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An all digital implementation of a modified Hamming net for video compression with prediction and quantization circuits

The hardware and algorithms used to vector quantize (VQ) predicted pixel intensity differences for real-time video compression are described. The hardware is designed for rapid vector quantization performance, which entails the development of application-specific associative memory circuits. A modified DPCM algorithm is originally examined to determine how neural circuitry could enhance its operation. It was determined that quantization and encoding could be improved by consolidating these two functions into one, and by increasing the amount of information (i.e. number of pixels) quantized at a time. The result is a predictive scheme that vector quantizes differential values. Some of the disadvantages of VQ algorithms are solved using associative memories. The video compression algorithm and the associative memory design are described.

Kaul, Richard

Weighted MinMax Algorithm for Color Image Quantization

The maximum intercluster distance and the maximum quantization error that are minimized by the MinMax algorithm are shown to be inappropriate error measures for color image quantization. A fast and effective (improves image quality) method for generalizing activity weighting to any histogram-based color quantization algorithm is presented. A new non-hierarchical color quantization technique called weighted MinMax that is a hybrid between the MinMax and Linde-Buzo-Gray (LBG) algorithms is also described. The weighted MinMax algorithm incorporates activity weighting and seeks to minimize WRMSE, whereby obtaining high quality quantized images with significantly less visual distortion than the MinMax algorithm.

Reitan, Paula J.

From Quantum Time to Manifestly Covariant QFT: On the Need for a Quantum-Action-Based Quantization

In quantum time (QT) schemes, time is promoted to a degree of freedom, allowing Lorentz covariance to be made explicit for single particles. We ask whether this can be lifted to QFT so that Lorentz covariance becomes manifest at the Hilbert-space level, rather than being hidden as in the standard canonical formulation. We address this question by proposing a second-quantized approach in which the elementary particle is the QT particle itself, leading naturally to the notion of spacetime field algebras and of quantum action. We show, however, that a naive many-body construction runs into inconsistencies. To pinpoint their origin we introduce a classical counterpart of the second-quantized formalism, spacetime classical mechanics (SCM), and prove a no-go theorem: Dirac quantization of SCM collapses back to standard QFT and therefore hides covariance. We circumvent this problem by presenting a quantum-action-based quantization that yields a spacetime version of quantum mechanics (SQM), making covariance manifest for (interacting) QFTs. Finally, we show that this resolution is tied to a genuine spacetime generalization of the notion of a quantum state, required by causality and closely connected to recent “states over time” proposals and, in dS/CFT–motivated settings, to microscopic notions of timelike entanglement and emergent time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Uniform quantizers for noisy channels

We consider optimum uniform data quantization for noisy channels. We present a general formulation for natural encoding that results in simple expressions for the mean-square error. Specifically, we show that the optimum location of the center of the quantizer is at the mean of the distribution for all error rates. The optimum levels for quantization and the corresponding mean-square error are presented for Gaussian and uniform data. For the latter the width of the optimum quantizer for noisy channels is shown to be smaller than the entire range of probability distribution.

Murthy, B. R. N.

The effects of quantization on signal processing

Typically an analog signal from a space system is sampled, quantized by Analog-to-Digital (A/D) conversion, merged into a bit stream, communicated to a ground station, received by the ground station, and processed by the ground station to extract useful information for dissemination to the users. The cost of each of these steps is reduced as the number of quantization steps is reduced in the A/D converter. The number of quantization steps should be as small as possible without losing the required information content. This report deals specifically with the accuracy of averages as a function of the number of quantized samples used to compute the averages with the noise on the analog signal as a parameter. For example, the success of the Visible Infrared Spin Scan Radiometer (VISSR) Atmospheric Sounder (VAS) Demonstration depends upon temporally averaging multiple samples in an effort to reduce noise to a sufficiently low level such that temperature profile sounding is made possible. A tutorial description of this process is presented.

Montgomery, H. E.

Improving the performance of soft decision Viterbi decoding in a non-Gaussian environment through non-linear quantization

The performance of Viterbi decoding in a non-Gaussian environment is investigated using a nonlinear quantization strategy. The channel model consists of a convolutionally encoded BPSK signal transmitted to a satellite where it is corrupted with additive white Gaussian noise and pulsed radio frequency interference (RFI). The resultant signal is then passed through a satellite nonlinearity and transmitted to a ground station where it is coherently detected. Interleaving is assumed in order to make the channel memoryless. The presence of RFI makes the channel statistics non-Gaussian, leading to a nonlinear log-likelihood function. A near optimum quantization scheme is found by maximizing a channel parameter, or by matching the quantizer to the log-likelihood function in a mean square error sense. Bit error rate performance improvement is achieved by using such nonlinear quantization.

