@Article{NMTMA-3-461,
author = {Bai , ZhongZhiHuang , Yu-MeiK. Ng , Michael and Yang , Xi},
title = {Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2010},
volume = {3},
number = {4},
pages = {461--474},
abstract = {<p style="text-align: justify;">Image restoration is often solved by minimizing an energy function
consisting of a data-fidelity term and a regularization term. A
regularized convex term can usually preserve the image edges well
in the restored image. In this paper, we consider a class of convex
and edge-preserving regularization functions, i.e., multiplicative
half-quadratic regularizations, and we use the Newton method to
solve the correspondingly reduced systems of nonlinear equations. At
each Newton iteration, the preconditioned conjugate gradient method,
incorporated with a constraint preconditioner, is employed to solve
the structured Newton equation that has a symmetric positive
definite coefficient matrix. The eigenvalue bounds of the
preconditioned matrix are deliberately derived, which can be used to
estimate the convergence speed of the preconditioned conjugate
gradient method. We use experimental results to demonstrate that
this new approach is efficient, and the effect of image restoration
is reasonably good.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2010.m9014},
url = {http://global-sci.org/intro/article_detail/nmtma/6009.html}
}