Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields

The aim of this paper is to propose diffusion strategies for distributed estimation over adaptive networks, assuming the presence of spatially correlated measurements distributed according to a Gaussian Markov random field (GMRF) model. The proposed methods incorporate prior information about the statistical dependency among observations, while at the same time processing data in real-time and in a fully decentralized manner. A detailed mean-square analysis is carried out in order to prove stability and evaluate the steady-state performance of the proposed strategies. Finally, we also illustrate how the proposed techniques can be easily extended in order to incorporate thresholding operators for sparsity recovery applications. Numerical results show the potential advantages of using such techniques for distributed learning in adaptive networks deployed over GMRF.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin note: text overlap with arXiv:1206.309

High-Rate Vector Quantization for the Neyman-Pearson Detection of Correlated Processes

This paper investigates the effect of quantization on the performance of the Neyman-Pearson test. It is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process. Each sample is passed through an N-point quantizer and transmitted to a decision device which performs a binary hypothesis test. For any false alarm level, it is shown that the miss probability of the Neyman-Pearson test converges to zero exponentially as the number of samples tends to infinity, assuming that the observed process satisfies certain mixing conditions. The main contribution of this paper is to provide a compact closed-form expression of the error exponent in the high-rate regime i.e., when the number N of quantization levels tends to infinity, generalizing previous results of Gupta and Hero to the case of non-independent observations. If d represents the dimension of one sample, it is proved that the error exponent converges at rate N^{2/d} to the one obtained in the absence of quantization. As an application, relevant high-rate quantization strategies which lead to a large error exponent are determined. Numerical results indicate that the proposed quantization rule can yield better performance than existing ones in terms of detection error.Comment: 47 pages, 7 figures, 1 table. To appear in the IEEE Transactions on Information Theor

Entropy of Highly Correlated Quantized Data

This paper considers the entropy of highly correlated quantized samples. Two results are shown. The first concerns sampling and identically scalar quantizing a stationary continuous-time random process over a finite interval. It is shown that if the process crosses a quantization threshold with positive probability, then the joint entropy of the quantized samples tends to infinity as the sampling rate goes to infinity. The second result provides an upper bound to the rate at which the joint entropy tends to infinity, in the case of an infinite-level uniform threshold scalar quantizer and a stationary Gaussian random process. Specifically, an asymptotic formula for the conditional entropy of one quantized sample conditioned on the previous quantized sample is derived. At high sampling rates, these results indicate a sharp contrast between the large encoding rate (in bits/sec) required by a lossy source code consisting of a fixed scalar quantizer and an ideal, sampling-rate-adapted lossless code, and the bounded encoding rate required by an ideal lossy source code operating at the same distortion

On the Estimation of Randomly Sampled 2D Spatial Fields under Bandwidth Constraints

In this paper, we address the problem of the estimation of a spatial field defined over a two-dimensional space with wireless sensor networks. We assume that the field is (spatially) bandlimited and that it is sampled by a set of sensors which are randomly deployed in a given geographical area. Further, we impose a total bandwidth constraint which forces the quantization error in the sensor-to-FC (Fusion Center) channels to depend on the actual number of sensors in the network. With these assumptions, we derive an analytical expression of the mean-square error (MSE) in the reconstructed random field and, on that basis, an approximate closed-form expression of the optimal sensor density which attains the best trade-off in terms of observation, sampling and quantization noises. The analysis is carried out both in Gaussian and Rayleigh-fading scenarios without transmit Channel State Information (CSI). For the latter scenario, we also derive an expression of the common and constant rate at which the observations must be quantized. Computer simulation results illustrate the dependency of the optimal operating point on the variance of the observation noise or the signal-to-noise ratio in the sensor-to-FC channels, as well as the scaling law of the reconstruction MSE (which is also derived analytically) for both scenarios

Study and simulation of low rate video coding schemes

The semiannual report is included. Topics covered include communication, information science, data compression, remote sensing, color mapped images, robust coding scheme for packet video, recursively indexed differential pulse code modulation, image compression technique for use on token ring networks, and joint source/channel coder design

Distributed Detection and Estimation in Wireless Sensor Networks

In this article we consider the problems of distributed detection and estimation in wireless sensor networks. In the first part, we provide a general framework aimed to show how an efficient design of a sensor network requires a joint organization of in-network processing and communication. Then, we recall the basic features of consensus algorithm, which is a basic tool to reach globally optimal decisions through a distributed approach. The main part of the paper starts addressing the distributed estimation problem. We show first an entirely decentralized approach, where observations and estimations are performed without the intervention of a fusion center. Then, we consider the case where the estimation is performed at a fusion center, showing how to allocate quantization bits and transmit powers in the links between the nodes and the fusion center, in order to accommodate the requirement on the maximum estimation variance, under a constraint on the global transmit power. We extend the approach to the detection problem. Also in this case, we consider the distributed approach, where every node can achieve a globally optimal decision, and the case where the decision is taken at a central node. In the latter case, we show how to allocate coding bits and transmit power in order to maximize the detection probability, under constraints on the false alarm rate and the global transmit power. Then, we generalize consensus algorithms illustrating a distributed procedure that converges to the projection of the observation vector onto a signal subspace. We then address the issue of energy consumption in sensor networks, thus showing how to optimize the network topology in order to minimize the energy necessary to achieve a global consensus. Finally, we address the problem of matching the topology of the network to the graph describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Monte Carlo optimization of decentralized estimation networks over directed acyclic graphs under communication constraints

Motivated by the vision of sensor networks, we consider decentralized estimation networks over bandwidth–limited communication links, and are particularly interested in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We employ a class of in–network processing strategies that admits directed acyclic graph representations and yields a tractable Bayesian risk that comprises the cost of communications and estimation error penalty. This perspective captures a broad range of possibilities for processing under network constraints and enables a rigorous design problem in the form of constrained optimization. A similar scheme and the structures exhibited by the solutions have been previously studied in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization scheme involves integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both the in–network processing strategies and their optimization. The proposed Monte Carlo optimization procedure operates in a scalable and efficient fashion and, owing to the non-parametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk