25,454 research outputs found
A Robust Information Source Estimator with Sparse Observations
In this paper, we consider the problem of locating the information source
with sparse observations. We assume that a piece of information spreads in a
network following a heterogeneous susceptible-infected-recovered (SIR) model
and that a small subset of infected nodes are reported, from which we need to
find the source of the information. We adopt the sample path based estimator
developed in [1], and prove that on infinite trees, the sample path based
estimator is a Jordan infection center with respect to the set of observed
infected nodes. In other words, the sample path based estimator minimizes the
maximum distance to observed infected nodes. We further prove that the distance
between the estimator and the actual source is upper bounded by a constant
independent of the number of infected nodes with a high probability on infinite
trees. Our simulations on tree networks and real world networks show that the
sample path based estimator is closer to the actual source than several other
algorithms
Optimized Compressed Sensing Matrix Design for Noisy Communication Channels
We investigate a power-constrained sensing matrix design problem for a
compressed sensing framework. We adopt a mean square error (MSE) performance
criterion for sparse source reconstruction in a system where the
source-to-sensor channel and the sensor-to-decoder communication channel are
noisy. Our proposed sensing matrix design procedure relies upon minimizing a
lower-bound on the MSE. Under certain conditions, we derive closed-form
solutions to the optimization problem. Through numerical experiments, by
applying practical sparse reconstruction algorithms, we show the strength of
the proposed scheme by comparing it with other relevant methods. We discuss the
computational complexity of our design method, and develop an equivalent
stochastic optimization method to the problem of interest that can be solved
approximately with a significantly less computational burden. We illustrate
that the low-complexity method still outperforms the popular competing methods.Comment: Submitted to IEEE ICC 2015 (EXTENDED VERSION
Neural Connectivity with Hidden Gaussian Graphical State-Model
The noninvasive procedures for neural connectivity are under questioning.
Theoretical models sustain that the electromagnetic field registered at
external sensors is elicited by currents at neural space. Nevertheless, what we
observe at the sensor space is a superposition of projected fields, from the
whole gray-matter. This is the reason for a major pitfall of noninvasive
Electrophysiology methods: distorted reconstruction of neural activity and its
connectivity or leakage. It has been proven that current methods produce
incorrect connectomes. Somewhat related to the incorrect connectivity
modelling, they disregard either Systems Theory and Bayesian Information
Theory. We introduce a new formalism that attains for it, Hidden Gaussian
Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden
by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS
is equivalent to a frequency domain Linear State Space Model (LSSM) but with
sparse connectivity prior. The mathematical contribution here is the theory for
high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS
can attenuate the leakage effect in the most critical case: the distortion EEG
signal due to head volume conduction heterogeneities. Its application in EEG is
illustrated with retrieved connectivity patterns from human Steady State Visual
Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence
for noninvasive procedures of neural connectivity: concurrent EEG and
Electrocorticography (ECoG) recordings on monkey. Open source packages are
freely available online, to reproduce the results presented in this paper and
to analyze external MEEG databases
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