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Are there needles in a (moving) haystack? Adaptive sensing for detection and estimation of static and dynamically evolving signals

Presented by: 
Rui Castro
Thursday 28th June 2018 - 14:45 to 15:30
INI Seminar Room 1
In this work we investigate the problem of testing for the presence of dynamically evolving sparse signals. This is motivated by settings were the signal of interest changes rapidly while measurements are being collected (e.g., monitoring of the electromagnetic spectrum, or detection of hot spots of a rapidly spreading disease). We model the signal as an n dimensional vector that has s non-zero components, and at each time a fraction of the non-zero components may change their location. The statistical problem is to decide whether the signal is a zero vector or in fact it has non-zero components. This decision is based on m noisy observations of individual signal components. We consider two different sensing paradigms, namely adaptive and non-adaptive sensing. For non-adaptive sensing the choice of components to measure has to be decided before the data collection process started, while for adaptive sensing one can adjust the sensing process based on observations collected earlier. We characterize the difficulty of this detection problem in both sensing paradigms, with special interest to the speed of change of the active components. In addition we provide an adaptive sensing algorithm for this problem and contrast its performance to that of best non-adaptive detection algorithms. Interestingly, when the number of measurements is small (on the order n/s), there is a significant difference in performance between the two sensing paradigms, as non-adaptive sensing is unable to exploit the dynamic nature of the signal (based on joint works with Ervin Tánczos).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons