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576
A Discrepancy Principle For Tikhonov Regularization With Approximately Specified Data
 NUMER. FUNCT. ANAL. OPTIM
, 2000
"... Many discrepancy principles are known for choosing the parameter ff in the regularized operator equation (T T + ffI)x ffi ff = T y ffi , ky \Gamma y ffi k ffi, in order to approximate the minimal norm leastsquares solution of the operator equation Tx = y. In this paper we consider a c ..."
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Cited by 1 (0 self)
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Many discrepancy principles are known for choosing the parameter ff in the regularized operator equation (T T + ffI)x ffi ff = T y ffi , ky \Gamma y ffi k ffi, in order to approximate the minimal norm leastsquares solution of the operator equation Tx = y. In this paper we consider a
Parameter Selection for Total Variation Based Image Restoration Using Discrepancy Principle
"... The key issues in solving image restoration problem successfully are: the estimation of the regularization parameter which balances the datafidelity with the regularity of the solution; and the development of efficient numerical techniques for computing the solution. In this paper, we derive a fast ..."
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Cited by 5 (2 self)
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fast algorithm that simultaneously estimates the regularization parameter and restores the image. The new approach is based on totalvariation (TV) regularized strategy and Morozov discrepancy principle. The TV norm is represented by the dual formulation that changes the minimization problem into a
Morozov’s Discrepancy Principle for Tikhonovtype functionals with nonlinear operators
, 2009
"... In this paper we deal with Morozov’s discrepancy principle as an aposteriori parameter choice rule for Tikhonov regularization with general convex penalty terms Ψ for nonlinear inverse problems. It is shown that a regularization parameter α fulfilling the discprepancy principle exists, whenever th ..."
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Cited by 16 (9 self)
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In this paper we deal with Morozov’s discrepancy principle as an aposteriori parameter choice rule for Tikhonov regularization with general convex penalty terms Ψ for nonlinear inverse problems. It is shown that a regularization parameter α fulfilling the discprepancy principle exists, whenever
A discrepancy principle for the source points location in using the MFS for solving the BHCP
 Int. J. Comput. Meth
, 2009
"... Based on the discrepancy principle, we develop in this paper a new method of choosing the location of source points to solve the backward heat conduction problem (BHCP) by using the method of fundamental solutions (MFS). The standard Tikhonov regularization technique with the L curve method for an ..."
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Cited by 1 (0 self)
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Based on the discrepancy principle, we develop in this paper a new method of choosing the location of source points to solve the backward heat conduction problem (BHCP) by using the method of fundamental solutions (MFS). The standard Tikhonov regularization technique with the L curve method
Convergence rates for Morozov’s Discrepancy Principle using Variational Inequalities
"... We derive convergence rates for Tikhonovtype regularization with convex penalty terms, where the regularization parameter is chosen according to Morozov’s discrepancy principle and variational inequalities are used to generalize classical source and nonlinearity conditions. Rates are obtained first ..."
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Cited by 7 (1 self)
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We derive convergence rates for Tikhonovtype regularization with convex penalty terms, where the regularization parameter is chosen according to Morozov’s discrepancy principle and variational inequalities are used to generalize classical source and nonlinearity conditions. Rates are obtained
DISCREPANCY PRINCIPLE FOR STATISTICAL INVERSE PROBLEMS WITH APPLICATION TO CONJUGATE GRADIENT ITERATION
"... who passed away too early at the age of 60. Abstract. The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is welldefined, however a plain use of it may occasionally ..."
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Cited by 2 (1 self)
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who passed away too early at the age of 60. Abstract. The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is welldefined, however a plain use of it may
A Theory of Diagnosis from First Principles
 ARTIFICIAL INTELLIGENCE
, 1987
"... Suppose one is given a description of a system, together with an observation of the system's behaviour which conflicts with the way the system is meant to behave. The diagnostic problem is to determine those components of the system which, when assumed to be functioning abnormally, will explain ..."
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Cited by 1120 (5 self)
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, will explain the discrepancy between the observed and correct system behaviour. We propose a general theory for this problem. The theory requires only that the system be described in a suitable logic. Moreover, there are many such suitable logics, e.g. firstorder, temporal, dynamic, etc. As a result
On the discrepancy principle for some Newton type methods for solving nonlinear inverse problems
, 2008
"... ..."
REGULARIZATION ERROR ESTIMATES AND DISCREPANCY PRINCIPLE FOR OPTIMAL CONTROL PROBLEMS WITH INEQUALITY CONSTRAINTS
"... In this article we study the regularization of optimization problems by Tikhonov regularization. The optimization problems are subject to pointwise inequality constraints in L²(Ω). We derive apriori regularization error estimates if the regularization parameter as well as the noise level tend to ze ..."
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In this article we study the regularization of optimization problems by Tikhonov regularization. The optimization problems are subject to pointwise inequality constraints in L²(Ω). We derive apriori regularization error estimates if the regularization parameter as well as the noise level tend to zero. We rely on an assumption that is a combination of a source condition and of a structural assumption on the active sets. Moreover, we introduce a strategy to choose the regularization parameter in dependence of the noise level. We prove convergence of this parameter choice rule with optimal order.
ARCANGELI’S TYPE DISCREPANCY PRINCIPLES FOR A CLASS OF REGULARIZATION METHODS USING A MODIFIED PROJECTION SCHEME
, 2001
"... Solodkiı ̆ (1998) applied the modified projection scheme of Pereverzev (1995) for obtaining error estimates for a class of regularization methods for solving illposed operator equations. But, no a posteriori procedure for choosing the regularization parameter is discussed. In this paper, we conside ..."
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consider Arcangeli’s type discrepancy principles for such a general class of regularization methods with modified projection scheme. 1.
Results 11  20
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576