Mcgregor, D. N.

An adaptive vector quantization scheme

Vector quantization is known to be an effective compression scheme to achieve a low bit rate so as to minimize communication channel bandwidth and also to reduce digital memory storage while maintaining the necessary fidelity of the data. However, the large number of computations required in vector quantizers has been a handicap in using vector quantization for low-rate source coding. An adaptive vector quantization algorithm is introduced that is inherently suitable for simple hardware implementation because it has a simple architecture. It allows fast encoding and decoding because it requires only addition and subtraction operations.

Cheung, K.-M.

A hybrid LBG/lattice vector quantizer for high quality image coding

It is well known that a vector quantizer is an efficient coder offering a good trade-off between quantization distortion and bit rate. The performance of a vector quantizer asymptotically approaches the optimum bound with increasing dimensionality. A vector quantized image suffers from the following types of degradations: (1) edge regions in the coded image contain staircase effects, (2) quasi-constant or slowly varying regions suffer from contouring effects, and (3) textured regions lose details and suffer from granular noise. All three of these degradations are due to the finite size of the code book, the distortion measures used in the design, and due to the finite training procedure involved in the construction of the code book. In this paper, we present an adaptive technique which attempts to ameliorate the edge distortion and contouring effects.

Ramamoorthy, V.

A constrained joint source/channel coder design and vector quantization of nonstationary sources

The emergence of broadband ISDN as the network for the future brings with it the promise of integration of all proposed services in a flexible environment. In order to achieve this flexibility, asynchronous transfer mode (ATM) has been proposed as the transfer technique. During this period a study was conducted on the bridging of network transmission performance and video coding. The successful transmission of variable bit rate video over ATM networks relies on the interaction between the video coding algorithm and the ATM networks. Two aspects of networks that determine the efficiency of video transmission are the resource allocation algorithm and the congestion control algorithm. These are explained in this report. Vector quantization (VQ) is one of the more popular compression techniques to appear in the last twenty years. Numerous compression techniques, which incorporate VQ, have been proposed. While the LBG VQ provides excellent compression, there are also several drawbacks to the use of the LBG quantizers including search complexity and memory requirements, and a mismatch between the codebook and the inputs. The latter mainly stems from the fact that the VQ is generally designed for a specific rate and a specific class of inputs. In this work, an adaptive technique is proposed for vector quantization of images and video sequences. This technique is an extension of the recursively indexed scalar quantization (RISQ) algorithm.

Sayood, Khalid

Image-adapted visually weighted quantization matrices for digital image compression

A method for performing image compression that eliminates redundant and invisible image components is presented. The image compression uses a Discrete Cosine Transform (DCT) and each DCT coefficient yielded by the transform is quantized by an entry in a quantization matrix which determines the perceived image quality and the bit rate of the image being compressed. The present invention adapts or customizes the quantization matrix to the image being compressed. The quantization matrix comprises visual masking by luminance and contrast techniques and by an error pooling technique all resulting in a minimum perceptual error for any given bit rate, or minimum bit rate for a given perceptual error.

Watson, Andrew B.

Cascade Error Projection with Low Bit Weight Quantization for High Order Correlation Data

In this paper, we reinvestigate the solution for chaotic time series prediction problem using neural network approach. The nature of this problem is such that the data sequences are never repeated, but they are rather in chaotic region. However, these data sequences are correlated between past, present, and future data in high order. We use Cascade Error Projection (CEP) learning algorithm to capture the high order correlation between past and present data to predict a future data using limited weight quantization constraints. This will help to predict a future information that will provide us better estimation in time for intelligent control system. In our earlier work, it has been shown that CEP can sufficiently learn 5-8 bit parity problem with 4- or more bits, and color segmentation problem with 7- or more bits of weight quantization. In this paper, we demonstrate that chaotic time series can be learned and generalized well with as low as 4-bit weight quantization using round-off and truncation techniques. The results show that generalization feature will suffer less as more bit weight quantization is available and error surfaces with the round-off technique are more symmetric around zero than error surfaces with the truncation technique. This study suggests that CEP is an implementable learning technique for hardware consideration.

Duong, Tuan A.

