Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems

We study the problem of reconstructing solutions inverse problems when only noisy measurements are available. assume that can be modeled with an infinite-dimensional forward operator is not continuously invertible. Then, we restrict this to finite-dimensional spaces so Lipschitz continuous. For operator, demonstrate there exists a neural network which robust-to-noise approximation operator. In addition, show these networks learned from appropriately perturbed training data. admissibility approach wide range practical interest. Numerical examples given support theoretical findings.