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The proportional mean decomposition: A bridge between the Gaussian and Bernoulli ensembles

Oymak, Samet and Hassibi, Babak (2015) The proportional mean decomposition: A bridge between the Gaussian and Bernoulli ensembles. In: 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE , Piscataway, NJ, pp. 3322-3326. ISBN 978-1-4673-6997-8. https://resolver.caltech.edu/CaltechAUTHORS:20160722-153039699

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Abstract

We consider ill-posed linear inverse problems involving the estimation of structured sparse signals. When the sensing matrix has i.i.d. standard normal entries, there is a full-fledged theory on the sample complexity and robustness properties. In this work, we propose a way of making use of this theory to get good bounds for the i.i.d. Bernoulli ensemble. We first provide a deterministic relation between the two ensembles that relates the restricted singular values. Then, we show how one can get non-asymptotic results with small constants for the Bernoulli ensemble. While our discussion focuses on Bernoulli measurements, the main idea can be extended to any discrete distribution with little difficulty.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ICASSP.2015.7178586 DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7178586PublisherArticle
Additional Information:© 2015 IEEE. We thank the anonymous reviewers for their helpful comments and suggestions.
Subject Keywords:compressed sensing, sample complexity, gaussian processes, restricted singular value
Record Number:CaltechAUTHORS:20160722-153039699
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160722-153039699
Official Citation:S. Oymak and B. Hassibi, "The proportional mean decomposition: A bridge between the Gaussian and bernoulli ensembles," 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South Brisbane, QLD, 2015, pp. 3322-3326. doi: 10.1109/ICASSP.2015.7178586
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69178
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Jul 2016 21:21
Last Modified:03 Oct 2019 10:19

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