@inproceedings{f7125fa712674ae4a878d831cc19ea95,
title = "Estimation of simultaneously structured covariance matrices from quadratic measurements",
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.",
keywords = "Convex Relaxation, Low-Rank, Quadratic Sampling, Sparse",
author = "Yuxin Chen and Yuejie Chi and Goldsmith, {Andrea J.}",
year = "2014",
doi = "10.1109/ICASSP.2014.6855092",
language = "English (US)",
isbn = "9781479928927",
series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "7669--7673",
booktitle = "2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014",
address = "United States",
note = "2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 ; Conference date: 04-05-2014 Through 09-05-2014",
}