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Signal Reconstruction From Noisy Random Projections

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2 Author(s)
Haupt, J. ; Dept. of Electr. Eng., Wisconsin Univ., Madison, WI ; Nowak, R.

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

Published in:

Information Theory, IEEE Transactions on  (Volume:52 ,  Issue: 9 )

Date of Publication:

Sept. 2006

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