). In this paper, we compute the precise range of $r$-values to which Graf-Luschgy formula extends.

Full-Duplex Relaying With Quantize-Map-and-Forward

The quantize-map-and-forward (QMF) has been recently proved to achieve the capacity of arbitrary networks within a bounded gap and optimal diversity-multiplex tradeoff performance. This paper investigates and analyzes the QMF for the full-duplex (FD) relaying. Different from previous works, the relay has no access to any instantaneous channel state information (CSI), and only the statistical CSI of all channels is available. A closed-form expression for the outage probability is then derived. Due to the non-smoothness of the resulting expression, an approximate one with the smooth outage performance is further given. However, the resulting one is non-convex in general, and four suboptimal solutions of the quantizer design are derived. For comparison, the FD relaying with hybrid QMF/decode-and-forward is also studied. Besides, when the direct transmission (DT) is not available in both schemes, outage probability analysis and optimal quantizer design are also investigated. Simulation results demonstrate the correctness and tightness of the derived closed-form expressions for outage probabilities and close-to-optimal performance of the suboptimal quantizer design with DT.

Optimal Quantizers for Some Absolutely Continuous Probability Measures

The representation of a given quantity with less information is often referred to as ‘quantization’ and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit discs, squares, and the real line. For these probability measures the optimal sets of \(n\)-means and the \(n\)th quantization errors are calculated for some positive integers \(n\).

Optimal Quantization Scheme for Data-Efficient Target Tracking via UWSNs Using Quantized Measurements.

Target tracking is one of the broad applications of underwater wireless sensor networks (UWSNs). However, as a result of the temporal and spatial variability of acoustic channels, underwater acoustic communications suffer from an extremely limited bandwidth. In order to reduce network congestion, it is important to shorten the length of the data transmitted from local sensors to the fusion center by quantization. Although quantization can reduce bandwidth cost, it also brings about bad tracking performance as a result of information loss after quantization. To solve this problem, this paper proposes an optimal quantization-based target tracking scheme. It improves the tracking performance of low-bit quantized measurements by minimizing the additional covariance caused by quantization. The simulation demonstrates that our scheme performs much better than the conventional uniform quantization-based target tracking scheme and the increment of the data length affects our scheme only a little. Its tracking performance improves by only 4.4% from 2- to 3-bit, which means our scheme weakly depends on the number of data bits. Moreover, our scheme also weakly depends on the number of participate sensors, and it can work well in sparse sensor networks. In a sensor network, compared with sensor networks, the number of participant sensors increases by 334.92%, while the tracking accuracy using 1-bit quantized measurements improves by only 50.77%. Overall, our optimal quantization-based target tracking scheme can achieve the pursuit of data-efficiency, which fits the requirements of low-bandwidth UWSNs.

Optimizing the image R/D coding performance by tuning quantization parameters

Uniform quantization schemas with dead zone are widely used in image and video codecs. The design of these quantizers affects to the final R/D performance, being two of the quantizer parameters the responsible for that variations: the dead zone size and the reconstruction point location inside each quantization step. In this work we tune the quantizer to obtain the optimum quantization parameters that provide the best R/D behavior for different quality metrics and rate ranges. Based on a representative image set, we provide the quantization parameters to encode general imagery, with a R/D performance close to the optimum one. The same study was done including the Contrast Sensitivity Function in the quantization stage. After an exhaustive experimental test, the results show that the estimated quantization parameters are able to provide bit rate savings up to 11% at low and moderate bit rates without additional computational cost.

Robust tracking of respiratory rate in high-dynamic range scenes using mobile thermal imaging.

