Sparse non-negative super-resolution — simplified and stabilised

We consider the problem of non-negative super-resolution, which concerns reconstructing a signal x=?i=1kai?ti from m samples its convolution with window function ?(s?t), form y(sj)=?i=1kai?(sj?ti)+?j, where ?j indicates an inexactness in sample value. first show that x is unique measure consistent samples, provided are exact. Moreover, we characterise solutions xˆ within bound ?j=1m?j2??2. integrals and over (ti??,ti+?) converge to one another as ? ? approach zero similarly close generalised Wasserstein distance. Lastly, make these results precise for ?(s?t) Gaussian. The main innovation non-negativity sufficient localise point sources regularisers such total variation not required setting.