Regularization Methods for Nonlinear Ill-Posed Problems with Applications to Phase Reconstruction

Inverse Problems in Medical Imaging and Nondestructive Testing ◽

10.1007/978-3-7091-6521-8_3 ◽

1997 ◽

pp. 17-35 ◽

Author(s):

Barbara Blaschke-Kaltenbacher ◽

Heinz W. Engl

Keyword(s):

Regularization Methods ◽

Phase Reconstruction ◽

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On the Optimality of Regularization Methods for Solving Linear Ill-Posed Problems

Zeitschrift für Analysis und ihre Anwendungen ◽

10.4171/zaa/494 ◽

1994 ◽

Vol 13 (4) ◽

pp. 297-710 ◽

Author(s):

T. Schröter ◽

Ulrich Tautenhahn

Keyword(s):

Regularization Methods ◽

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On the Convergence of Regularization Methods for Ill-Posed Linear Operator Equations

Improperly Posed Problems and Their Numerical Treatment ◽

10.1007/978-3-0348-5460-3_6 ◽

1983 ◽

pp. 81-95 ◽

Author(s):

Heinz W. Engl

Keyword(s):

Linear Operator ◽

Regularization Methods ◽

Operator Equations ◽

Ill Posed ◽

Linear Operator Equations

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A posteriori parameter choice for general regularization methods for solving linear ill-posed problems

Applied Numerical Mathematics ◽

10.1016/0168-9274(88)90017-7 ◽

1988 ◽

Vol 4 (5) ◽

pp. 395-417 ◽

Author(s):

Heinz W. Engl ◽

Helmut Gfrerer

Keyword(s):

Regularization Methods ◽

A Posteriori ◽

Parameter Choice ◽

A Posteriori Parameter Choice ◽

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Convergence Rates of Spectral Regularization Methods: A Comparison between Ill-Posed Inverse Problems and Statistical Kernel Learning

SIAM Journal on Numerical Analysis ◽

10.1137/19m1256038 ◽

2020 ◽

Vol 58 (6) ◽

pp. 3504-3529

Author(s):

Sabrina Guastavino ◽

Federico Benvenuto

Keyword(s):

Inverse Problems ◽

Convergence Rates ◽

Kernel Learning ◽

Regularization Methods ◽

Spectral Regularization ◽

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Nonlinear regularization methods for ill-posed problems with piecewise constant or strongly varying solutions

Inverse Problems ◽

10.1088/0266-5611/25/11/115014 ◽

2009 ◽

Vol 25 (11) ◽

pp. 115014 ◽

Author(s):

H Egger ◽

A Leitão

Keyword(s):

Regularization Methods ◽

Piecewise Constant ◽

Ill Posed ◽

Nonlinear Regularization

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Iterative Regularization Methods for Nonlinear Ill-Posed Problems

10.1515/9783110208276 ◽

2008 ◽

Author(s):

Barbara Kaltenbacher ◽

Andreas Neubauer ◽

Otmar Scherzer

Keyword(s):

Regularization Methods ◽

Iterative Regularization ◽

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A class of regularization methods for ill-posed problems with nonexact data

Numerical Functional Analysis and Optimization ◽

10.1080/01630569208816502 ◽

1992 ◽

Vol 13 (5-6) ◽

pp. 601-614 ◽

Author(s):

Teresa Regińska

Keyword(s):

Regularization Methods ◽

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Regularization Methods for Ill-Posed Problems

Handbook of Mathematical Methods in Imaging ◽

10.1007/978-1-4939-0790-8_3 ◽

2015 ◽

pp. 91-123

Author(s):

Jin Cheng ◽

Bernd Hofmann

Keyword(s):

Regularization Methods ◽

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Approximation of Ill-Posed Volterra Problems via Predictor–Corrector Regularization Methods

SIAM Journal on Applied Mathematics ◽

10.1137/s0036139994274496 ◽

1996 ◽

Vol 56 (2) ◽

pp. 524-541 ◽

Author(s):

Patricia K. Lamm

Keyword(s):

Regularization Methods ◽

Ill Posed ◽

Predictor Corrector ◽

Volterra Problems

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Some insights into the regularization of III-posed problems

Mathematical Problems in Engineering ◽

10.1155/s1024123x99001040 ◽

1999 ◽

Vol 5 (2) ◽

pp. 161-171 ◽

Author(s):

J. Hańćkowiak

Keyword(s):

Regularization Methods ◽

In this paper a simple introduction to the problem of the regularization of ill-posed problems (IPP) is presented. We describe three regularization methods with simple examples which illustrate the principle that for “bad” equations it is unprofitable to carry out exact computations.

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