Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisation
<|reference_start|>Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisation: The incorporation of generative models as regularisers within variational formulations for inverse problems has proven effective across numerous image reconstruction tasks. However, the resulting optimisation problem is often non-convex and challenging to solve. In this work, we show that score-based generative models (SGMs) can be used in a graduated optimisation framework to solve inverse problems. We show that the resulting graduated non-convexity flow converge to stationary points of the original problem and provide a numerical convergence analysis of a 2D toy example. We further provide experiments on computed tomography image reconstruction, where we show that this framework is able to recover high-quality images, independent of the initial value. The experiments highlight the potential of using SGMs in graduated optimisation frameworks. The source code is publicly available on GitHub.<|reference_end|>
@article{fernsel2024convergence,
    title={Convergence Properties of Score-Based Models for Linear Inverse Problems
  Using Graduated Optimisation},
    author={Pascal Fernsel, v{Z}eljko Kereta, Alexander Denker},
    journal={arXiv preprint arXiv:2404.18699},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.18699},
    primaryClass={cs.LG cs.CV eess.IV}
}