Cyclic Pure Greedy Algorithms for Recovering Compressively Sampled Sparse Signals

Bob L. Sturm, Mads Græsbøll Christensen, Remi Gribonval

Research output: Contribution to journalConference article in JournalResearchpeer-review

9 Citations (Scopus)
254 Downloads (Pure)

Abstract

The pure greedy algorithms
matching pursuit (MP) and complementary MP (CompMP)
are extremely computationally simple,
but can perform poorly in solving the linear inverse problems posed by
the recovery of compressively sampled sparse signals.
We show that by applying a cyclic minimization principle,
the performance of both are significantly improved
while remaining computationally simple.
Our simulations show that while MP and CompMP
may not be competitive with state-of-the-art recovery algorithms,
their cyclic variations are.
We discuss ways in which their complexity can be further reduced,
but our simulations show these can hurt recovery performance.
Finally, we derive the exact recovery condition of CompMP and both cyclic algorithms.
Original languageEnglish
JournalAsilomar Conference on Signals, Systems and Computers. Conference Record
Pages (from-to)1143-1147
Number of pages5
ISSN1058-6393
DOIs
Publication statusPublished - 2011
EventAsilomar Conference on Signals, Systems and computers, Nov. 6-9, 2011 - Pacific Grove, United States
Duration: 6 Nov 20119 Nov 2011

Seminar

SeminarAsilomar Conference on Signals, Systems and computers, Nov. 6-9, 2011
CountryUnited States
CityPacific Grove
Period06/11/201109/11/2011

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Recovery
Inverse problems

Cite this

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title = "Cyclic Pure Greedy Algorithms for Recovering Compressively Sampled Sparse Signals",
abstract = "The pure greedy algorithmsmatching pursuit (MP) and complementary MP (CompMP)are extremely computationally simple, but can perform poorly in solving the linear inverse problems posed by the recovery of compressively sampled sparse signals.We show that by applying a cyclic minimization principle,the performance of both are significantly improvedwhile remaining computationally simple.Our simulations show that while MP and CompMP may not be competitive with state-of-the-art recovery algorithms,their cyclic variations are.We discuss ways in which their complexity can be further reduced,but our simulations show these can hurt recovery performance.Finally, we derive the exact recovery condition of CompMP and both cyclic algorithms.",
author = "Sturm, {Bob L.} and Christensen, {Mads Gr{\ae}sb{\o}ll} and Remi Gribonval",
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doi = "10.1109/ACSSC.2011.6190193",
language = "English",
pages = "1143--1147",
journal = "Asilomar Conference on Signals, Systems and Computers. Conference Record",
issn = "1058-6393",
publisher = "I E E E Computer Society",

}

Cyclic Pure Greedy Algorithms for Recovering Compressively Sampled Sparse Signals. / Sturm, Bob L.; Christensen, Mads Græsbøll; Gribonval, Remi.

In: Asilomar Conference on Signals, Systems and Computers. Conference Record, 2011, p. 1143-1147.

Research output: Contribution to journalConference article in JournalResearchpeer-review

TY - GEN

T1 - Cyclic Pure Greedy Algorithms for Recovering Compressively Sampled Sparse Signals

AU - Sturm, Bob L.

AU - Christensen, Mads Græsbøll

AU - Gribonval, Remi

PY - 2011

Y1 - 2011

N2 - The pure greedy algorithmsmatching pursuit (MP) and complementary MP (CompMP)are extremely computationally simple, but can perform poorly in solving the linear inverse problems posed by the recovery of compressively sampled sparse signals.We show that by applying a cyclic minimization principle,the performance of both are significantly improvedwhile remaining computationally simple.Our simulations show that while MP and CompMP may not be competitive with state-of-the-art recovery algorithms,their cyclic variations are.We discuss ways in which their complexity can be further reduced,but our simulations show these can hurt recovery performance.Finally, we derive the exact recovery condition of CompMP and both cyclic algorithms.

AB - The pure greedy algorithmsmatching pursuit (MP) and complementary MP (CompMP)are extremely computationally simple, but can perform poorly in solving the linear inverse problems posed by the recovery of compressively sampled sparse signals.We show that by applying a cyclic minimization principle,the performance of both are significantly improvedwhile remaining computationally simple.Our simulations show that while MP and CompMP may not be competitive with state-of-the-art recovery algorithms,their cyclic variations are.We discuss ways in which their complexity can be further reduced,but our simulations show these can hurt recovery performance.Finally, we derive the exact recovery condition of CompMP and both cyclic algorithms.

U2 - 10.1109/ACSSC.2011.6190193

DO - 10.1109/ACSSC.2011.6190193

M3 - Conference article in Journal

SP - 1143

EP - 1147

JO - Asilomar Conference on Signals, Systems and Computers. Conference Record

JF - Asilomar Conference on Signals, Systems and Computers. Conference Record

SN - 1058-6393

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