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General Perturbations in Compressed Sensing

Abstract : We analyze the Basis Pursuit recovery of signals when observing K-sparse data with general perturbations (i.e., additive, as well as multiplicative noise). This completely perturbed model extends the previous work of Cand`es, Romberg and Tao on stable signal recovery from incomplete and inaccurate measurements. Our results show that, under suitable conditions, the stability of the recovered signal is limited by the noise level in the observation. Moreover, this accuracy is within a constant multiple of the best-case reconstruction using the technique of least squares.
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https://hal.inria.fr/inria-00369493
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Submitted on : Friday, March 20, 2009 - 10:04:20 AM
Last modification on : Wednesday, August 7, 2019 - 12:19:20 PM
Long-term archiving on: : Friday, October 12, 2012 - 1:55:31 PM

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Matthew A. Herman, Thomas Strohmer. General Perturbations in Compressed Sensing. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Inria Rennes - Bretagne Atlantique, Apr 2009, Saint Malo, France. ⟨inria-00369493⟩

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