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The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact

Publication ,  Conference
Reeves, G; Pfister, HD
Published in: IEEE International Symposium on Information Theory - Proceedings
August 10, 2016

This paper considers the fundamental limit of compressed sensing for i.i.d. signal distributions and i.i.d. Gaussian measurement matrices. Its main contribution is a rigorous characterization of the asymptotic mutual information (MI) and minimum mean-square error (MMSE) in this setting. Under mild technical conditions, our results show that the limiting MI and MMSE are equal to the values predicted by the replica method from statistical physics. This resolves a well-known problem that has remained open for over a decade.

Duke Scholars

Published In

IEEE International Symposium on Information Theory - Proceedings

DOI

ISSN

2157-8095

ISBN

9781509018062

Publication Date

August 10, 2016

Volume

2016-August

Start / End Page

665 / 669
 

Citation

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Reeves, G., & Pfister, H. D. (2016). The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact. In IEEE International Symposium on Information Theory - Proceedings (Vol. 2016-August, pp. 665–669). https://doi.org/10.1109/ISIT.2016.7541382
Reeves, G., and H. D. Pfister. “The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact.” In IEEE International Symposium on Information Theory - Proceedings, 2016-August:665–69, 2016. https://doi.org/10.1109/ISIT.2016.7541382.
Reeves G, Pfister HD. The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact. In: IEEE International Symposium on Information Theory - Proceedings. 2016. p. 665–9.
Reeves, G., and H. D. Pfister. “The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact.” IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August, 2016, pp. 665–69. Scopus, doi:10.1109/ISIT.2016.7541382.
Reeves G, Pfister HD. The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact. IEEE International Symposium on Information Theory - Proceedings. 2016. p. 665–669.

Published In

IEEE International Symposium on Information Theory - Proceedings

DOI

ISSN

2157-8095

ISBN

9781509018062

Publication Date

August 10, 2016

Volume

2016-August

Start / End Page

665 / 669