On the earth mover's distance as a performance metric for sparse support recovery

A. Lavrenko; F. Römer; G. Del Galdo; R. Thoma

doi:10.1109/GlobalSIP.2016.7906065

On the earth mover's distance as a performance metric for sparse support recovery

A. Lavrenko, F. Römer, G. Del Galdo, R. Thoma

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

2 Citations (Scopus)

Abstract

Compressed Sensing (CS) is a recently emerged framework for simultaneous sampling and compression of signals that are sparse or compressible in some representation. Besides signal reconstruction, the CS framework is often adopted for compressive parameter estimation. Performance metrics commonly used in CS are well suited for performance evaluation in terms of recovery rates but provide little insight into the estimation accuracy in a parameter estimation setting. In this contribution, we study an alternative metric based on the Earth Mover's Distance (EMD). We define the EMD in the context of support recovery and derive exact formulas for its calculation for supports with equal as well as arbitrary cardinalities. Our simulation results suggest that the EMD provides a better alternative to common CS metrics in that it reflects the distance between the individual estimates in case of the imperfect support recovery.

Original language	English
Title of host publication	2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016 - Proceedings
Place of Publication	Piscataway, NJ
Publisher	IEEE
Pages	1368-1372
Number of pages	5
ISBN (Electronic)	978-1-5090-4545-7, 978-1-5090-4544-0 (USB)
ISBN (Print)	978-1-5090-4546-4
DOIs	https://doi.org/10.1109/GlobalSIP.2016.7906065
Publication status	Published - 19 Apr 2017
Externally published	Yes
Event	2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016 - Washington, United States Duration: 7 Dec 2016 → 9 Dec 2016

Conference

Conference	2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016
Abbreviated title	GlobalSIP 2016
Country/Territory	United States
City	Washington
Period	7/12/16 → 9/12/16

Keywords

Compressed sensing
Earth Mover's Distance
Parameter estimation
n/a OA procedure

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10.1109/GlobalSIP.2016.7906065

Cite this

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title = "On the earth mover's distance as a performance metric for sparse support recovery",

abstract = "Compressed Sensing (CS) is a recently emerged framework for simultaneous sampling and compression of signals that are sparse or compressible in some representation. Besides signal reconstruction, the CS framework is often adopted for compressive parameter estimation. Performance metrics commonly used in CS are well suited for performance evaluation in terms of recovery rates but provide little insight into the estimation accuracy in a parameter estimation setting. In this contribution, we study an alternative metric based on the Earth Mover's Distance (EMD). We define the EMD in the context of support recovery and derive exact formulas for its calculation for supports with equal as well as arbitrary cardinalities. Our simulation results suggest that the EMD provides a better alternative to common CS metrics in that it reflects the distance between the individual estimates in case of the imperfect support recovery.",

keywords = "Compressed sensing, Earth Mover's Distance, Parameter estimation, n/a OA procedure",

author = "A. Lavrenko and F. R{\"o}mer and {Del Galdo}, G. and R. Thoma",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016, GlobalSIP 2016 ; Conference date: 07-12-2016 Through 09-12-2016",

year = "2017",

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day = "19",

doi = "10.1109/GlobalSIP.2016.7906065",

language = "English",

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Lavrenko, A, Römer, F, Del Galdo, G & Thoma, R 2017, On the earth mover's distance as a performance metric for sparse support recovery. in 2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016 - Proceedings., 7906065, IEEE, Piscataway, NJ, pp. 1368-1372, 2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016, Washington, United States, 7/12/16. https://doi.org/10.1109/GlobalSIP.2016.7906065

On the earth mover's distance as a performance metric for sparse support recovery. / Lavrenko, A.; Römer, F.; Del Galdo, G. et al.
2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016 - Proceedings. Piscataway, NJ: IEEE, 2017. p. 1368-1372 7906065.

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

TY - GEN

T1 - On the earth mover's distance as a performance metric for sparse support recovery

AU - Lavrenko, A.

AU - Römer, F.

AU - Del Galdo, G.

AU - Thoma, R.

PY - 2017/4/19

Y1 - 2017/4/19

N2 - Compressed Sensing (CS) is a recently emerged framework for simultaneous sampling and compression of signals that are sparse or compressible in some representation. Besides signal reconstruction, the CS framework is often adopted for compressive parameter estimation. Performance metrics commonly used in CS are well suited for performance evaluation in terms of recovery rates but provide little insight into the estimation accuracy in a parameter estimation setting. In this contribution, we study an alternative metric based on the Earth Mover's Distance (EMD). We define the EMD in the context of support recovery and derive exact formulas for its calculation for supports with equal as well as arbitrary cardinalities. Our simulation results suggest that the EMD provides a better alternative to common CS metrics in that it reflects the distance between the individual estimates in case of the imperfect support recovery.

AB - Compressed Sensing (CS) is a recently emerged framework for simultaneous sampling and compression of signals that are sparse or compressible in some representation. Besides signal reconstruction, the CS framework is often adopted for compressive parameter estimation. Performance metrics commonly used in CS are well suited for performance evaluation in terms of recovery rates but provide little insight into the estimation accuracy in a parameter estimation setting. In this contribution, we study an alternative metric based on the Earth Mover's Distance (EMD). We define the EMD in the context of support recovery and derive exact formulas for its calculation for supports with equal as well as arbitrary cardinalities. Our simulation results suggest that the EMD provides a better alternative to common CS metrics in that it reflects the distance between the individual estimates in case of the imperfect support recovery.

KW - Compressed sensing

KW - Earth Mover's Distance

KW - Parameter estimation

KW - n/a OA procedure

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M3 - Conference contribution

AN - SCOPUS:85019189119

SN - 978-1-5090-4546-4

SP - 1368

EP - 1372

BT - 2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016 - Proceedings

PB - IEEE

CY - Piscataway, NJ

T2 - 2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016

Y2 - 7 December 2016 through 9 December 2016

ER -

On the earth mover's distance as a performance metric for sparse support recovery

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