NEW RULE FOR CHOICE OF THE REGULARIZATION PARAMETER IN (ITERATED) TIKHONOV METHOD
نویسندگان
چکیده
منابع مشابه
A Parameter Choice Method for Tikhonov Regularization
Abstract. A new parameter choice method for Tikhonov regularization of discrete ill-posed problems is presented. Some of the regularized solutions of a discrete ill-posed problem are less sensitive than others to the perturbations in the right-hand side vector. This method chooses one of the insensitive regularized solutions using a certain criterion. Numerical experiments show that the new met...
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In this paper we develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minim...
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We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and balancing principle, are studied for choosing an appropriate (vector-valued) regularization parameter, and some theoretical results are presented. In particular, t...
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The electrocardiographic imaging (ECGI) inverse problem is highly ill-posed and regularization is needed to stabilize the problem and to provide a unique solution. When Tikhonov regularization is used, choosing the regularization parameter is a challenging problem. Mathematically, a suitable value for this parameter needs to fulfill the Discrete Picard Condition (DPC). In this study, we propose...
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ژورنال
عنوان ژورنال: Mathematical Modelling and Analysis
سال: 2009
ISSN: 1392-6292,1648-3510
DOI: 10.3846/1392-6292.2009.14.187-198