Quantization Error Reduction Research Articles

A Systematic Literature Review on Binary Neural Networks

This paper presents an extensive literature review on Binary Neural Network (BNN). BNN utilizes binary weights and activation function parameters to substitute the full-precision values. In digital implementations, BNN replaces the complex calculations of Convolutional Neural Networks (CNNs) with simple bitwise operations. BNN optimizes large computation and memory storage requirements, which leads to less area and power consumption compared to full-precision models. Although there are many advantages of BNN, the binarization process has a significant impact on the performance and accuracy of the generated models. To reflect the state-of-the-art in BNN and explore how to develop and improve BNN-based models, we conduct a systematic literature review on BNN with data extracted from 239 research studies. Our review discusses various BNN architectures and the optimization approaches developed to improve their performance. There are three main research directions in BNN: accuracy optimization, compression optimization, and acceleration optimization. The accuracy optimization approaches include quantization error reduction, special regularization, gradient error minimization, and network structure. The compression optimization approaches combine fractional BNN and pruning. The acceleration optimization approaches comprise computing in-memory, FPGA-based implementations, and ASIC-based implementations. At the end of our review, we present a comprehensive analysis of BNN applications and their evaluation metrics. Also, we shed some light on the most common BNN challenges and the future research trends of BNN.

3D reconstruction accuracy improvement of a stereo vision system by changing the convergence angle of the cameras

Stereo vision systems are commonly used for 3D depth reconstruction. The measurement accuracy of these scanners is affected by the quantization error caused by the camera sensors. In this paper, the effect of changing the convergence angle of the cameras on the quantization uncertainty is discussed. First, the mathematical model of a stereo vision scanner with the ability to adjust the convergence angle is introduced. Then, the effect of changing the convergence angle on the quantization error reduction is investigated. Finally, physical experiments are designed to validate the proposed approach. The experimental results show that the 3D reconstruction accuracy can be improved by changing the convergence angle of the cameras.

Reduction of quantization error in position encoders

The paper describes estimate of the quantization error of a real position encoder taking into account the factors specified above, and the method of minimization of this error by an additional adjustment of the scale is proposed.

Quantized measurements in Q-learning based model-free optimal control

Quantization noise is present in many real-time applications due to the resolution of analog-to-digital conversions. This can lead to error in policies that are learned by model-free Q-learning. A method for quantization error reduction for Q-learning algorithms is developed using the sample time and an exploration noise that is added to the control input. The method is illustrated with discrete-time policy and value iteration algorithms using both a simulated environment and a real-time physical system.

Non-linear quantization error reduction for the temperature measurement subsystem on-board LISA Pathfinder.

Laser Interferometer Space Antenna (LISA) Pathfinder is a mission to test the technology enabling gravitational wave detection in space and to demonstrate that sub-femto-g free fall levels are possible. To do so, the distance between two free falling test masses is measured to unprecedented sensitivity by means of laser interferometry. Temperature fluctuations are one of the noise sources limiting the free fall accuracy and the interferometer performance and need to be known at the ∼10 μK Hz-1/2 level in the sub-millihertz frequency range in order to validate the noise models for the future space-based gravitational wave detector LISA. The temperature measurement subsystem on LISA Pathfinder is in charge of monitoring the thermal environment at key locations with noise levels of 7.5 μK Hz-1/2 at the sub-millihertz. However, its performance worsens by one to two orders of magnitude when slowly changing temperatures are measured due to errors introduced by analog-to-digital converter non-linearities. In this paper, we present a method to reduce this effect by data post-processing. The method is applied to experimental data available from on-ground validation tests to demonstrate its performance and the potential benefit for in-flight data. The analog-to-digital converter effects are reduced by a factor between three and six in the frequencies where the errors play an important role. An average 2.7 fold noise reduction is demonstrated in the 0.3 mHz-2 mHz band.

