Convergence Properties of Score-Based Models for Linear Inverse Problems Using Graduated Optimisation
This work addresses the problem of reliable optimization for inverse problems in image reconstruction, though it appears incremental as it builds on existing graduated optimization methods with score-based models.
The authors tackled the challenge of solving non-convex optimization problems in inverse image reconstruction by using score-based generative models within a graduated optimization framework, showing convergence to stationary points and demonstrating high-quality image recovery in computed tomography experiments.
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.