14,587 research outputs found
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
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