The ability to monitor the respiratory rate, one of the vital signs, is extremely important for the medical treatment, healthcare and fitness sectors. In many situations, mobile methods, which allow users to undertake everyday activities, are required. However, current monitoring systems can be obtrusive, requiring users to wear respiration belts or nasal probes. Alternatively, contactless digital image sensor based remote-photoplethysmography (PPG) can be used. However, remote PPG requires an ambient source of light, and does not work properly in dark places or under varying lighting conditions. Recent advances in thermographic systems have shrunk their size, weight and cost, to the point where it is possible to create smart-phone based respiration rate monitoring devices that are not affected by lighting conditions. However, mobile thermal imaging is challenged in scenes with high thermal dynamic ranges (e.g. due to the different environmental temperature distributions indoors and outdoors). This challenge is further amplified by general problems such as motion artifacts and low spatial resolution, leading to unreliable breathing signals. In this paper, we propose a novel and robust approach for respiration tracking which compensates for the negative effects of variations in the ambient temperature and motion artifacts and can accurately extract breathing rates in highly dynamic thermal scenes. The approach is based on tracking the nostril of the user and using local temperature variations to infer inhalation and exhalation cycles. It has three main contributions. The first is a novel Optimal Quantization technique which adaptively constructs a color mapping of absolute temperature to improve segmentation, classification and tracking. The second is the Thermal Gradient Flow method that computes thermal gradient magnitude maps to enhance the accuracy of the nostril region tracking. Finally, we introduce the Thermal Voxel method to increase the reliability of the captured respiration signals compared to the traditional averaging method. We demonstrate the extreme robustness of our system to track the nostril-region and measure the respiratory rate by evaluating it during controlled respiration exercises in high thermal dynamic scenes (e.g. strong correlation (r = 0.9987) with the ground truth from the respiration-belt sensor). We also demonstrate how our algorithm outperformed standard algorithms in settings with different amounts of environmental thermal changes and human motion. We open the tracked ROI sequences of the datasets collected for these studies (i.e. under both controlled and unconstrained real-world settings) to the community to foster work in this area.

On the Minimum Average Distortion of Quantizers With Index-Dependent Distortion Measures

In many applications, one is interested in optimally deploying a network of unidentical agents to a certain area of interest; examples include heterogeneous sensor networks and cellular networks. Such deployment problems can equivalently be formulated as quantizer design problems, where different distortion measures should be associated with different quantization indices. In this paper, we consider the case where the distortion measure is the $r$ th power $(r\geq 1)$ of the distance between the reproduction point and the source sample weighted by a factor that varies from one index to another. For a uniform distribution of source samples, we determine the corresponding optimal scalar quantizers and their average distortions. For nonuniform distributions and vector quantization, we provide a high-resolution analysis of the minimum possible average distortion. Applications to sensor and cellular networks are also discussed together with numerical design examples.

Secret Key Generation Based on Estimated Channel State Information for TDD-OFDM Systems Over Fading Channels

One of the fundamental problems in cryptography is the generation of a common secret key between two legitimate parties to prevent eavesdropping. In this paper, we propose an information-theoretic secret key generation (SKG) method for time division duplexing (TDD)-based orthogonal frequency-division multiplexing (OFDM) systems over multipath fading channels. By exploring physical layer properties of the wireless medium, i.e., the reciprocity, randomness, and privacy features of the radio channel, an SKG method is proposed to maximize the number of secret bits given a target secret key disagreement ratio (SKDR). In the proposed SKG method, the phase information of the estimated channel state information (CSI) is distilled for SKG, and a special guard band (GB) scheme is designed to achieve the target SKDR with a small phase information loss. The proposed GB consists of both the amplitude GB (AGB) and phase GB (PGB), where the AGB is determined by the average signal-to-interference plus noise ratio (SINR), whereas the PGB adapts itself to the instantaneous SINR and thus incurs a smaller phase information loss in the higher SINR region. Analyses show that this GB scheme trades off a small loss of channel phase information for a better SKDR performance, and achieves a much larger number of quantization levels for a given SKDR due to the fact that the PGB decreases quickly as the SINR increases. Based on the performance analysis on the SKDR, the average secret key length, the phase information loss percentage (PILP), and the optimal GB and quantization level of the adaptive quantizor are derived for a given target SKDR. Both analytical and simulation results are presented to demonstrate the superiority of the proposed scheme for TDD-OFDM systems over frequency-selective fading channels.