Perceptual Optimization of DCT Color Quantization Matrices

Many image compression schemes employ a block Discrete Cosine Transform (DCT) and uniform quantization. Acceptable rate/distortion performance depends upon proper design of the quantization matrix. In previous work, we showed how to use a model of the visibility of DCT basis functions to design quantization matrices for arbitrary display resolutions and color spaces. Subsequently, we showed how to optimize greyscale quantization matrices for individual images, for optimal rate/perceptual distortion performance. Here we describe extensions of this optimization algorithm to color images.

Watson, Andrew B.

Optimum quantization

Design of optimum quantizers for quantizer-input message signal and quantizer-input message signal contaminated by noise

SIGNAL NOISE

Effects of Landau quantization on neutrino emission and absorption

Some neutron stars known as magnetars possess very strong magnetic fields, with surface fields as large as 10 15 G and internal fields that are possibly stronger. Recent observations of the radio pulsar GLEAM-X J1627 suggest it may have a surface field as strong as 10 16 G. In the presence of a strong magnetic field, Leinson and Perez showed and Baiko and Yakovlev confirmed that the energy levels of electrons and protons are quantized and the direct Urca process allows neutron stars to cool rapidly, even at low density. For the case of magnetic fields 𝐵 ≳ 10 16 G, we find features in the emissivity due to energy quantization that are not captured by the frequently employed quasiclassical approximation where energy levels are treated as nearly continuous. Resonances can result in amplification of the neutrino emissivity at specific densities compared to a calculation that neglects quantization, particularly at low temperature. These effects are not important for the thermal evolution of an entire neutron star, but may be relevant for phenomena that depend on behavior at specific densities. Here, we present a fully relativistic calculation of the direct Urca rate in a strong magnetic field using the standard V-A weak Lagrangian incorporating mean field nuclear effects and discuss approaches to the numerical challenge the modified wave functions present and a new semianalytic approximation. These tools are also applicable to calculating neutrino opacities in strong magnetic fields in the ejecta of binary neutron star mergers. We calculate the opacities for neutrinos capturing on free nucleons at subsaturation densities and temperatures exceeding an MeV. We find an enhancement to capture processes of the lowest energy neutrinos by an order of magnitude or more due to suppression of electron Pauli blocking in the case of capture on neutrons, and from the effect of the nucleon magnetic moments in the case of capture on protons.

astrophysical electromagnetic fields

Limit cycles resulting from quantization in digital control systems.

The existence of quantizer-induced limit cycles in digital control systems is a well-known phenomenon. This paper reports the results of an investigation into the discrete describing function technique which is applicable not only to the quantizer nonlinearity but also to any nonlinearity in an otherwise linear discrete system. First a general expression is developed for the discrete describing function that is applicable to any nonlinearity. The describing function is then obtained for the quantizer nonlinearity. Finally, the use of the discrete describing function is illustrated by an example of a digital control system.

Phillips, C. L.

Quantized vortices around wavefront nodes, 2

Quantized vortices can occur around nodal points in wavefunctions. The derivation depends only on the wavefunction being single valued, continuous, and having continuous first derivatives. Since the derivation does not depend upon the dynamical equations, the quantized vortices are expected to occur for many types of waves such as electromagnetic and acoustic. Such vortices have appeared in the calculations of the H + H2 molecular collisions and play a role in the chemical kinetics. In a companion paper, it is shown that quantized vortices occur when optical waves are internally reflected from the face of a prism or particle beams are reflected from potential energy barriers.

Hirschfelder, J. O.

Implementation of digital filters for minimum quantization errors

In this paper a technique is developed for choosing programing forms and bit configurations for digital filters that minimize the quantization errors. The technique applies to digital filters operating in fixed-point arithmetic in either open-loop or closed-loop systems, and is implemented by a digital computer program that is based on a digital simulation of the system. As an output the program gives the programing form required for minimum quantization errors, the total bit configuration required in the filter, and the location of the binary decimal point at each quantizer within the filter.

Phillips, C. L.

Optimal sampling and quantization of synthetic aperture radar signals

Some theoretical and experimental results on optimal sampling and quantization of synthetic aperture radar (SAR) signals are presented. It includes a description of a derived theoretical relationship between the pixel signal to noise ratio of processed SAR images and the number of quantization bits per sampled signal, assuming homogeneous extended targets. With this relationship known, a solution may be realized for the problem of optimal allocation of a fixed data bit-volume (for specified surface area and resolution criterion) between the number of samples and the number of bits per sample. The results indicate that to achieve the best possible image quality for a fixed bit rate and a given resolution criterion, one should quantize individual samples coarsely and thereby maximize the number of multiple looks. The theoretical results are then compared with simulation results obtained by processing aircraft SAR data.

Wu, C.