One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks

This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive quantization, coding, and field reconstruction scheme is developed and an upper-bound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatio-temporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain weak technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the per-sensor bitrate and sensing-related network overhead rate simultaneously go to zero. The proposed scheme achieves the order-optimal MSE versus sensor density scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review format), 4 figures. Submitted to IEEE Transactions on Signal Processing. Current version is updated for journal submission: revised author list, modified formulation and framework. Previous version appeared in Proceedings of Allerton Conference On Communication, Control, and Computing 200

Rhythmic Representations: Learning Periodic Patterns for Scalable Place Recognition at a Sub-Linear Storage Cost

Robotic and animal mapping systems share many challenges and characteristics: they must function in a wide variety of environmental conditions, enable the robot or animal to navigate effectively to find food or shelter, and be computationally tractable from both a speed and storage perspective. With regards to map storage, the mammalian brain appears to take a diametrically opposed approach to all current robotic mapping systems. Where robotic mapping systems attempt to solve the data association problem to minimise representational aliasing, neurons in the brain intentionally break data association by encoding large (potentially unlimited) numbers of places with a single neuron. In this paper, we propose a novel method based on supervised learning techniques that seeks out regularly repeating visual patterns in the environment with mutually complementary co-prime frequencies, and an encoding scheme that enables storage requirements to grow sub-linearly with the size of the environment being mapped. To improve robustness in challenging real-world environments while maintaining storage growth sub-linearity, we incorporate both multi-exemplar learning and data augmentation techniques. Using large benchmark robotic mapping datasets, we demonstrate the combined system achieving high-performance place recognition with sub-linear storage requirements, and characterize the performance-storage growth trade-off curve. The work serves as the first robotic mapping system with sub-linear storage scaling properties, as well as the first large-scale demonstration in real-world environments of one of the proposed memory benefits of these neurons.Comment: Pre-print of article that will appear in the IEEE Robotics and Automation Letter

Robust 1-bit compressed sensing and sparse logistic regression: A convex programming approach

This paper develops theoretical results regarding noisy 1-bit compressed sensing and sparse binomial regression. We show that a single convex program gives an accurate estimate of the signal, or coefficient vector, for both of these models. We demonstrate that an s-sparse signal in R^n can be accurately estimated from m = O(slog(n/s)) single-bit measurements using a simple convex program. This remains true even if each measurement bit is flipped with probability nearly 1/2. Worst-case (adversarial) noise can also be accounted for, and uniform results that hold for all sparse inputs are derived as well. In the terminology of sparse logistic regression, we show that O(slog(n/s)) Bernoulli trials are sufficient to estimate a coefficient vector in R^n which is approximately s-sparse. Moreover, the same convex program works for virtually all generalized linear models, in which the link function may be unknown. To our knowledge, these are the first results that tie together the theory of sparse logistic regression to 1-bit compressed sensing. Our results apply to general signal structures aside from sparsity; one only needs to know the size of the set K where signals reside. The size is given by the mean width of K, a computable quantity whose square serves as a robust extension of the dimension.Comment: 25 pages, 1 figure, error fixed in Lemma 4.

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