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

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 `p-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.