On the regularizing behavior of the SDA and SDC gradient methods in the solution of linear ill-posed problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:302

Article

De Asmundis, Roberta¹  Di Serafino, Daniela²  Landia, Germana³ 

[1] Univ Roma La Sapienza, Dipartimento Ingn Informat Automat & Gest Antonio, Via Ariosto 25, I-00185 Rome, Italy

[2] Univ Naples 2, Dipartimento Matemat & Fis, Viale A Lincoln 5, I-81100 Caserta, Italy

[3] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40127 Bologna, Italy

关键词: Discrete linear inverse problems;    Least squares problems;    Iterative regularization;    Gradient methods;   

DOI  :  10.1016/j.cam.2016.01.007

来源: Elsevier

【 摘 要 】

We analyze the regularization properties of two recently proposed gradient methods, SDA and SDC, applied to discrete linear inverse problems. By studying their filter factors, we show that the tendency of these methods to eliminate first the eigencomponents of the gradient corresponding to large singular values allows to reconstruct the most significant part of the solution, thus yielding a useful filtering effect. This behavior is confirmed by numerical experiments performed on some image restoration problems. Furthermore, the experiments show that, for severely ill-conditioned problems and high noise levels, the SDA and SDC methods can be competitive with the Conjugate Gradient (CG) method, since they are slightly slower than CG, but exhibit a better semiconvergence behavior. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free