Hosam A. Khalil

The asymptotic closed-loop approach to predictive vector quantizer design with application in video coding

The basic vector quantization (VQ) technique employed in video coding belongs to the category of predictive vector quantization (PVQ), as it involves quantization of the (motion compensated) frame prediction error. It is well known that the design of PVQ suffers from fundamental difficulties, due to the prediction loop, which have an impact on the convergence and the stability of the design procedure. We propose an approach to PVQ design that enjoys the stability of open-loop design while it ensures ultimate optimization of the closed-loop system. The method is derived for general predictive quantization, and we demonstrate it on video compression at low bit rates, where it provides substantial improvement over standard open and closed loop design techniques. Further, the approach outperforms standard DCT-based video coding.

Predictive vector quantizer design using deterministic annealing

A new approach is proposed for predictive vector quantizer (PVQ) design, which is inherently probabilistic, and is based on ideas from information theory and analogies to statistical physics. The approach effectively resolves three longstanding fundamental shortcomings of standard PVQ design. The first complication is due to the PVQ prediction loop, which has a detrimental impact on the convergence and the stability of the design procedure. The second shortcoming is due to the piecewise constant nature of the quantizer function, which makes it difficult to optimize the predictor with respect to the overall reconstruction error. Finally, a shortcoming inherited from standard VQ design is the tendency of the design algorithm to terminate at a locally, rather than the globally, optimal solution. We propose a new PVQ design approach that embeds our previous asymptotic closed-loop (ACL) approach within a deterministic annealing (DA) framework. The overall DA-ACL method profits from its two main components in a complementary way. ACL is used to overcome the first difficulty and offers the means for stable quantizer design as it provides an open-loop design platform, yet allows the PVQ design algorithm to asymptotically converge to optimization of the closed-loop performance objective. DA simultaneously mitigates or eliminates the remaining design shortcomings. Its probabilistic framework replaces hard quantization with a differentiable expected cost function that can be jointly optimized for the predictor and quantizer parameters, and its annealing schedule allows the avoidance of many poor local optima. Substantial performance gains over traditional methods have been achieved in the simulations.

Three-dimensional video compression using subband/wavelet transform with lower buffering requirements

Three-dimensional (3-D) video compression using wavelets decomposition along the temporal axis dictates that a number of video frames must be buffered to allow for the temporal decomposition. Buffering of frames allows for the temporal correlation to be made use of, and the larger the buffer the more effective the decomposition. One problem inherent in such a set up in interactive applications such as video conferencing, is that buffering translates into a corresponding time delay. We show that 3-D coding of such image sequences can be achieved in the true sense of temporal direction decomposition but with much less buffering requirements. For a practical coder, this can be achieved by introducing an approximation to the way the transform coefficients are encoded. Applying wavelet decomposition using some types of filters may introduce edge errors, which become more prominent in short signal segments. We also present a solution to this problem for the Daubechies (1988) family of filters.

Robust predictive vector quantizer design

The design of predictive quantizers generally suffers from difficulties due to the prediction loop, which have an impact on the convergence and the stability of the design procedure. We previously proposed an asymptotically closed-loop approach to quantizer design for predictive coding applications, which benefits from the stability of open-loop design while asymptotically optimizing the actual closed-loop system. In this paper, we present an enhancement to the approach where joint optimization of both predictor and quantizer is performed within the asymptotically closed-loop framework. The proposed design method is tested on synthetic sources (first-order Gauss and Laplacian-Markov sequences), and on natural sources, in particular, line spectral frequency parameters of speech signals.

Multistage vector quantizer optimization for packet networks

A multistage vector quantizer (MSVQ) based coding system is source-channel optimized for packet networks. Resilience to packet loss is enhanced by a proposed interleaving approach that ensures that a single lost packet only eliminates a subset of the vector stages. The design is optimized while taking into account compression efficiency, packet loss rate, and the interleaving technique in use. The new source-channel-optimized MSVQ is tested on memoryless speech line spectral frequency (LSF) parameter quantization as well as block-based image compression. With LSF coding, a source-channel-optimized MSVQ is shown to yield gains of up to 2.0 dB in signal-to-ratio (SNR) over traditional MSVQ and to substantially enhance the robustness of packetized speech transmission. Substantial gains were also obtained in the case of block-based image compression. Although the formulation is given in the context of packet networks, the work is directly extendible to the broader category of erasure channels.

Selective splitting approach to entropy-constrained single/multistage vector quantizer design

A practical tool is proposed to improve the design of various vector quantizer (VQ) structures. Particular emphasis is placed on the design of entropy-constrained VQ (ECVQ), and entropy-constrained multi-stage VQ (EC-MSVQ), whose optimization is notoriously difficult. Traditional design techniques involve an indirect approach where a fixed rate quantizer is gradually modified into a variable rate VQ. We propose a direct design procedure based on selective codevector splitting. The codebooks are grown, using splitting according to a rate-distortion Lagrangian trade-off, to the desired operating point of average bit rate. Extensive simulations in image and video compression are presented and show consistent, significant improvement over standard techniques. For example, in ECVQ design for compression of video residuals, PSNR gains of about 1.0 dB were achieved.

Asymptotic closed-loop design of predictive multi-stage vector quantizers

This work considers the design of a multi-stage vector quantizer (MSVQ) for application to the motion compensated prediction error of video signals. It is well known that the design of predictive vector quantizers suffers from fundamental difficulties due to the prediction loop, which have an impact on the convergence and the stability of the design procedure. We propose an approach to predictive MSVQ design that enjoys the stability of open-loop design while ensuring ultimate optimization of the closed-loop system. The proposed design method is tested on video compression at low bit rates, where it significantly outperforms widely-used closed-loop design techniques, and achieves improvement over the H.263 standard.

Predictive multistage vector quantizer design using asymptotic closed-loop optimization

This correspondence builds on the asymptotic closed-loop approach to predictive vector quantizer design (Khalil et al. 2001), and extends it to the design of predictive multistage vector quantizers for low bit rate video coding. The design approach resolves longstanding shortcomings, in particular, design stability and empty-cell problems. Simulation results show substantial gains over traditional design approaches.

Lowering frame-buffering requirements of 3-D wavelet transform coding of interactive video

In this paper, we present a 3-D wavelet compression technique for image sequences in video conferencing applications. One of the main requirements for such applications is that the delay has to be within some acceptable limit. When applying wavelet decomposition in the temporal direction, we must store a large number of frames so that such a decomposition can be effective. But this translates into a correspondingly large algorithmic delay. A technique to avoid this obstacle will be proposed. The basic idea is to overlap the decomposition with previous frames that have already been transmitted and selectively transmitting only the new wavelet coefficients.

MSVQ design for packet networks with application to LSF quantization

The design of a multi-stage vector quantizer (MSVQ) based source-channel coding system is optimized for packet networks. Resilience to packet loss is further enhanced by a proposed interleaving approach that ensures that a single lost packet only eliminates a subset of the vector stages. The design is optimized while taking into account compression efficiency, packet loss rate, and the interleaving technique in use. The new source-channel-optimized MSVQ is tested on memoryless line spectral frequency (LSF) parameter quantization in speech coders. A source-channel-optimization MSVQ is shown to yield a gain of up to 2.0 dB in SNR, for coding the LSFs, over traditional MSVQ and to substantially enhance the robustness of packetized speech transmission. Although the formulation is given in the context of packet networks, the work is directly extendible to the broader category of erasure channels.