Modern regularization methods for inverse problems

By Martin Benning, Martin Burger. Acta Numerica, 2018

423 citations recorded by the source corpus.

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses. In the last two decades interest has shifted from linear to nonlinear regularization methods, even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this shift towards modern nonlinear regularization methods, including their analysis, applications and issues for future research. In particular we will discuss variational methods and techniques derived from them, since they have attracted much recent interest and link to other fields, such as image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions and learning theory.

Subfields: Biomedical Engineering, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/de2e9799e9ad70afb4e5b9b0fc789840a9818b2a

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In Biomedical Engineering

1. Carola-Bibiane Schönlieb
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3. Simon Robert Arridge
4. Peter Maass
5. Shuhao Cao

In Computational Mechanics

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Citations in the corpus

• Inverting Gradients - How easy is it to break privacy in federated learning? (2020, background): “If p < n, then reconstruction is at least as difficult as image recovery from incomplete data [4, 2], but even when p > n, which we would expect in most computer vision applications, the difficulty of regularized “inversion" of∇θLθ relates to the non-linearity of the gradient operator as well as its”
• Solving inverse problems using data-driven models (2019, methodology): “UCL, Institute of Education, on 18 Oct 2019 at 15:29:08, subject to the Cambridge Core terms of use, available at methods for approximating solutions in a stable way in the presence of noise (Engl, Hanke and Neubauer 2000, Benning and Burger 2018, Louis 1989, Kirsch 2011).”