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.
Zama, F., Loli Piccolomini, E., Landi, G. (2004). A descent method for computing the Tikhonov regularized solution of linear inverse problems, 5562, 152-160 [10.1117/12.555819].
A descent method for computing the Tikhonov regularized solution of linear inverse problems
Zama F.;Loli Piccolomini E.;Landi G.
2004
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
