A descent method for computing the Tikhonov regularized solution of linear inverse problems

Fabiana Zama; Elena Loli Piccolomini; Germana Landi

doi:10.1117/12.555819

22 October 2004 A descent method for computing the Tikhonov regularized solution of linear inverse problems

Fabiana Zama, Elena Loli Piccolomini, Germana Landi

Proceedings Volume 5562, Image Reconstruction from Incomplete Data III; (2004) https://doi.org/10.1117/12.555819
Event: Optical Science and Technology, the SPIE 49th Annual Meeting, 2004, Denver, Colorado, United States

Abstract

In this paper we describe an iterative algorithm, called Descent-TCG, based on truncated Conjugate Gradient iterations to compute Tikhonov regularized solutions of linear ill-posed problems. Suitable termination criteria are built-up to define an inner-outer iteration scheme for the computation of a regularized solution. Numerical experiments are performed to compare the algorithm with other well-established regularization methods. We observe that the best Descent-TCG results occur for highly noised data and we always get fairly reliable solutions, preventing the dangerous error growth often appearing in other well-established regularization methods. Finally, the Descent-TCG method is computationally advantageous especially for large size problems.

Citation Download Citation

Fabiana Zama, Elena Loli Piccolomini, and Germana Landi "A descent method for computing the Tikhonov regularized solution of linear inverse problems", Proc. SPIE 5562, Image Reconstruction from Incomplete Data III, (22 October 2004); https://doi.org/10.1117/12.555819

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