  In mathematics, a super-resolution problem can be formulated as acquiring
high-frequency data from low-frequency measurements. This extrapolation problem
in the frequency domain is well-known to be unstable. We propose the
model-based super-resolution framework (Model-SR) to address this
ill-posedness. Within this framework, we can recover the signal by solving a
nonlinear least square problem and achieve the super-resolution. Theoretically,
the resolution-enhancing map is proved to have Lipschitz continuity under mild
conditions, leading to a stable solution to the super-resolution problem. We
apply the general theory to three concrete models and give the stability
estimates for each model. Numerical experiments are conducted to show the
super-resolution behavior of the proposed framework. The model-based
mathematical framework can be extended to problems with similar structures.
