Work

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

Year: 2024

Type: conference-paper

Abstract: 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 code is available11https://github.com/alexdenker/GradOpt-SGM.

Source: IEEE International Workshop on Machine Learning for Signal Processing (MLSP)

DOI: 10.1109/mlsp58920.2024.10734770

Authors: Pascal Fernsel, Željko Kereta, Alexander Denker

Institutions: University of Bremen, University College London

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Engineering and Physical Sciences Research Council

Awards: G6454571012, GRK 2224: Pi3: Parameter Identifikation – Analyse, Algorithmen, Anwendungen