Linear transformations and restricted isometry property

Leslie Ying; Ming Zou Yi

doi:10.1109/ICASSP.2009.4960245

Linear transformations and restricted isometry property

Leslie Ying
, Ming Zou Yi

Department of Biomedical Engineering

University of Wisconsin-Milwaukee

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

The Restricted Isometry Property (RIP) introduced by Candés and Tao is a fundamental property in compressed sensing theory. It says that if a sampling matrix satisfies the RIP of certain order proportional to the sparsity of the signal, then the original signal can be reconstructed even if the sampling matrix provides a sample vector which is much smaller in size than the original signal. This short note addresses the problem of how a linear transformation will affect the RIP. This problem arises from the consideration of extending the sensing matrix and the use of compressed sensing in different bases. As an application, the result is applied to the redundant dictionary setting in compressed sensing.

Original language	English
Title of host publication	2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009
Pages	2961-2964
Number of pages	4
DOIs	https://doi.org/10.1109/ICASSP.2009.4960245
State	Published - 2009
Event	2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009 - Taipei, Taiwan, Province of China Duration: Apr 19 2009 → Apr 24 2009

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)	1520-6149

Conference

Conference	2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009
Country/Territory	Taiwan, Province of China
City	Taipei
Period	04/19/09 → 04/24/09

Keywords

Compressed sensing
Concentration inequalities
Restricted isometry property

Access to Document

10.1109/ICASSP.2009.4960245

Cite this

Ying, L., & Yi, M. Z. (2009). Linear transformations and restricted isometry property. In 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009 (pp. 2961-2964). Article 4960245 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2009.4960245

@inproceedings{2035a202cdd24347a97af8bad7c53b64,

title = "Linear transformations and restricted isometry property",

abstract = "The Restricted Isometry Property (RIP) introduced by Cand{\'e}s and Tao is a fundamental property in compressed sensing theory. It says that if a sampling matrix satisfies the RIP of certain order proportional to the sparsity of the signal, then the original signal can be reconstructed even if the sampling matrix provides a sample vector which is much smaller in size than the original signal. This short note addresses the problem of how a linear transformation will affect the RIP. This problem arises from the consideration of extending the sensing matrix and the use of compressed sensing in different bases. As an application, the result is applied to the redundant dictionary setting in compressed sensing.",

keywords = "Compressed sensing, Concentration inequalities, Restricted isometry property",

author = "Leslie Ying and Yi, \{Ming Zou\}",

year = "2009",

doi = "10.1109/ICASSP.2009.4960245",

language = "English",

isbn = "9781424423545",

series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

pages = "2961--2964",

booktitle = "2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009",

note = "2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009 ; Conference date: 19-04-2009 Through 24-04-2009",

}

Ying, L & Yi, MZ 2009, Linear transformations and restricted isometry property. in 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009., 4960245, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, pp. 2961-2964, 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009, Taipei, Taiwan, Province of China, 04/19/09. https://doi.org/10.1109/ICASSP.2009.4960245

Linear transformations and restricted isometry property. / Ying, Leslie; Yi, Ming Zou.
2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009. 2009. p. 2961-2964 4960245 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Linear transformations and restricted isometry property

AU - Ying, Leslie

AU - Yi, Ming Zou

PY - 2009

Y1 - 2009

N2 - The Restricted Isometry Property (RIP) introduced by Candés and Tao is a fundamental property in compressed sensing theory. It says that if a sampling matrix satisfies the RIP of certain order proportional to the sparsity of the signal, then the original signal can be reconstructed even if the sampling matrix provides a sample vector which is much smaller in size than the original signal. This short note addresses the problem of how a linear transformation will affect the RIP. This problem arises from the consideration of extending the sensing matrix and the use of compressed sensing in different bases. As an application, the result is applied to the redundant dictionary setting in compressed sensing.

AB - The Restricted Isometry Property (RIP) introduced by Candés and Tao is a fundamental property in compressed sensing theory. It says that if a sampling matrix satisfies the RIP of certain order proportional to the sparsity of the signal, then the original signal can be reconstructed even if the sampling matrix provides a sample vector which is much smaller in size than the original signal. This short note addresses the problem of how a linear transformation will affect the RIP. This problem arises from the consideration of extending the sensing matrix and the use of compressed sensing in different bases. As an application, the result is applied to the redundant dictionary setting in compressed sensing.

KW - Compressed sensing

KW - Concentration inequalities

KW - Restricted isometry property

UR - https://www.scopus.com/pages/publications/70349208541

U2 - 10.1109/ICASSP.2009.4960245

DO - 10.1109/ICASSP.2009.4960245

M3 - Conference contribution

AN - SCOPUS:70349208541

SN - 9781424423545

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 2961

EP - 2964

BT - 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009

T2 - 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009

Y2 - 19 April 2009 through 24 April 2009

ER -

Linear transformations and restricted isometry property

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this