Change Detection with Compressive Measurements

Quickest change point detection is concerned with the detection of statistical change(s) in sequences while minimizing the detection delay subject to false alarm constraints. In this letter, the problem of change point detection is studied when the decision maker only has access to compressive measu...

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Bibliographic Details
Published in:IEEE signal processing letters 2015-02, Vol.22 (2), p.182-186
Main Author: Atia, George K.
Format: Article
Language:English
Subjects:
Asymptotic properties
Bayes methods
Compressing
Compressive measurements
concentration inequalities
Delay
Delays
False alarms
Gaussian
Materials
Monitoring
Projection
quickest change detection
Random variables
Sensors
Signal processing
Signal to noise ratio
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Summary:Quickest change point detection is concerned with the detection of statistical change(s) in sequences while minimizing the detection delay subject to false alarm constraints. In this letter, the problem of change point detection is studied when the decision maker only has access to compressive measurements. First, an expression for the average detection delay of Shiryaev's procedure with compressive measurements is derived in the asymptotic regime where the probability of false alarm goes to zero. Second, the dependence of the delay on the compression ratio and the signal to noise ratio is explicitly quantified. The ratio of delays with and without compression is studied under various sensing matrix constructions, including Gaussian ensembles and random projections. For a target delay ratio, a sufficient condition on the number of measurements required to meet this objective with prespecified probability is derived.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2014.2352116