Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisation

Pascal Fernsel, Željko Kereta, Alexander Denker
4/29/2024
cs.LGcs.CVeess.IV

No official code found. Best implementation: alexdenker/GradOpt-SGM (2 stars, MIT, last commit 2024-08-12).

Abstract

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.

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alexdenker/GradOpt-SGMCommunity100%
MIT

Official Implementation of "Convergence Properties of Score-Based Models using Graduated Optimisation for Linear Inverse Problems"

20Python, Jupyter NotebookJul 18, 20242 years agoMIT

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Cite this paper

@article{fernsel2024convergence,
  title  = {Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisation},
  author = {Pascal Fernsel and Željko Kereta and Alexander Denker},
  year   = {2024},
  eprint = {2404.18699},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2404.18699v2}
}

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