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
Keywords
Signal reconstructionCompressed sensingOrthonormal basisComputer scienceRandom projectionAlgorithmIterative reconstructionSIGNAL (programming language)Noise (video)Signal processingArtificial intelligenceDigital signal processing
Affiliated Institutions
Related Publications
Compressed sensing
Suppose x is an unknown vector in Ropf <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> (a digital image or signal); we pla...
Compressed sensing
Suppose x is an unknown vector in Ropfm (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible ...
Rapid MR Imaging with "Compressed Sensing" and Randomly Under-Sampled 3DFT Trajectories
Recently a rapid imaging method was proposed [1] that exploits the fact that sparse or compressible signals, such as MR images, 3D randomly under-sampled Cartesian trajectory ca...
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
This paper demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with $m$ nonzero entries in ...
Sparsity and incoherence in compressive sampling
We consider the problem of reconstructing a sparse signal x^0\\in{\\bb R}^n from a limited number of linear measurements. Given m randomly selected samples of Ux0, where U is an...
Publication Info
- Year
- 2006
- Type
- article
- Volume
- 52
- Issue
- 9
- Pages
- 4036-4048
- Citations
- 614
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
614
OpenAlex
Cite This
Jarvis Haupt,
Robert D. Nowak
(2006).
Signal Reconstruction From Noisy Random Projections.
IEEE Transactions on Information Theory
, 52
(9)
, 4036-4048.
https://doi.org/10.1109/tit.2006.880031
Identifiers
- DOI
- 10.1109/tit.2006.880031