What can you learn from the sample covariance of a signal from its compressive measurements, today we have an answer on this issue from Extreme Compressive Sampling for Covariance Estimation by Martin Azizyan, Akshay Krishnamurthy, Aarti Singh
We consider the problem of estimating the covariance of a collection of vectors given extremely compressed measurements of each vector. We propose and study an estimator based on back-projections of these compressive samples. We show, via a distribution-free analysis, that by observing just a single compressive measurement of each vector one can consistently estimate the covariance matrix, in both infinity and spectral norm. Via information theoretic techniques, we also establish lower bounds showing that our estimator is minimax-optimal for both infinity and spectral norm estimation problems. Our results show that the effective sample complexity for this problem is scaled by a factor of
m2/d2where mis the compression dimension and dis the ambient dimension. We mention applications to subspace learning (Principal Components Analysis) and distributed sensor networks.
Credit: NASA, APL, SwRI
Description: OpNav Campaign 4, LORRI 4X4
Time: 2015-06-11 05:29:16 UTC
Exposure: 2967 msec
Range: 39.6M km
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