Article ID Journal Published Year Pages File Type
4637884 Journal of Computational and Applied Mathematics 2016 13 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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