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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Communication dans un congrès
Rémi Gribonval. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Apr 2009, Saint Malo, France. 2009
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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. Rémi Gribonval. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Apr 2009, Saint Malo, France. 2009. 〈inria-00369373〉

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