Friday, June 12, 2015

Extreme Compressive Sampling for Covariance Estimation

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/d2 where m is the compression dimension and d is the ambient dimension. We mention applications to subspace learning (Principal Components Analysis) and distributed sensor networks.

Description: OpNav Campaign 4, LORRI 4X4
Time: 2015-06-11 05:29:16 UTC
Exposure: 2967 msec
Target: PLUTO
Range: 39.6M km
Join the CompressiveSensing subreddit or the Google+ Community and post there !
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.

No comments: