Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisation
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arXiv
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| Format: | Preprint |
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2024
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| author | Fernsel, Pascal Kereta, Željko Denker, Alexander |
| author_facet | Fernsel, Pascal Kereta, Željko Denker, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisation Fernsel, Pascal Kereta, Željko Denker, Alexander Machine Learning Computer Vision and Pattern Recognition Image and Video Processing 68T10 (Primary) 65K10, 94A08 (Secondary) G.1.6; G.1.10; I.4.0; I.4.5 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. |
| title | Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisation |
| topic | Machine Learning Computer Vision and Pattern Recognition Image and Video Processing 68T10 (Primary) 65K10, 94A08 (Secondary) G.1.6; G.1.10; I.4.0; I.4.5 |
| url | https://arxiv.org/abs/2404.18699 |