Last edited by Zolozshura

Saturday, July 25, 2020 | History

6 edition of **Ill-Posed Variational Problems and Regularization Techniques** found in the catalog.

- 274 Want to read
- 35 Currently reading

Published
**February 15, 2000**
by Springer-Verlag Telos
.

Written in English

- Decision theory: general,
- Differential equations,
- Numerical analysis,
- Operational research,
- Calculus Of Variations,
- Mathematics,
- Science/Mathematics,
- Calculus,
- Economics - General,
- Operations Research,
- Mathematical Analysis,
- Improperly posed problems,
- Variational inequalities (Math,
- Variational inequalities (Mathematics)

**Edition Notes**

Contributions | M. A. Thera (Editor), Rainer Tichatschke (Editor) |

The Physical Object | |
---|---|

Format | Paperback |

Number of Pages | 274 |

ID Numbers | |

Open Library | OL12809679M |

ISBN 10 | 3540663231 |

ISBN 10 | 9783540663232 |

Page - Well-posedness and convergence of some regularization methods for nonlinear ill-posed problems, Inverse Problems, 5() [69] M. Appears in 7 books from Page - . Abstract: Variational methods have started to be widely applied to ill-posed inverse problems since they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters, which can be estimated through computationally expensive and time-consuming processes.

In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is the process of adding information in order to solve an ill-posed problem or to prevent overfitting.. Regularization applies to objective functions in ill-posed optimization problems. Abstract. In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on .

the negative-log of the Poisson likelihood function is an ill-posed problem, and hence some form of regularization is required. In previous work, the authors have performed theoretical analyses of two approaches for regularization in this setting: standard Tikhonov regularization in and total. This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving.

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Ill-posed Variational Problems and Regularization Techniques Paperback – Novem by Michel Thera (Editor)Author: Michel Thera. Buy Ill-posed Variational Problems and Regularization Techniques (Lecture Notes in Economics and Mathematical Systems) on FREE SHIPPING on qualified orders Ill-posed Variational Problems and Regularization Techniques (Lecture Notes in Economics and Mathematical Systems): Théra, Michel, Tichatschke, Rainer: : Books.

Book Title Ill-posed Variational Problems and Regularization Techniques Book Subtitle Proceedings of the “Workshop on Ill-Posed Variational Problems and Regulation Techniques” held at the University of Trier, September 3–5, Editors.

Michel Thera; Rainer Tichatschke; Series Title Lecture Notes in Economics and Mathematical Systems Series Volume Ill-posed Variational Ill-Posed Variational Problems and Regularization Techniques book and Regularization Techniques Proceedings of the “Workshop on Ill-Posed Variational Problems and Regulation Techniques” held at the University of Trier, September 3–5, Editors (view affiliations) Search within book.

Front Matter. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study.

Solutions of Ill-Posed Problems (A. Tikhonov and V. Arsenin) Related Databases. Ensemble-Based Variational Method for Nonlinear Inversion of Surface Gravity Waves. A new investigation into regularization techniques for the method of fundamental solutions. Regularization of ill-posed problems Uno H¨amarik University of Tartu, Estonia Content 1.

Ill-posed problems (deﬁnition and examples) 2. Regularization of ill-posed problems with noisy data 3. Parameter choice rules for exact noise level 4. Iterative methods 5. Discretization methods 6. Lavrentiev and Tikhonov methods and modiﬁcations 7.

Stochastic errors. Approximation and regularization of the solution of linear problems in case of stochastic errors. 5 Iterative algorithms for solving non-linear ill-posed problems with tnonotonic operators.

Principle of iterative regularization Variational inequalities as a way of formulating non-linear problems aspects of regularization methods, and it is used worldwide as an advanced textbook as well as a scientific reference (see A, B, D above).

citations: P. HansenAnalysis of discrete ill, -posed problems by means of the L-curve, SIAM Review, 34 (), – The L-curve criterion is among the most successful methods for choosing.

The regularization toolbox provides a variety of func-tions for solving inverse problems, including the SVD and generalized SVD, truncated SVD solutions, Tikhonov reg-ularization, maximum entropy regularization, and a variety of examples.

[Han98] Per Christian Hansen. Rank{De cient and Discrete Ill-Posed Prob-lems. SIAM, Philadelphia, M2. This book presents practical optimization techniques used in image processing and computer vision problems.

Ill-posed problems are introduced and used as examples to show how each type of problem is related to typical image processing and computer vision problems. Unconstrained optimization gives.

point regularization for ill-posed VI’s with monotone operators and convex opti- In the monograph "Stable Methods for Ill-posed Variational Problems" [], the purpose was to give a general framework to the investigation of the case that reference is given to explicit statements or techniques.

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. solve a severely ill-posed problem. To address this prob-lem, various regularization techniques have been used in the literature.

For the purpose of infarct detection, sparse regularization in the spatial gradient domain of the ac-tion potential has been shown to be effective [2].

It is based on the idea that between depolarization and repo. 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. Abstract. We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing.

We are motivated by the problem of restoring noisy and blurry images via variational methods by using total variation regularization. In: M. Théra and R. Tichatschke (Eds.), Ill-posed Variational Problems and Regularization Techniques, pp.

99– Springer, Berlin/Heidelberg.] to a general class of smoothing functions and show that a weak second-order necessary optimality condition holds at the limit point of a sequence of stationary points found by the smoothing method.

Ill-posed variational problems and regularization techniques: proceedings of the "Workshop on Ill-Posed Variational Problems and Regulation Techniques" held at the University of Trier, September Regularization methods are a key tool in the solution of inverse problems.

They are used to introduce prior knowledge and allow a robust approxima-tion of ill-posed (pseudo-) inverses.

In the last two decades interest has shifted from linear to nonlinear regularization methods, even for linear inverse prob-lems. Add tags for "Ill-posed Variational Problems and Regularization Techniques: Proceedings of the "Workshop on Ill-Posed Variational Problems and Regulation Techniques" held at the University of Trier, September".

Be the first. Description: This book is devoted to the mathematical theory of regularization methods and gives an account of the currently available results about regularization methods for linear and nonlinear ill-posed problems.

Both continuous and iterative regularization methods are considered in detail with special emphasis on the development of parameter choice and stopping rules which lead to optimal .3 Ill-Posed Inverse Problems and Regularization In this section we give a very brief account of linear inverse problems and regularization theory [15], [7].

Let H and K be two Hilbert spaces and A: H! K a linear bounded operator. Consider the equation Af = g (3) where g ;g 2 K and kg g kK. Here g represents the exact, unknown data and g the. Unfortunately it is a well known fact that is not continuously invertible on, and this implies that the problem of inversion is ill-posed.

For this reason, regularization methods have to be introduced to stabilize the inversion in the presence of data noise.