16,638 research outputs found
Info-Greedy sequential adaptive compressed sensing
We present an information-theoretic framework for sequential adaptive
compressed sensing, Info-Greedy Sensing, where measurements are chosen to
maximize the extracted information conditioned on the previous measurements. We
show that the widely used bisection approach is Info-Greedy for a family of
-sparse signals by connecting compressed sensing and blackbox complexity of
sequential query algorithms, and present Info-Greedy algorithms for Gaussian
and Gaussian Mixture Model (GMM) signals, as well as ways to design sparse
Info-Greedy measurements. Numerical examples demonstrate the good performance
of the proposed algorithms using simulated and real data: Info-Greedy Sensing
shows significant improvement over random projection for signals with sparse
and low-rank covariance matrices, and adaptivity brings robustness when there
is a mismatch between the assumed and the true distributions.Comment: Preliminary results presented at Allerton Conference 2014. To appear
in IEEE Journal Selected Topics on Signal Processin
An excess power statistic for detection of burst sources of gravitational radiation
We examine the properties of an excess power method to detect gravitational
waves in interferometric detector data. This method is designed to detect
short-duration (< 0.5 s) burst signals of unknown waveform, such as those from
supernovae or black hole mergers. If only the bursts' duration and frequency
band are known, the method is an optimal detection strategy in both Bayesian
and frequentist senses. It consists of summing the data power over the known
time interval and frequency band of the burst. If the detector noise is
stationary and Gaussian, this sum is distributed as a chi-squared (non-central
chi-squared) deviate in the absence (presence) of a signal. One can use these
distributions to compute frequentist detection thresholds for the measured
power. We derive the method from Bayesian analyses and show how to compute
Bayesian thresholds. More generically, when only upper and/or lower bounds on
the bursts duration and frequency band are known, one must search for excess
power in all concordant durations and bands. Two search schemes are presented
and their computational efficiencies are compared. We find that given
reasonable constraints on the effective duration and bandwidth of signals, the
excess power search can be performed on a single workstation. Furthermore, the
method can be almost as efficient as matched filtering when a large template
bank is required. Finally, we derive generalizations of the method to a network
of several interferometers under the assumption of Gaussian noise.Comment: 22 pages, 6 figure
Regression analysis with missing data and unknown colored noise: application to the MICROSCOPE space mission
The analysis of physical measurements often copes with highly correlated
noises and interruptions caused by outliers, saturation events or transmission
losses. We assess the impact of missing data on the performance of linear
regression analysis involving the fit of modeled or measured time series. We
show that data gaps can significantly alter the precision of the regression
parameter estimation in the presence of colored noise, due to the frequency
leakage of the noise power. We present a regression method which cancels this
effect and estimates the parameters of interest with a precision comparable to
the complete data case, even if the noise power spectral density (PSD) is not
known a priori. The method is based on an autoregressive (AR) fit of the noise,
which allows us to build an approximate generalized least squares estimator
approaching the minimal variance bound. The method, which can be applied to any
similar data processing, is tested on simulated measurements of the MICROSCOPE
space mission, whose goal is to test the Weak Equivalence Principle (WEP) with
a precision of . In this particular context the signal of interest is
the WEP violation signal expected to be found around a well defined frequency.
We test our method with different gap patterns and noise of known PSD and find
that the results agree with the mission requirements, decreasing the
uncertainty by a factor 60 with respect to ordinary least squares methods. We
show that it also provides a test of significance to assess the uncertainty of
the measurement.Comment: 12 pages, 4 figures, to be published in Phys. Rev.
Array signal processing for maximum likelihood direction-of-arrival estimation
Emitter Direction-of-Arrival (DOA) estimation is a fundamental problem in a variety of applications including radar, sonar, and wireless communications. The research has received considerable attention in literature and numerous methods have been proposed. Maximum Likelihood (ML) is a nearly optimal technique producing superior estimates compared to other methods especially in unfavourable conditions, and thus is of significant practical interest. This paper discusses in details the techniques for ML DOA estimation in either white Gaussian noise or unknown noise environment. Their performances are analysed and compared, and evaluated against the theoretical lower bounds
Detection of False Data Injection Attacks in Smart Grid under Colored Gaussian Noise
In this paper, we consider the problems of state estimation and false data
injection detection in smart grid when the measurements are corrupted by
colored Gaussian noise. By modeling the noise with the autoregressive process,
we estimate the state of the power transmission networks and develop a
generalized likelihood ratio test (GLRT) detector for the detection of false
data injection attacks. We show that the conventional approach with the
assumption of Gaussian noise is a special case of the proposed method, and thus
the new approach has more applicability. {The proposed detector is also tested
on an independent component analysis (ICA) based unobservable false data attack
scheme that utilizes similar assumptions of sample observation.} We evaluate
the performance of the proposed state estimator and attack detector on the IEEE
30-bus power system with comparison to conventional Gaussian noise based
detector. The superior performance of {both observable and unobservable false
data attacks} demonstrates the effectiveness of the proposed approach and
indicates a wide application on the power signal processing.Comment: 8 pages, 4 figures in IEEE Conference on Communications and Network
Security (CNS) 201
Orthogonal Matching Pursuit: A Brownian Motion Analysis
A well-known analysis of Tropp and Gilbert shows that orthogonal matching
pursuit (OMP) can recover a k-sparse n-dimensional real vector from 4 k log(n)
noise-free linear measurements obtained through a random Gaussian measurement
matrix with a probability that approaches one as n approaches infinity. This
work strengthens this result by showing that a lower number of measurements, 2
k log(n - k), is in fact sufficient for asymptotic recovery. More generally,
when the sparsity level satisfies kmin <= k <= kmax but is unknown, 2 kmax
log(n - kmin) measurements is sufficient. Furthermore, this number of
measurements is also sufficient for detection of the sparsity pattern (support)
of the vector with measurement errors provided the signal-to-noise ratio (SNR)
scales to infinity. The scaling 2 k log(n - k) exactly matches the number of
measurements required by the more complex lasso method for signal recovery with
a similar SNR scaling.Comment: 11 pages, 2 figure
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