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Recovery of Non-Negative Signals from Compressively Sampled Observations Via Non-Negative Quadratic Programming

Abstract : The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction. In this paper, we consider a special case of Compressive Sampling where the uncompressed signal is non-negative, and propose an extension of Non-negative Quadratic Programming - which utilises Iteratively Reweighted Least Squares - for the recovery of non-negative minimum lp-norm solutions, 0 <= p <= 1. Furthermore, we investigate signal recovery performance where the sampling matrix has entries drawn from a Gaussian distribution with decreasing number of negative values, and demonstrate that - unlike standard Compressive Sampling - the standard Gaussian distribution is unsuitable for this special case.
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https://hal.inria.fr/inria-00369373
Contributor : Ist Rennes <>
Submitted on : Thursday, March 19, 2009 - 3:26:30 PM
Last modification on : Monday, June 20, 2016 - 2:10:32 PM
Long-term archiving on: : Friday, October 12, 2012 - 1:50:15 PM

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  • HAL Id : inria-00369373, version 1

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Paul D. O'Grady, Scott T. Rickard. Recovery of Non-Negative Signals from Compressively Sampled Observations Via Non-Negative Quadratic Programming. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Inria Rennes - Bretagne Atlantique, Apr 2009, Saint Malo, France. ⟨inria-00369373⟩

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