Visual Coding: Design of Psychovisual Quantizers

This paper describes a new methodology in the design of psychovisual quantizers for a given visual subband image coding scheme. The quantizer design needs to specify a set of decision thresholds (T_k,k= 0, . . . ,l) and reconstruction levels (L_k,k= 0, . . . ,l− 1) for which any input level lying between the thresholdsT_kandT_k+1is mapped toL_k, thekth reconstruction level. To specify the optimal quantization, psychophysical experiments based on the visibility of quantization noise have been conducted. The contrast masking function has been determined by considering complex signals, spatial frequency aspects of the quantized signals, and the spatial combination of degradations. The stimuli used have been characterized by their local band-limited contrast. With this representation, within a subband, the first important result is that the decision thresholds and the reconstruction levels of the quantization follow a linear law regardless of the importance of the contrast. From one subband to another the quantization step varies according to radial spatial frequency and orientation. In order to examine the masking effects between subbands, further experiments have been conducted and two other important results have been obtained. First, when it occurs, masking does not modify the linear behavior of the optimal quantization law. Secondly, masking is due to the adjacent angular subbands rather than the adjacent radial ones, even if a slight increase in the quantization step is observed in this last case.     

Vector Quantizers and Predictive Quantizers for Gauss-Markov Sources

Low-rate vector quantizers are designed and simulated for highly correlated Gauss-Markov sources and the resulting performance is compared with Arnstein's optimized predictive quantizer and with Huang and Schultheiss' optimized transform coder. Two implementations of vector quantizers are considered: full search vector quantizers-which are optimal but require large codebook searches-and tree searched vector quantizers-which are suboptimal but require far less searching. The various systems are compared on the basis of performance, complexity, and generality of design techniques.     

Design of Quantizers for DPCM Coding of Picture Signals

Visual thresholds play an important role in the process of incorporating properties of the human visual system in encoding picture signals. They tell us how much the picture signal can be perturbed without the perturbations being visible to human observers. We describe psychovisual experiments to determine the amplitude thresholds at a single edge having a given slope and then present methods to incorporate the visual threshold data directly into the design of quantizers for use in Differential Pulse Code Modulation (DPCM) systems. In the first class of methods, quantizer characteristics are obtained such that the quantization error is kept below the visual threshold as determined by the slope at a picture element and either (a) the number of quantizer levels, or (b) the entropy of the quantized output is minimized. In the second class of methods, different measures of the suprathreshold quantization error are minimized for a fixed number of levels, or for a given constraint on the entropy of the quantized signal. We present empirical relationships between the various distortion measures and the subjective quality of the pictures rated on a five point impairment scale. We then discuss the structure of the quantizers obtained by the above mentioned optimization methods, evaluate their performance on real pictures, and compare them with the ones described in the literature.     

一种分布式信源编码中最优量化器的设计

针对传统的向量量化压缩的不足性,提高量化效果的方法主要是增加向量的维数,但同时增加了计算的复杂性.为了解决分布式编码中量化器的设计问题,在联合条件熵约束的条件下,着重从WZ量化器的最优条件分析,提出了一种Lloyd迭代算法,通过实验证明,该算法比传统的算法更可以保证量化器的局部最优性.     

Design of DPCM Quantizers for Video Signals Using Subjective Tests

The application of differential pulse code modulation (DPCM) for broadcast color television signals requires a design which produces no visible impairments under normal viewing conditions. This paper describes a quantizer design which is based on measured visibility thresholds of the various kinds of DPCM impairments such as granular noise, edge busyness, and slope overload. The visibility thresholds are determined by subjective tests based on comparisons of DPCM and PCM encoded pictures. Constructions of quantizers are carried out such that the number of levels is minimized without exceeding the measured visibility thresholds. Besides nonadaptive quantizers, adaptive quantizers are also constructed which are controlled by the signal changes of surrounding picture elements. These investigations show that for component coding of color video signals with two-dimensional prediction, a transmission rate of 31.7 Mbits/s is possible for natural types of test pictures without visible impairments using constant word length coding.     

