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

• URL: http://arxiv.org/abs/2404.18699v2
• Date: Mon, 12 Aug 2024 18:12:44 GMT
• Title: Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisation
• Authors: Pascal Fernsel, Željko Kereta, Alexander Denker,
• Abstract summary: We show that score-based generative models (SGMs) can be used to solve inverse problems. We show that we are able to recover high-Ms images, independent of the initial value. The source is publicly available on GitHub.
• Score: 44.99833362998488
• License: http://creativecommons.org/licenses/by/4.0/
• 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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