Multivariate super-resolution without separation

Abstract In this paper, we study the high-dimensional super-resolution imaging problem. Here, are given an image of a number point sources light whose locations and intensities unknown. The is pixelized blurred by known point-spread function arising from device. We encode unknown their via non-negative measure propose convex optimization program to find it. Assuming device’s componentwise decomposable, show that optimal solution true in noiseless case, it approximates well noisy case with respect generalized Wasserstein distance. Our main assumption components form Tchebychev system ($T$-system) $T^{*}$-system mild conditions satisfied Gaussian functions. work generalization all dimensions [14] where same analysis carried out two dimensions. also extend results [27] when decomposes.