An Algorithm for the Design of Labeled-Transition Finite-State Vector Quantizers

A finite-state vector quantizer (FSVQ) is a switched vector quantizer where the sequence of quantizers selected by the encoder can be tracked by the decoder. It can be viewed as an adaptive vector quantizer with backward estimation, a vector generalization of an AQB system. Recently a family of algorithms for the design of FSVQ's for waveform coding application has been introduced. These algorithms first design an initial set of vector quantizers together with a next-state function giving the rule by which the next quantizer is selected. The codebooks of this initial FSVQ are then iteratively improved by a natural extension of the usual memoryless vector quantizer design algorithm. The next-state function, however, is not modified from its initial form. In this paper we present two extensions of the FSVQ design algorithms. First, the algorithm for FSVQ design for waveform coders is extended to FSVQ design of linear predictive coded (LPC) speech parameter vectors using an Itakura-Saito distortion measure. Second, we introduce a new technique for the iterative improvement of the next-state function based on an algorithm from adaptive stochastic automata theory. The design algorithms are simulated for an LPC FSVQ and the results are compared with each other and to ordinary memoryless vector quantization. Several open problems suggested by the simulation results are presented.     

Hardware Realization of Waveform Vector Quantizers

A real-time full search vector quantization system for speech waveform coding is implemented using LSTTL and CMOS devices. The system consists of low-pass filters, A/D and D/A converters, an algorithm for discriminating voiced and unvoiced speed, a full search vector quantizer encoder and decoder, and a microprocessor-based controller. The system is designed to operate at two possible rates: one bit/sample using a dimension 8 vector quantizer (6500 bits/s) or 2 bits/sample using a dimension 4 vector quantizer (13 000 bits/s). In both cases the codebooks have rate 8 bits/vector. Separate codebooks were designed for voiced and unvoiced speech based on a training sequence of 640 000 samples containing five different speakers. The subjective and quantitative results are compared to both simulations and with a real-time array processor based implementation.     

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.     

Applications of Ali-Silvey Distance Measures in the Design Generalized Quantizers for Binary Decision Systems

The Ali-Silvey class of distance measures is applied to the problem of designing quantizers for use in binary detection systems. To find optimal solutions the notion of quantization must be generalized slightly, and necessary conditions are established for the selection of quantizer parameters in this context. Local, or small-signal, conditions are also derived and these are seen to agree with asymptotic results based on Pitman efficiency. As an example, four-level generalized quantization for detecting a constant signal in additive generalizedGaussian noise is investigated.     

Design of Semi-Uniform Quantizers and Their Application in Sigma Delta A/D Converters

In this paper a new type of non-uniform quantizer, semi-uniform quantizer, is introduced. A k-bit semi-uniform quantizer uses the thresholds defined by a (k + 1)-bit uniform quantizer and arranges them in such a way that small-amplitude inputs will be quantized by small quantization steps and large-amplitude inputs by large quantization steps. Therefore the total quantization error power could be reduced and the modulator's dynamic range could be increased by 1-bit. The condition for a semi-uniform quantizer to achieve a better performance than a uniform quantizer is analyzed and verified using a second order 3-bit sigma delta modulator prototype chip, fabricated in 0.35 μm CMOS process. At 32× oversampling ratio the modulator achieves 81 dB dynamic range and 63.8 dB peak SNDR with 3-bit semi-uniform quantizer. With 3-bit uniform quantizer the dynamic range is 70 dB and the peak SNDR is 54.1 dB.     

On the Design of Quantizers for DPCM Coders: Influence of the Subjective Testing Methodology

In the Candy design procedure for DPCM quantizers, the subject is given a specific task to perform. We test the hypothesis that the form of this task influences the results that are obtained. In one experiment the viewers were permitted unlimited time to evaluate noise visibility; in another test using a different testing procedure viewing time was reduced to one second. Visibility functions were obtained from these tests, and quantizers were designed and then evaluated on the basis of impairment ratings of coded pictures. Our results indicate that the design procedure is indeed sensitive to the viewing conditions.     

