  Non-stationary blind super-resolution is an extension of the traditional
super-resolution problem, which deals with the problem of recovering fine
details from coarse measurements. The non-stationary blind super-resolution
problem appears in many applications including radar imaging, 3D
single-molecule microscopy, computational photography, etc. There is a growing
interest in solving non-stationary blind super-resolution task with convex
methods due to their robustness to noise and strong theoretical guarantees.
Motivated by the recent work on atomic norm minimization in blind inverse
problems, we focus here on the signal denoising problem in non-stationary blind
super-resolution. In particular, we use an atomic norm regularized
least-squares problem to denoise a sum of complex exponentials with unknown
waveform modulations. We quantify how the mean square error depends on the
noise variance and the true signal parameters. Numerical experiments are also
implemented to illustrate the theoretical result.
