Estimation of simultaneously structured covariance matrices from quadratic measurements

Yuxin Chen, Yuejie Chi, Andrea J. Goldsmith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

This paper explores covariance estimation from energy measurements that are collected via a quadratic form of measurement vectors. A popular structural model is considered where the covariance matrices possess low-rank and sparse structures simultaneously. We investigate a weighted convex relaxation algorithm tailored for this joint structure, which guarantees exact and universal recovery from a small number of measurements. The algorithm is also robust against noise and imperfect structural assumptions. In particular, when the non-zero entries of the covariance matrix exhibit power-law decay, our algorithm admits exact recovery as soon as the number of measurements exceeds the theoretic limit. Our method is related to sparse phase retrieval: the analysis framework herein recovers and strengthens the best-known performance guarantees by extending them to approximately sparse and noisy scenarios as well as a broader class of measurement vectors, and our results are derived using much simpler analysis methods.

Original languageEnglish (US)
Title of host publication2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7669-7673
Number of pages5
ISBN (Print)9781479928927
DOIs
StatePublished - Jan 1 2014
Externally publishedYes
Event2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 - Florence, Italy
Duration: May 4 2014May 9 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
CountryItaly
CityFlorence
Period5/4/145/9/14

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • Convex Relaxation
  • Low-Rank
  • Quadratic Sampling
  • Sparse

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