Simpler Gradient Methods for Blind Super-Resolution with Lower Iteration Complexity
<|reference_start|>Simpler Gradient Methods for Blind Super-Resolution with Lower Iteration Complexity: We study the problem of blind super-resolution, which can be formulated as a low-rank matrix recovery problem via vectorized Hankel lift (VHL). The previous gradient descent method based on VHL named PGD-VHL relies on additional regularization such as the projection and balancing penalty, exhibiting a suboptimal iteration complexity. In this paper, we propose a simpler unconstrained optimization problem without the above two types of regularization and develop two new and provable gradient methods named VGD-VHL and ScalGD-VHL. A novel and sharp analysis is provided for the theoretical guarantees of our algorithms, which demonstrates that our methods offer lower iteration complexity than PGD-VHL. In addition, ScalGD-VHL has the lowest iteration complexity while being independent of the condition number. Furthermore, our novel analysis reveals that the blind super-resolution problem is less incoherence-demanding, thereby eliminating the necessity for incoherent projections to achieve linear convergence. Empirical results illustrate that our methods exhibit superior computational efficiency while achieving comparable recovery performance to prior arts.<|reference_end|>
@article{li2024simpler,
    title={Simpler Gradient Methods for Blind Super-Resolution with Lower Iteration
  Complexity},
    author={Jinsheng Li, Wei Cui, and Xu Zhang},
    journal={arXiv preprint arXiv:2409.18387},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.18387},
    primaryClass={cs.IT math.IT}
}