15,064 research outputs found
Sensing Capacity for Markov Random Fields
This paper computes the sensing capacity of a sensor network, with sensors of
limited range, sensing a two-dimensional Markov random field, by modeling the
sensing operation as an encoder. Sensor observations are dependent across
sensors, and the sensor network output across different states of the
environment is neither identically nor independently distributed. Using a
random coding argument, based on the theory of types, we prove a lower bound on
the sensing capacity of the network, which characterizes the ability of the
sensor network to distinguish among environments with Markov structure, to
within a desired accuracy.Comment: To appear in the proceedings of the 2005 IEEE International Symposium
on Information Theory, Adelaide, Australia, September 4-9, 200
The Sensing Capacity of Sensor Networks
This paper demonstrates fundamental limits of sensor networks for detection
problems where the number of hypotheses is exponentially large. Such problems
characterize many important applications including detection and classification
of targets in a geographical area using a network of sensors, and detecting
complex substances with a chemical sensor array. We refer to such applications
as largescale detection problems. Using the insight that these problems share
fundamental similarities with the problem of communicating over a noisy
channel, we define a quantity called the sensing capacity and lower bound it
for a number of sensor network models. The sensing capacity expression differs
significantly from the channel capacity due to the fact that a fixed sensor
configuration encodes all states of the environment. As a result, codewords are
dependent and non-identically distributed. The sensing capacity provides a
bound on the minimal number of sensors required to detect the state of an
environment to within a desired accuracy. The results differ significantly from
classical detection theory, and provide an ntriguing connection between sensor
networks and communications. In addition, we discuss the insight that sensing
capacity provides for the problem of sensor selection.Comment: Submitted to IEEE Transactions on Information Theory, November 200
Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
This paper presents a new Bayesian collaborative sparse regression method for
linear unmixing of hyperspectral images. Our contribution is twofold; first, we
propose a new Bayesian model for structured sparse regression in which the
supports of the sparse abundance vectors are a priori spatially correlated
across pixels (i.e., materials are spatially organised rather than randomly
distributed at a pixel level). This prior information is encoded in the model
through a truncated multivariate Ising Markov random field, which also takes
into consideration the facts that pixels cannot be empty (i.e, there is at
least one material present in each pixel), and that different materials may
exhibit different degrees of spatial regularity. Secondly, we propose an
advanced Markov chain Monte Carlo algorithm to estimate the posterior
probabilities that materials are present or absent in each pixel, and,
conditionally to the maximum marginal a posteriori configuration of the
support, compute the MMSE estimates of the abundance vectors. A remarkable
property of this algorithm is that it self-adjusts the values of the parameters
of the Markov random field, thus relieving practitioners from setting
regularisation parameters by cross-validation. The performance of the proposed
methodology is finally demonstrated through a series of experiments with
synthetic and real data and comparisons with other algorithms from the
literature
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
Optimal decision making for sperm chemotaxis in the presence of noise
For navigation, microscopic agents such as biological cells rely on noisy
sensory input. In cells performing chemotaxis, such noise arises from the
stochastic binding of signaling molecules at low concentrations. Using
chemotaxis of sperm cells as application example, we address the classic
problem of chemotaxis towards a single target. We reveal a fundamental
relationship between the speed of chemotactic steering and the strength of
directional fluctuations that result from the amplification of noise in the
chemical input signal. This relation implies a trade-off between slow, but
reliable, and fast, but less reliable, steering.
By formulating the problem of optimal navigation in the presence of noise as
a Markov decision process, we show that dynamic switching between reliable and
fast steering substantially increases the probability to find a target, such as
the egg. Intriguingly, this decision making would provide no benefit in the
absence of noise. Instead, decision making is most beneficial, if chemical
signals are above detection threshold, yet signal-to-noise ratios of gradient
measurements are low. This situation generically arises at intermediate
distances from a target, where signaling molecules emitted by the target are
diluted, thus defining a `noise zone' that cells have to cross.
Our work addresses the intermediate case between well-studied perfect
chemotaxis at high signal-to-noise ratios close to a target, and random search
strategies in the absence of navigation cues, e.g. far away from a target. Our
specific results provide a rational for the surprising observation of decision
making in recent experiments on sea urchin sperm chemotaxis. The general theory
demonstrates how decision making enables chemotactic agents to cope with high
levels of noise in gradient measurements by dynamically adjusting the
persistence length of a biased persistent random walk.Comment: 9 pages, 5 figure
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