Quantization-based hashing: a general framework for scalable image and video retrieval

Nowadays, due to the exponential growth of user generated images and videos, there is an increasing interest in learning-based hashing methods. In computer vision, the hash functions are learned in such a way that the hash codes can preserve essential properties of the original space (or label information). Then the Hamming distance of the hash codes can approximate the data similarity. On the other hand, vector quantization methods quantize the data into different clusters based on the criteria of minimal quantization error, and then perform the search using look-up tables. While hashing methods using Hamming distance can achieve faster search speed, their accuracy is often outperformed by quantization methods with the same code length, due to the low quantization error and more flexible distance lookups. To improve the effectiveness of the hashing methods, in this work, we propose Quantization-based Hashing (QBH), a general framework which incorporates the advantages of quantization error reduction methods into conventional property preserving hashing methods. The learned hash codes simultaneously preserve the properties in the original space and reduce the quantization error, and thus can achieve better performance. Furthermore, the hash functions and a quantizer can be jointly learned and iteratively updated in a unified framework, which can be readily used to generate hash codes or quantize new data points. Importantly, QBH is a generic framework that can be integrated to different property preserving hashing methods and quantization strategies, and we apply QBH to both unsupervised and supervised hashing models as showcases in this paper. Experimental results on three large-scale unlabeled datasets (i.e., SIFT1M, GIST1M, and SIFT1B), three labeled datastes (i.e., ESPGAME, IAPRTC and MIRFLICKR) and one video dataset (UQ_VIDEO) demonstrate the superior performance of our QBH over existing unsupervised and supervised hashing methods.

Reduction of Quantization Error in Multirate Output Feedback Control

[abstFig src='/00280005/04.jpg' width='250' text='Multirate output feedback control' ] In the new design method we propose for a multirate output feedback control system, the hold interval of control input is longer than the sampling interval of plant output. In this system, unknown state variables are calculated using control input and plant output without observers. The multirate output feedback control system has been extended by introducing new design parameters that are designed independent of the calculation of the state variable. To our knowledge, however, no systematic design scheme has ever been proposed for design parameters in this case. In this study, quantization error is dealt with statistically and design parameters are decided to minimize quantization error.

조명과 해상도에 강인한 자동 결함 검사를 위한 향상된 히스토그램 정합 방법

Machine vision inspection systems have replaced human inspectors in defect inspection fields for several decades. However, the inspection results of machine vision are often affected by small changes of illumination. When small changes of illumination appear in image histograms, the influence of illumination can be decreased by transformation of the histogram. In this paper, we propose an enhanced histogram matching algorithm which corrects distorted histograms by variations of illumination. We use the resolution resizing method for an optimal matching of input and reference histograms and reduction of quantization errors from the digitizing process. The proposed algorithm aims not only for improvement of the accuracy of defect detection, but also robustness against variations of illumination in machine vision inspection. The experimental results show that the proposed method maintains uniform inspection error rates under dramatic illumination changes whereas the conventional inspection method reveals inconsistent inspection results in the same illumination conditions.

Method for suppressing the quantization error of Newton’s rings fringe pattern

Newton’s rings fringe pattern is often encountered in optical measurement. The digital processing of the fringe pattern is widely used to enable automatic analysis and improve the accuracy and flexibility. Before digital processing, sampling and quantization are necessary, which introduce quantization errors in the fringe pattern. Quantization errors are always analyzed and suppressed in the Fourier transform (FT) domain. But Newton’s rings fringe pattern is demonstrated to be a two-dimensional chirp signal, and the traditional methods based on the FT domain are not efficient when suppressing quantization errors in such signals with large bandwidth as chirp signals. This paper proposes a method for suppressing quantization errors in the fractional Fourier transform (FRFT) domain, for chirp signals occupies little bandwidth in the FRFT domain. This method has better effect on reduction of quantization errors in the fringe pattern than traditional methods. As an example, a standard Newton’s rings fringe pattern is analyzed in the FRFT domain and then 8.5 dB of improvement in signal-to-quantization-noise ratio and about 1.4 bits of increase in accuracy are obtained compared to the case of the FT domain. Consequently, the image quality of Newton’s rings fringe pattern is improved, which is beneficial to optical metrology.

An Improved Quantization Scheme for Lattice-Reduction Aided MIMO Detection Based on Gram-Schmidt Orthogonalization

Lattice-reduction (LR) technique has been adopted to improve the performance and reduce the complexity in MIMO data detection. This paper presents an improved quantization scheme for LR aided MIMO detection based on Gram-Schmidt orthogonalization. For the LR aided detection, the quantization step applies the simple rounding operation, which often leads to the quantization errors. Meanwhile, these errors may result in the detection errors. Hence the purpose of the proposed detection is to further solve the problem of degrading the performance due to the quantization errors in the signal estimation. In this paper, the proposed quantization scheme decreases the quantization errors using a simple tree search with a threshold function. Through the analysis and the simulation results, we observe that the proposed detection can achieve the nearly optimal performance with very low complexity, and require a little additional complexity compared to the conventional LR-MMSE detection in the high Eb/N0 region. Furthermore, this quantization error reduction scheme is also efficient even for the high modulation order.

