IJPAM: Volume 49, No. 3 (2008)

REGULARIZATION METHODS FOR DISCRETE
ILL-POSED PROBLEMS IN IMAGING

G. Landi$^1$, E. Loli Piccolomini$^2$, F. Zama$^3$
$^{1,2,3}$Department of Mathematics
University of Bologna
Via Zamboni, Bologna, 33-40126, ITALY
$^1$e-mail: landig@dm.unibo.it
$^2$e-mail: piccolom@dm.unibo.it
$^3$e-mail: zama@dm.unibo.it


Abstract.The analysis of inverse ill posed problems, modeled by Fredholm first kind integral equations, is performed by means of the linear compact operator theory. The regularization methods are introduced by means of the singular value expansion.

The Tikhonov regularization method is developed to treat discrete problems arising in the area of image reconstruction. Some examples are reported in the numerical results section.

Received: August 14, 2008

AMS Subject Classification: 65R32, 45B05, 45Q05

Key Words and Phrases: ill-posed problems, regularization methods, Tikhonov method, image restoration

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 3