Joint inversion of multiple observation models has important applications in many disciplines including geoscience, image processing and computational biology. One of the methodologies for joint inversion of ill-posed...
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Joint inversion of multiple observation models has important applications in many disciplines including geoscience, image processing and computational biology. One of the methodologies for joint inversion of ill-posed observation equations naturally leads to multi-parameter regularization, which has been intensively studied over the last several years. However, problems such as the choice of multiple regularizationparameters remain unsolved. In the present study, we discuss a rather general approach to the regularization of multiple observation models, based on the idea of the linear aggregation of approximations corresponding to different values of the regularizationparameters. We show how the well-known linear functional strategy can be used for such an aggregation and prove that the error of a constructive aggregator differs from the ideal error value by a quantity of an order higher than the best guaranteed accuracy from the most trustable observation model. The theoretical analysis is illustrated by numerical experiments with simulated data.
For the solution of linear ill-posed problems, in this paper we introduce a simple algorithm for the choice of the regularizationparameters when performing multi-parameter Tikhonov regularization through an iterative...
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For the solution of linear ill-posed problems, in this paper we introduce a simple algorithm for the choice of the regularizationparameters when performing multi-parameter Tikhonov regularization through an iterative scheme. More specifically, the new technique is based on the use of the Arnoldi-Tikhonov method and the discrepancy principle. Numerical experiments arising from the discretization of integral equations are presented.
We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong...
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We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multiparameterregularization over the single parameterregularization.
We propose multi-parameter regularization methods for high-resolution image reconstruction which is described by an ill-posed problem. The regularization operator for the ill-posed problem is decomposed in a multiscal...
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We propose multi-parameter regularization methods for high-resolution image reconstruction which is described by an ill-posed problem. The regularization operator for the ill-posed problem is decomposed in a multiscale manner by using bi-orthogonal wavelets or tight frames. In the multiscale framework, for different scales of the operator we introduce different regularization. parameters. These methods are analyzed under certain reasonable hypotheses. Numerical examples are presented to demonstrate the efficiency and accuracy of these methods.
The iteratively regularized Gauss-Newton algorithm with simple bounds on the variables is extended to the multi-parameter case. The global regularization matrix is computed by using the L-curve method for a sequence o...
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The iteratively regularized Gauss-Newton algorithm with simple bounds on the variables is extended to the multi-parameter case. The global regularization matrix is computed by using the L-curve method for a sequence of one-parameterregularization problems. Numerical results concerning the joint retrieval of O-3 and NO2 profiles using the scattered light from the limb of the atmosphere are presented. (C) 2004 Elsevier B.V. All rights reserved.
For solving linear ill-posed problems, regularization methods are required when the right-hand side and/or the operator are corrupted by some noise. In the present paper, regularized solutions are constructed using re...
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For solving linear ill-posed problems, regularization methods are required when the right-hand side and/or the operator are corrupted by some noise. In the present paper, regularized solutions are constructed using regularized total least squares (RTLS) and dual regularized total least squares (DRTLS). We discuss computational aspects and provide order optimal error bounds that characterize the accuracy of the regularized solutions. The results extend earlier results where the operator is exactly given. We also present some numerical experiments, which shed light on the relationship between RTLS, DRTLS, and the standard Tikhonov regularization.
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