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

Autor:	Fernsel, Pascal, Kereta, Željko, Denker, Alexander
Rok vydání:	2024
Předmět:	Computer Science - Machine Learning Computer Science - Computer Vision and Pattern Recognition Electrical Engineering and Systems Science - Image and Video Processing 68T10 (Primary) 65K10 94A08 (Secondary) G.1.6 G.1.10 I.4.0 I.4.5
Druh dokumentu:	Working Paper
Popis:	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. Comment: 8 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.18699 Zobrazit plný text záznamu View this record from Arxiv