Quantization error reduction for MIMO detection based on orthogonal lattices

Quantization error reduction for MIMO detection based on orthogonal lattices

A Multi-User MIMO Downlink Receiver and Quantizer Design Based on SINR Optimization

In a quantization based multiuser multiple-input/multiple-output (MU-MIMO) broadcast channel, the effective channel gain (i.e., the norm of a channel vector obtained from the receive combiner) needs to be considered in addition to a reduction of quantization errors for maximizing the signal-to-interference plus noise ratio (SINR). In this work, we prove that the effective channel gains in the space limited by an N_R x M_T MIMO channel form a min(M_T,N_R)-dimensional ellipsoid in the channel space. Utilizing the geometric proof, the achievable effective channel gain is derived as a function of its direction for a given MIMO channel. Based on the derivation, we finally propose a quantization vector selection criterion and an optimal receive combiner to maximize the SINR. The proposed maximum SINR based combining (MSC) is proven to be a better solution for maximizing the SINR compared to quantization based combining (QBC) and maximum gain based combining (MGC), each of which attempts to minimize quantization errors and maximize the effective channel gain.

Continuous state/action reinforcement learning: A growing self-organizing map approach

This paper proposes an algorithm to deal with continuous state/action space in the reinforcement learning (RL) problem. Extensive studies have been done to solve the continuous state RL problems, but more research should be carried out for RL problems with continuous action spaces. Due to non-stationary, very large size, and continuous nature of RL problems, the proposed algorithm uses two growing self-organizing maps (GSOM) to elegantly approximate the state/action space through addition and deletion of neurons. It has been demonstrated that GSOM has a better performance in topology preservation, quantization error reduction, and non-stationary distribution approximation than the standard SOM. The novel algorithm proposed in this paper attempts to simultaneously find the best representation for the state space, accurate estimation of Q-values, and appropriate representation for highly rewarded regions in the action space. Experimental results on delayed reward, non-stationary, and large-scale problems demonstrate very satisfactory performance of the proposed algorithm.

Reduction of quantization errors caused by dynamic LCD backlight scaling

Dynamic backlight scaling (DBS), a technique for LCD power reduction, often deteriorates image quality because of a flicker (unintended temporal variation of the luminance) generated in the frame at which the backlight level changes. This paper proposes a novel DBS algorithm to reduce the flicker by decreasing the quantization errors (QEs) that are created in the multiplication of the input gray level and the DBS scaling ratio as well as in the mapping of the multiplication result to an integer gray level. The proposed DBS algorithm reduces the QE down to 28.8% when compared with the conventional DBS algorithm.

Quantization Error Reduction for the Phased Array with 2-bit Phase Shifter

It has been widely believed that phased array antenna should use at least 3-bit (as phase controlling bit) phase shifter to provide the satisfactory scanning capability and the unnoticeable parasit...

Quantization Error Reduction in the Measurement of Fourier Intensity for Phase Retrieval

The quantization error in the measurement of Fourier intensity for phase retrieval is discussed and a multispectra method is proposed to reduce this error. The Fourier modulus used for phase retrieval is usually obtained by measuring Fourier intensity with a digital device. Therefore, quantization error in the measurement of Fourier intensity leads to an error in the reconstructed object when iterative Fourier transform algorithms are used. The multispectra method uses several Fourier intensity distributions for a number of measurement ranges to generate a Fourier intensity distribution with a low quantization error. Simulations show that the multispectra method is effective in retrieving objects with real or complex distributions when the iterative hybrid input-output algorithm (HIO) is used.

4713615 Quantization error reduction method for phase encode gradient in NMR imaging

In an improved NMR imaging method, where three-nominally orthogonal gradient fields are generated, the quantization error of the phase encode gradient is reduced without the necessity of a digital to analog converter of higher bit capacity. This is accomplished in one embodiment by providing a second smaller gradient waveform which is relatively narrow compared to the primary gradient waveform, the ratio of the waveforms being proportional to the improved resolution. The second waveform can occur either before or after the 180° excitation pulse used to produce a spin-echo signal. In another embodiment pulse width modulation is used to vary the area of the phase encode waveform in discrete increments.

An adaptive approach for the reduction of quantization errors

This paper presents an adaptive quantization scheme for the reduction of the percentage error in the output of the quantizer. The improvement in the system performance is illustrated by simulating a uniform step and an adaptive quantizer on a digital computer and comparing their outputs. A significant improvement in the output is achieved by using the suggested scheme.