English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We study the problem of reconstructing solutions of inverse problems whenonly noisy measurements are available. We assume that the problem can bemodeled with an infinite-dimensional forward operator that is not continuouslyinvertible. Then, we restrict this forward operator to finite-dimensionalspaces so that the inverse is Lipschitz continuous. For the inverse operator,we demonstrate that there exists a neural network which is a robust-to-noiseapproximation of the operator. In addition, we show that these neural networkscan be learned from appropriately perturbed training data. We demonstrate theadmissibility of this approach to a wide range of inverse problems of practicalinterest. Numerical examples are given that support the theoretical findings.

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