Adaptive Gradient Information and BFGS Based Inter Frame Rate Control for High Efficiency Video Coding

In order to meet the emerging demands of high-fidelity video services, a new video coding standard — High Efficiency Video Coding (HEVC) is developed to improve the compression performance of high definition (HD) videos and save half of the bitrate for the same perceptual video quality compared with H.264/Advanced Video Coding (AVC). Rate control still plays a significant role in HD video data transmission via the communication channel. However, R-lambda model based HEVC rate control algorithm does not take the relationship between the encoding complexity and Human Visual System (HVS) into account, what’s more, the convergence speed of Least Mean Square (LMS) algorithm is slow. In this paper, an adaptive gradient information and Broyden Fletcher Goldfarb Shanno (BFGS) based R-lambda model (GBRL) is proposed for the inter frame rate control, where the gradient based on Sobel operator can effectively measure the frame-content complexity and BFGS algorithm converges speedily than LMS algorithm. Experimental results show that the proposed GBRL method can achieve bitrate error reduction and peak signal to noise ratio (PSNR) improvement especially for the sequences with large motion, compared to the state-of-the-art rate control methods. In addition, if the optimal initial quantization parameter (QP) prediction model based on linear regression can be incorporated into the proposed GBRL method, the performance of rate control can be further improved.

Quantized feedback scheduling for MIMO-OFDM broadcast networks with subcarrier clustering

Feedback of user channel quality information (CQI) to base station (BS) is essential for efficient scheduling of multi-user (MU) multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) broadcast networks. This feedback overload increases linearly with the cardinality of users, transmit antennas and subcarriers present in MIMO-OFDM systems. Hence, clustering of adjacent subcarriers has been considered in literature for reduction in feedback load. Here users communicate the CQI of the center subcarrier of the clusters assuming that subcarriers of a cluster experience similar channel conditions. However, this method leads to inefficient resource scheduling for higher cluster sizes as it does not take advantage of CQI of other subcarriers that experience non-uniform channel conditions. This reason motivated us to develop a new limited feedback scheduling scheme where quantization of CQI with multiple bits is implemented along with clustering of adjacent subcarriers. In this scheme, the multi-bit quantized CQI of all the subcarriers of a cluster are examined for the efficient scheduling along with further reduction in the feedback overhead. Moreover, we proposed a less time consuming method to find the optimum quantization thresholds that play significant role in multi-bit quantization process by using genetic algorithm (GA). This GA methodology is computationally more efficient than exhaustive search process.

Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering

We take advantage of recent (see Graf et al., 2008; Pages and Wilbertz, 2012) and new results on optimal quantization theory to improve the quadratic optimal quantization error bounds for backward stochastic differential equations (BSDE) and nonlinear filtering problems. For both problems, a first improvement relies on a Pythagoras like Theorem for quantized conditional expectation. While allowing for some locally Lipschitz continuous conditional densities in nonlinear filtering, the analysis of the error brings into play a new robustness result about optimal quantizers, the so-called distortion mismatch property: the Ls-mean quantization error induced by Lr-optimal quantizers of size N converges at the same rate N−1d for every s∈(0,r+d).

SINGLE VERSUS MULTIPLE TRIAL VECTORS IN CLASSICAL DIFFERENTIAL EVOLUTION FOR OPTIMIZING THE QUANTIZATION TABLE IN JPEG BASELINE ALGORITHM

Quantization Table is responsible for compression / quality trade-off in baseline Joint Photographic Experts Group (JPEG) algorithm and therefore it is viewed as an optimization problem. In the literature, it has been found that Classical Differential Evolution (CDE) is a promising algorithm to generate the optimal quantization table. However, the searching capability of CDE could be limited due to generation of single trial vector in an iteration which in turn reduces the convergence speed. This paper studies the performance of CDE by employing multiple trial vectors in a single iteration. An extensive performance analysis has been made between CDE and CDE with multiple trial vectors in terms of Optimization process, accuracy, convergence speed and reliability. The analysis report reveals that CDE with multiple trial vectors improves the convergence speed of CDE and the same is confirmed using a statistical hypothesis test (t-test).

Quantization and centroidal Voronoi tessellations for probability measures on dyadic Cantor sets

Quantization of a probability distribution is the process of estimating a given probability by a discrete probability that assumes only a finite number of levels in its support. Centroidal Voronoi tessellations (CVT) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions. In this paper, we investigate the optimal quantization and the centroidal Voronoi tessellations with n generators for a Borel probability measure P on \mathbb R supported by a dyadic Cantor set generated by two self-similar mappings with similarity ratios r , where 0 < r \leq \frac{5-\sqrt{17}}2 .

Hybrid Laplace Distribution-Based Low Complexity Rate-Distortion Optimized Quantization.

