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Publication Detail
Iterative parameter choice by discrepancy principle
This work is concerned with the numerical implementation of the discrepancy principle for nonsmooth Tikhonov regularization for linear inverse problems. First, some theoretical properties of the solutions to the discrepancy equation, i.e., uniqueness and upper bounds, are discussed. Then, the idea of Padé approximation is exploited for designing model functions with model parameters iteratively updated. Two algorithms are proposed for its efficient numerical realization, i.e., a two-parameter algorithm based on model functions and a quasi-Newton method, and their convergence properties are briefly discussed. Numerical results for four nonsmooth models are presented to demonstrate the accuracy of the principle and to illustrate the efficiency and robustness of the proposed algorithms. © 2012 The author 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
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