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A case for orthogonal measurements in linear inverse problems

Oymak, Samet and Hassibi, Babak (2014) A case for orthogonal measurements in linear inverse problems. In: 2014 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 3175-3179.

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We investigate the random matrices that have orthonormal rows and provide a comparison to matrices with independent Gaussian entries. We find that, orthonormality provides an inherent advantage for the conditioning. In particular, for any given subset S of ℝ^n, we show that orthonormal matrices have better restricted eigenvalues compared to Gaussians. We consider implications of this result for the linear inverse problems; in particular, we investigate the noisy sparse estimation setup and applications to restricted isometry property. We relate our findings to the results known for Gaussian processes and precise undersampling theorems. We then discuss and illustrate universality of the noise robustness behavior for partial unitary matrices including Hadamard and Discrete Cosine Transform.

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Additional Information:© 2014 IEEE. This work was supported in part by the National Science Foundation under grants CCF-0729203, CNS-0932428 and CIF-1018927, by the Office of Naval Research under the MURI grant N00014-08-1-0747, and by a grant from Qualcomm Inc.
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Office of Naval Research (ONR)N00014-08-1-0747
Record Number:CaltechAUTHORS:20150224-071049082
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55123
Deposited By: Shirley Slattery
Deposited On:05 Mar 2015 00:56
Last Modified:03 Oct 2019 08:03

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