Rate distortion optimized quantization (RDOQ) is an efficient encoder optimization method that plays an important role in improving the rate-distortion (RD) performance of the high-efficiency video coding (HEVC) codecs. However, the superior performance of RDOQ is achieved at the expense of high computational complexity cost in two stages RD minimization, including the determination of optimal quantized level among available candidates for each transformed coefficient and the determination of best quantized coefficients for transform units with the minimum total cost, to softly optimize the quantized coefficients. To reduce the computational cost of the RDOQ algorithm in HEVC, we propose a low-complexity RDOQ scheme by modeling the statistics of the transform coefficients with hybrid Laplace distribution. In this manner, specifically designed block level rate and distortion models are established based on the coefficient distribution. Therefore, the optimal quantization levels can be directly determined by optimizing the RD performance of the whole block, while the complicated RD cost calculations can be eventually avoided. Extensive experimental results show that with about 0.3%-0.4% RD performance degradation, the proposed low-complexity RDOQ algorithm is able to reduce around 70% quantization time with up to 17% total encoding time reduction compared with the original RDOQ implementation in HEVC on average.

FEATURE VECTOR CONSTRUCTION METHOD FOR IRIS RECOGNITION

Abstract. One of the basic stages of iris recognition pipeline is iris feature vector construction procedure. The procedure represents the extraction of iris texture information relevant to its subsequent comparison. Thorough investigation of feature vectors obtained from iris showed that not all the vector elements are equally relevant. There are two characteristics which determine the vector element utility: fragility and discriminability. Conventional iris feature extraction methods consider the concept of fragility as the feature vector instability without respect to the nature of such instability appearance. This work separates sources of the instability into natural and encodinginduced which helps deeply investigate each source of instability independently. According to the separation concept, a novel approach of iris feature vector construction is proposed. The approach consists of two steps: iris feature extraction using Gabor filtering with optimal parameters and quantization with separated preliminary optimized fragility thresholds. The proposed method has been tested on two different datasets of iris images captured under changing environmental conditions. The testing results show that the proposed method surpasses all the methods considered as a prior art by recognition accuracy on both datasets.

Robust image authentication via locality sensitive hashing with core alignment

Robust image hashing is a promising technique to represent image’s perceptual content. However, when it comes to image authentication, tradeoff between robustness and discrimination is a non-negligible issue. The allowed content preserving operations and sensitive malicious manipulations on images are quite subjective to human’s perception. So it needs tactics to design good hashing methods. In this paper we incorporate the novel concept of core alignment into hashing, where the proposed core alignment improves the performances of balance. First, we formulize the hashing as a supervised minimal optimization problem based on Locality Sensitive Hashing, in which p-stable distribution is exploited to maintain high dimensional locality features. Then we solve this problem by two sub-optimization problems, i.e., searching for optimal shift and searching for optimal quantization intervals. By using particle swarm optimization and simulated annealing programming approaches we develop two stochastic solutions to those two problems, respectively. Experimental results show that our proposed hashing optimizations can find optimal solutions with limited steps, and the hashing method is superior to other state-of-the-art methods in terms of authentication and robustness.

Reception power quantization–based emergency message vehicle-to-vehicle multihop broadcast transmission scheme for vehicle accident prevention

In this article, an emergency message reception power quantization–based time-slot broadcast scheme is proposed for vehicle-to-vehicle multihop communications. The power quantization–based time-slot broadcast scheme derives the optimal reception power quantization size such that time-slot assignments can be made to minimize the average time delay to support quick multihop emergency message broadcasting. The mathematical and simulation performance analysis demonstrates that the proposed power quantization–based time-slot broadcast protocol can reduce the average time delay when compared to the infrastructure-less framework, binary-partition-assisted broadcast, and the trinary-partitioned black-burst-based broadcast schemes.

Optimal Input and Quantization Interval for Quantized Feedback System With Variable Quantizer

Networked control systems (NCSs) have received much attention in the field of robot teleoperation, telesurgery, and other applications. In an NCS, it is important to compress data transmitted over a limited communication network while preserving the data required for control. We address a quantized feedback system in which the output of a plant is quantized with a variable quantization interval. For such a system, we present a novel optimal quantized feedback control. The proposed approach derives not only an optimal input, but also an optimal quantization interval in the quantizer simultaneously using the model predictive control. The approach also satisfies constraints on the state, input, and quantization interval. The effectiveness of the proposed approach is validated through cart-positioning experiments.