Sparse non-negative super-resolution - simplified and stabilised

We consider the problem of non-negative super-resolution, which concerns reconstructing a non-negative signal x = Sigma(k )(i=1)a(i)delta(ti) from m samples of its convolution with a window function phi(s - t), of the form y(s(j)) = Sigma(k)(i=1) a(i) phi(s(j) - t(i)) + delta(j), where delta(j) indicates an inexactness in the sample value. We first show that x is the unique non-negative measure consistent with the samples, provided the samples are exact. Moreover, we characterise non-negative solutions (x) over cap consistent with the samples within the bound Sigma(m)(j=1) delta(2)(j)