Separation of a subspace-sparse signal: Algorithms and conditions

Arvind Ganesh; Zihan Zhou; Yi Ma

doi:10.1109/ICASSP.2009.4960290

Separation of a subspace-sparse signal: Algorithms and conditions

Arvind Ganesh, Zihan Zhou, Yi Ma

College of Information Sciences and Technology

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

28 Scopus citations

Abstract

In this paper, we show how two classical sparse recovery algorithms, Orthogonal Matching Pursuit and Basis Pursuit, can be naturally extended to recover block-sparse solutions for subspace-sparse signals. A subspace-sparse signal is sparse with respect to a set of subspaces, instead of atoms. By generalizing the notion of mutual incoherence to the set of subspaces, we show that all classical sufficient conditions remain exactly the same for these algorithms to work for subspace-sparse signals, in both noiseless and noisy cases. The sufficient conditions provided are easy to verify for large systems. We conduct simulations to compare the performance of the proposed algorithms.

Original language	English (US)
Title of host publication	2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009
Pages	3141-3144
Number of pages	4
DOIs	https://doi.org/10.1109/ICASSP.2009.4960290
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	4/19/09 → 4/24/09

All Science Journal Classification (ASJC) codes

Software
Signal Processing
Electrical and Electronic Engineering

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10.1109/ICASSP.2009.4960290

Cite this

Ganesh, A., Zhou, Z., & Ma, Y. (2009). Separation of a subspace-sparse signal: Algorithms and conditions. In 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009 (pp. 3141-3144). Article 4960290 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2009.4960290

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title = "Separation of a subspace-sparse signal: Algorithms and conditions",

abstract = "In this paper, we show how two classical sparse recovery algorithms, Orthogonal Matching Pursuit and Basis Pursuit, can be naturally extended to recover block-sparse solutions for subspace-sparse signals. A subspace-sparse signal is sparse with respect to a set of subspaces, instead of atoms. By generalizing the notion of mutual incoherence to the set of subspaces, we show that all classical sufficient conditions remain exactly the same for these algorithms to work for subspace-sparse signals, in both noiseless and noisy cases. The sufficient conditions provided are easy to verify for large systems. We conduct simulations to compare the performance of the proposed algorithms.",

author = "Arvind Ganesh and Zihan Zhou and Yi Ma",

year = "2009",

doi = "10.1109/ICASSP.2009.4960290",

language = "English (US)",

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

pages = "3141--3144",

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",

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Ganesh, A, Zhou, Z & Ma, Y 2009, Separation of a subspace-sparse signal: Algorithms and conditions. in 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009., 4960290, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, pp. 3141-3144, 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009, Taipei, Taiwan, Province of China, 4/19/09. https://doi.org/10.1109/ICASSP.2009.4960290

Separation of a subspace-sparse signal: Algorithms and conditions. / Ganesh, Arvind; Zhou, Zihan; Ma, Yi.
2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009. 2009. p. 3141-3144 4960290 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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

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AB - In this paper, we show how two classical sparse recovery algorithms, Orthogonal Matching Pursuit and Basis Pursuit, can be naturally extended to recover block-sparse solutions for subspace-sparse signals. A subspace-sparse signal is sparse with respect to a set of subspaces, instead of atoms. By generalizing the notion of mutual incoherence to the set of subspaces, we show that all classical sufficient conditions remain exactly the same for these algorithms to work for subspace-sparse signals, in both noiseless and noisy cases. The sufficient conditions provided are easy to verify for large systems. We conduct simulations to compare the performance of the proposed algorithms.

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Separation of a subspace-sparse signal: Algorithms and conditions

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