A Simplified Approach to Recovery Conditions for Low Rank Matrices
Abstract
Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including ℓ_1 and nuclear norm minimization as well as ℓ_p minimization with p < 1. These algorithms are known to succeed if certain conditions on the measurement map are satisfied. Proofs for the recovery of matrices have so far been much more involved than in the vector case. In this paper, we show how several classes of recovery conditions can be extended from vectors to matrices in a simple and transparent way, leading to the best known restricted isometry and nullspace conditions for matrix recovery. Our results rely on the ability to "vectorize" matrices through the use of a key singular value inequality.
Additional Information
© 2011 IEEE. Date of Current Version: 03 October 2011. This work is supported in part by the National Science Foundation under CCF-0729203, CNS-0932428 and CCF-1018927 and supported in part by NSF CAREER grant ECCS-0847077.Attached Files
Submitted - A_20Simplified_20Approach_20to_20Recovery_20Conditions_20for_20Low_20Rank_20Matrices.pdf
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Additional details
- Eprint ID
- 30015
- Resolver ID
- CaltechAUTHORS:20120406-112117384
- NSF
- CCF-0729203
- NSF
- CNS-0932428
- NSF
- CCF-1018927
- NSF
- ECCS-0847077
- Created
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2012-04-06Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field