Vector quantization

During the past ten years Vector Quantization (VQ) has developed from a theoretical possibility promised by Shannon's source coding theorems into a powerful and competitive technique for speech and image coding and compression at medium to low bit rates. In this survey, the basic ideas behind the design of vector quantizers are sketched and some comments made on the state-of-the-art and current research efforts

Quantization Design for Distributed Optimization

We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a limited data-rate. A common technique to address the latter limitation is to apply quantization to the exchanged information. We propose two distributed optimization algorithms with an iteratively refining quantization design based on the inexact proximal gradient method and its accelerated variant. We show that if the parameters of the quantizers, i.e. the number of bits and the initial quantization intervals, satisfy certain conditions, then the quantization error is bounded by a linearly decreasing function and the convergence of the distributed algorithms is guaranteed. Furthermore, we prove that after imposing the quantization scheme, the distributed algorithms still exhibit a linear convergence rate, and show complexity upper-bounds on the number of iterations to achieve a given accuracy. Finally, we demonstrate the performance of the proposed algorithms and the theoretical findings for solving a distributed optimal control problem

Multiplication free vector quantization using the L 1 distortion measure and its variants

Journal ArticleVector quantization is a very powerful technique for data compression and consequently, it has attracted a lot for attention lately. One major drawback associated with this approach is its extreme computational complexity. This paper fist considers vector quantization that uses the L1 distortion measure for its implementation. The L1 distortion measure is very attractive from an implementational point of view, since no multiplication is required for computing the distortion measure. Unfortunately, the traditional Linde-Buzo-Gray (LBG) method for designing the code book for the L1 distortion measure involves several computations of medians of very large arrays and can become very complex. We propose a gradient-based approach for codebook design that does not require any multiplications or median computations. Convergence of this method is proved rigorously under very mild conditions. Simulation examples comparting the performance of this technique with the LBG algorithm show that the gradient-based method, in spite of its simplicity, produces codebooks with average distortions that are comparable to the LBG algorithm. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. Once again, by appro[riate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. Finally, we apply our techniques in predicitve vector quantization of images and demonstrate the viability of multiplication free predicitve vector quantization of image data

Multiplication-free vector quantization using the L l distortion measure and its variants

Journal ArticleVector quantization is a very powerful technique for data compression and consequently, it has attracted a lot of attention lately. One major drawback associated with this approach is its extreme computational complexity. This paper first considers vector quantization that uses the L1 distortion measure for its implementation. The L1 distortion measure is very attractive from an implementational point of view, since no multiplication is required for computing the distortion measure. Unfortunately, the traditional Linde-Buzo-Gray (LBG) method for designing the codebook for the L1 distortion measure can become extremely time-consuming, since it involves several computations of medians of very large arrays. We propose a gradient-based approach for codebook design that does not require any multiplications or median computations. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. Once again, by appropriate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. Finally, we apply our techniques in predictive vector quantization of images and demonstrate the viability of multiplication-free predictive vector quantization of image data

An Optimal Transmission Strategy for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgements

This paper presents a novel design methodology for optimal transmission policies at a smart sensor to remotely estimate the state of a stable linear stochastic dynamical system. The sensor makes measurements of the process and forms estimates of the state using a local Kalman filter. The sensor transmits quantized information over a packet dropping link to the remote receiver. The receiver sends packet receipt acknowledgments back to the sensor via an erroneous feedback communication channel which is itself packet dropping. The key novelty of this formulation is that the smart sensor decides, at each discrete time instant, whether to transmit a quantized version of either its local state estimate or its local innovation. The objective is to design optimal transmission policies in order to minimize a long term average cost function as a convex combination of the receiver's expected estimation error covariance and the energy needed to transmit the packets. The optimal transmission policy is obtained by the use of dynamic programming techniques. Using the concept of submodularity, the optimality of a threshold policy in the case of scalar systems with perfect packet receipt acknowledgments is proved. Suboptimal solutions and their structural results are also discussed. Numerical results are presented illustrating the performance of the optimal and suboptimal transmission policies.Comment: Conditionally accepted in IEEE Transactions on Control of Network System

Subband vector quantization of images using hexagonal filter banks

Journal ArticleAbstract Results of psychophysical experiments on human vision conducted in the last three decades indicate that the eye performs a multichannel decomposition of the incident images. This paper presents a subband vector quantization algorithm that employs hexagonal filter banks. The hexagonal filter bank provides an image decomposition similar to what the eye is believed to do. Consequently, the image coder is able to make use of the properties of the human visual system and produce compressed images of high quality at low bit rates. We present a systematic approach for optimal allocation of available bits among the subbands and also for the selection of the size of the vectors in each of the subbands