Signal reconstruction from noisy random projections

Jarvis Haupt; Robert Nowak

doi:10.1109/TIT.2006.880031

Signal reconstruction from noisy random projections

Jarvis Haupt
, Robert Nowak

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

483 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	4036-4048
Number of pages	13
Journal	IEEE Transactions on Information Theory
Volume	52
Issue number	9
DOIs	https://doi.org/10.1109/TIT.2006.880031
State	Published - 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.

Keywords

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

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10.1109/TIT.2006.880031

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author = "Jarvis Haupt and Robert Nowak",

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N2 - 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.

AB - 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.

KW - Complexity regularization

KW - Data compression

KW - Denoising

KW - Rademacher chaos

KW - Random projections

KW - Sampling

KW - Wireless sensor networks

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Signal reconstruction from noisy random projections

Abstract

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Keywords

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