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This work is concerned with the following fundamental question in scientificmachine learning: Can deep-learning-based methods solve noise-free inverseproblems to near-perfect accuracy? Positive evidence is provided for the firsttime, focusing on a prototypical computed tomography (CT) setup. We demonstratethat an iterative end-to-end network scheme enables reconstructions close tonumerical precision, comparable to classical compressed sensing strategies. Ourresults build on our winning submission to the recent AAPM DL-Sparse-View CTChallenge. Its goal was to identify the state-of-the-art in solving thesparse-view CT inverse problem with data-driven techniques. A specificdifficulty of the challenge setup was that the precise forward model remainedunknown to the participants. Therefore, a key feature of our approach was toinitially estimate the unknown fanbeam geometry in a data-driven calibrationstep. Apart from an in-depth analysis of our methodology, we also demonstrateits state-of-the-art performance on the open-access real-world dataset LoDoPaBCT.

Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning