期刊
ACTA NUMERICA
卷 27, 期 -, 页码 1-111出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0962492918000016
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资金
- Leverhulme Trust
- Isaac Newton Trust
- Cantab Capital Institute for the Mathematics of Information
- ERC via EU FP 7 - ERC [615216 LifeInverse]
- German Ministry for Science and Education (BMBF)
- Isaac Newton Institute for Mathematical Sciences, Cambridge - EPSRC [EP/K032208/1]
- EPSRC [EP/K032208/1] Funding Source: UKRI
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.
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