Model-based Super-resolution: Towards a Unified Framework for Super-resolution
<|reference_start|>Model-based Super-resolution: Towards a Unified Framework for Super-resolution: 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.<|reference_end|>
@article{fei2024model-based,
    title={Model-based Super-resolution: Towards a Unified Framework for
  Super-resolution},
    author={Zetao Fei, Hai Zhang},
    journal={arXiv preprint arXiv:2407.19480},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.19480},
    primaryClass={cs.IT eess.SP math.IT}
}