Statistical mechanics approach to sparse noise denoising

Mikko Vehkapera, Yoshiyuki Kabashima, Saikat Chatterjee

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

2 Citations (Scopus)

Abstract

Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the ℓ1-norm based convex optimization algorithm exhibits a phase transition between the possibility of perfect and imperfect reconstruction. Conditions characterizing this threshold are derived and the mean square error of the estimate is obtained for the case when perfect reconstruction is not possible. Detailed calculations are provided to expose the mathematical tools to a wide audience.

Original languageEnglish
Title of host publication2013 Proceedings of the 21st European Signal Processing Conference, EUSIPCO 2013
PublisherIEEE Institute of Electrical and Electronic Engineers
Pages241-245
ISBN (Electronic)978-0-9928626-0-2
ISBN (Print)978-1-4799-3687-8
Publication statusPublished - 1 Jan 2013
MoE publication typeA4 Article in a conference publication
Event2013 21st European Signal Processing Conference, EUSIPCO 2013 - Marrakech, Morocco
Duration: 9 Sep 201313 Sep 2013

Publication series

SeriesEuropean Signal Processing Conference
Volume21
ISSN2219-5491

Conference

Conference2013 21st European Signal Processing Conference, EUSIPCO 2013
CountryMorocco
CityMarrakech
Period9/09/1313/09/13

Fingerprint

Statistical mechanics
Convex optimization
Mean square error
Phase transitions

Keywords

  • replica method
  • sparse signals and noise
  • statistical mechanical analysis

Cite this

Vehkapera, M., Kabashima, Y., & Chatterjee, S. (2013). Statistical mechanics approach to sparse noise denoising. In 2013 Proceedings of the 21st European Signal Processing Conference, EUSIPCO 2013 (pp. 241-245). [6811435] IEEE Institute of Electrical and Electronic Engineers . European Signal Processing Conference, Vol.. 21
Vehkapera, Mikko ; Kabashima, Yoshiyuki ; Chatterjee, Saikat. / Statistical mechanics approach to sparse noise denoising. 2013 Proceedings of the 21st European Signal Processing Conference, EUSIPCO 2013. IEEE Institute of Electrical and Electronic Engineers , 2013. pp. 241-245 (European Signal Processing Conference, Vol. 21).
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Vehkapera, M, Kabashima, Y & Chatterjee, S 2013, Statistical mechanics approach to sparse noise denoising. in 2013 Proceedings of the 21st European Signal Processing Conference, EUSIPCO 2013., 6811435, IEEE Institute of Electrical and Electronic Engineers , European Signal Processing Conference, vol. 21, pp. 241-245, 2013 21st European Signal Processing Conference, EUSIPCO 2013, Marrakech, Morocco, 9/09/13.

Statistical mechanics approach to sparse noise denoising. / Vehkapera, Mikko; Kabashima, Yoshiyuki; Chatterjee, Saikat.

2013 Proceedings of the 21st European Signal Processing Conference, EUSIPCO 2013. IEEE Institute of Electrical and Electronic Engineers , 2013. p. 241-245 6811435 (European Signal Processing Conference, Vol. 21).

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

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Vehkapera M, Kabashima Y, Chatterjee S. Statistical mechanics approach to sparse noise denoising. In 2013 Proceedings of the 21st European Signal Processing Conference, EUSIPCO 2013. IEEE Institute of Electrical and Electronic Engineers . 2013. p. 241-245. 6811435. (European Signal Processing Conference, Vol. 21).