Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems
Not on the map. Why?
Abstract (arXiv)
We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible. Then, we restrict this forward operator to finite-dimensional spaces so that the inverse is Lipschitz continuous. For the inverse operator, we demonstrate that there exists a neural network which is a robust-to-noise approximation of the operator. In addition, we show that these neural networks can be learned from appropriately perturbed training data. We demonstrate the admissibility of this approach to a wide range of inverse problems of practical interest. Numerical examples are given that support the theoretical findings.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 23 of its 78 references that are in the map. First posted on arXiv 2 Jun 2022.
Builds on
23 of 78 references.
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11 more
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Citing papers per year: 2022: 1; 2023: 1; 2024: 1.
3 papers.