Note on the Error Signal of Block Quantizers

We show that the error signal incurred by block quantizing stationary data is nonstationary under some conditions. Examples are presented that indicate that the mean square error is largest at the block edges. When block quantizers are used to encode pictures at low bit rates, this effect tends to make the block edges visible in the reconstructed picture.     

Quantizers with uniform decoders and channel-optimized encoders

Scalar quantizers with uniform decoders and channel-optimized encoders are studied for a uniform source on [0,1] and binary symmetric channels. Two families of affine index assignments are considered: the complemented natural code (CNC), introduced here, and the natural binary code (NBC). It is shown that the NBC never induces empty cells in the quantizer encoder, whereas the CNC can. Nevertheless, we show that the asymptotic distributions of quantizer encoder cells for the NBC and the CNC are equal and are uniform over a proper subset of the source's support region. Empty cells act as a form of implicit channel coding. An effective channel code rate associated with a quantizer designed for a noisy channel is defined and computed for the codes studied. By explicitly showing that the mean-squared error (MSE) of the CNC can be strictly smaller than that of the NBC, we also demonstrate that the NBC is suboptimal for a large range of transmission rates and bit error probabilities. This contrasts with the known optimality of the NBC when either both the encoder and decoder are not channel optimized, or when only the decoder is channel optimized.     

On the Design of Quantizers for DPCM Coders: A Functional Relationship Between Visibility, Probability and Masking

Visibility functions measure the relative visibility of noise added to a picture at those points where some measure of local activity exceeds a given threshold. The functions are obtained from a series of subjective experiments and vary with the content of the picture. Visibility functions have been used to design quantizing characteristics for DPCM coding of monochrome and color signals and for three-dimensional transform coding. We consider an alternative approach to determining the visibility function that obviates the need for repeated picture-dependent subjective tests. The visibility function is assumed to consist of two parts, a picture-dependent component and viewer-dependent component (referred to as the masking function). The visibility function may be approximated by the quotient of a probability density function raised to a power and the masking function. The role of probability is found to be weaker where the viewer has more opportunity to scrutinize the picture.     

Performance of Phase Quantizers in Noncoherent Digital Correlation Detectors

This paper presents a performance analysis of phase quantizers in noncoherent digital correlation detectors for weak signals in additive narrow-band non-Gaussian noise. It will be shown that under certain regularity conditions the effects of quantization and correlation can be strictly separated. The result of an optimization is the uniform phase quantizer which confirms intuitive expectations.     

Quantizers with uniform encoders and channel optimized decoders

Scalar quantizers with uniform encoders and channel optimized decoders are studied for uniform sources and binary symmetric channels. It is shown that the natural binary code (NBC) and folded binary code (FBC) induce point density functions that are uniform on proper subintervals of the source support, whereas the Gray code (GC) does not induce a point density function. The mean-squared errors (MSE) for the NBC, FBC, GC, and for randomly chosen index assignments are calculated and the NBC is shown to be mean-squared optimal among all possible index assignments, for all bit-error rates and all quantizer transmission rates. In contrast, it is shown that almost all index assignments perform poorly and have degenerate codebooks.     

The Performance of Quantizers for a Class of Noise-Corrupted Signal Sources

An investigation is made of the performance of quantizers used as source encoders for noise-corrupted signal sources. The developmerit is pertinent to discrete-time, memoryless, signal-signal-sourse-independent noise sources with a given amplitude bound. A functional analysis approach is adopted to formulate the problem and derive the results. The derivations and intermediate results are in terms of an arbitrary quantizer and, consequently, are applicable to any quantizer and allow quantizer performance comparisons in the worstcase corrupting-noise source context. Examples are presented with this type of comparison in mind. These examples instructively illustrate the application of the results as well as file performance of the uniform quantizer and others under their worst-case additive noise conditions.