Convergence Properties of Score-Based Models using Graduated Optimisation for Linear Inverse Problems
arxiv(2024)
摘要
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.
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