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Modern regularization methods for inverse problems
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DOI：10.1017/S0962492918000016.png)
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Abstract
En 中文
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.
Keywords:
ILL-POSED PROBLEMS
POSTERIORI PARAMETER CHOICE
LINEAR OPERATOR-EQUATIONS
ITERATED TIKHONOV REGULARIZATION
VARIATIONAL IMAGE DECOMPRESSION
LOGARITHMIC CONVERGENCE-RATES
TOTAL VARIATION MINIMIZATION
TGV-BASED FRAMEWORK
GAUSS-NEWTON METHOD
EM-TV METHODS
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11.3
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89
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