Stability of Data-Dependent Ridge-Regularization for Inverse Problems
by Sebastian Neumayer, Fabian Altekrüger
Year:
2025
Publication:
Inverse Problems
Abstract:
Theoretical guarantees for the robust solution of inverse problems have important implications for applications. To achieve both guarantees and high reconstruction quality, we propose learning a pixel-based ridge regularizer with a data-dependent and spatially varying regularization strength. For this architecture, we establish the existence of solutions to the associated variational problem and the stability of its solution operator. Further, we prove that the reconstruction forms a maximum-a-posteriori approach. Simulations for biomedical imaging and material sciences demonstrate that the approach yields high-quality reconstructions even if only a small instance-specific training set is available.
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Brief introduction of the dida co-author(s) and relevance for dida's ML developments.
Fabian Altekrüger (PhD)
During his mathematics studies at TU Berlin, Fabian focused on functional analysis. In his subsequent doctoral research, he worked on the regularization and solution of Bayesian inverse problems in mathematical image processing, combining mathematical methods with neural networks. In this context, Fabian developed and applied conditional generative models, always with an emphasis on the stability and robustness of the methods. At dida, he contributes his skills as a machine learning scientist.