Project
AA5-11
Data-Adaptive Discretization of Inverse Problems
Project Heads
Tim Jahn
Project Members
Mikhail Kirilin
Project Duration
01.05.2024 − 30.04.2026
Located at
TU Berlin
Description
We plan to extend the recently introduced discretization-adaptive reguarization technique to two- and higher-dimensional inverse problems as they appear for example in mathematical imaging. Hereby we lay a focus onto the analysis and application of untrained neural networks as regularization methods, e.g the deep image prior (DIP). We use a pretraining procedure to reduce the dimensionality of the network. The final reduced dimension is determined in a data-driven way by applying discretiation-adaptive regularization.
External Website
Selected Publications
- T. Jahn, M. Kirilin. Dimensionality reduction of NNs via pretraining. under preparation
- T. Jahn, B. Jin. Early stopping of untrained convolutional neural networks. preprint
- T. Jahn. Discretization-adaptive regularization of inverse problems. preprint
- T. Jahn. Noise level free regularization of general linear inverse problems under unknown white noise. SIAM/ASA Journal of Uncertainty Quantification. 2023. arxiv
Selected Pictures
Training dynamics of the DIP reconstruction. Left: residual errors (and noise level, indicated by the red horizontal line). Right: reconstruction errors.