Signal reconstruction from noisy random projections

Jarvis Haupt, Robert Nowak

Research output: Contribution to journalArticlepeer-review

470 Scopus citations


Recent results show that a relatively small number of random projections of a signal can contain most of its salient information. It follows that if a signal is compressible in some orthonormal basis, then a very accurate reconstruction can be obtained from random projections. This "compressive sampling" approach is extended here to show that signals can be accurately recovered from random projections contaminated with noise. A practical iterative algorithm for signal reconstruction is proposed, and potential applications to coding, analog-digital (A/D) conversion, and remote wireless sensing are discussed.

Original languageEnglish (US)
Pages (from-to)4036-4048
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - Sep 2006

Bibliographical note

Funding Information:
Manuscript received April 12, 2005; revised April 19, 2006. This research was supported in part by the NSF under Grants CCR-0310889 and CCR-0325571, and by the Office of Naval Research, Grant N00014-00-1-0966. The material in this paper was presented in part at the IEEE Workshop on Statistical Signal Processing (SSP), Bordeaux, France, July 2005.


  • Complexity regularization
  • Data compression
  • Denoising
  • Rademacher chaos
  • Random projections
  • Sampling
  • Wireless sensor networks


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