AN INNER-OUTER REGULARIZING METHOD FOR ILL-POSED PROBLEMS

作者：Favati Paola^*; Lotti Grazia; Menchi Ornella; Romani Francesco

来源：Inverse Problems and Imaging, 2014, 8(2): 409-420.

DOI：10.3934/ipi.2014.8.409

• Regularization problems
• iterative methods
• conjugate gradient
• generalized cross validation
• inner-outer algorithms

Conjugate Gradient is widely used as a regularizing technique for solving linear systems with ill-conditioned coefficient matrix and right-hand side vector perturbed by noise. It enjoys a good convergence rate and computes quickly an iterate, say xk(opt), which minimizes the error with respect to the exact solution. This behavior can be a disadvantage in the regularization context, because also the high-frequency components of the noise enter quickly the computed solution, leading to a difficult detection of k(opt) and to a sharp increase of the error after the k(opt)th iteration. In this paper we propose an inner-outer algorithm based on a sequence of restarted Conjugate Gradients, with the aim of overcoming this drawback. A numerical experimentation validates the effectiveness of the proposed algorithm.

• 出版日期2014-5