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.

翻译：将生成模型作为正则化项融入逆问题的变分公式中，已在众多图像重建任务中展现出有效性。然而，由此产生的优化问题通常是非凸且难以求解的。在本工作中，我们证明分数生成模型（SGMs）可用于逐步优化框架以求解逆问题。我们表明，由此产生的逐步非凸性流收敛至原问题的驻点，并给出了一个二维玩具示例的数值收敛性分析。此外，我们在计算机断层扫描图像重建上进行了实验，结果表明该框架能够独立于初始值恢复高质量图像。这些实验凸显了在逐步优化框架中使用SGMs的潜力。