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)


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
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 Sept 201313 Sept 2013

Publication series

SeriesEuropean Signal Processing Conference


Conference2013 21st European Signal Processing Conference, EUSIPCO 2013


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


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