TY - JOUR
T1 - A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations
AU - Qianshun Chang, Xuecheng Tai & Lily Xing
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 353
EP - 376
PY - 2009
DA - 2009/02
SN - 2
DO - http://doi.org/10.4208/nmtma.2009.m9001s
UR - https://global-sci.org/intro/article_detail/nmtma/6029.html
KW - Algorithm of denoising, image restoration, total variation, second-order functional.
AB - <p style="text-align: justify;">In this paper, we propose a compound algorithm for the image restoration.
The algorithm is a convex combination of the ROF model and the LLT model with a
parameter function $\theta$. The numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models. In particular,
the errors of the compound algorithm in $L_2$ norm between the exact images and corresponding restored images are the smallest among the three models. For images with
strong noises, the restored images of the compound algorithm are the best in the corresponding restored images. The proposed algorithm combines the fixed point method,
an improved AMG method and the Krylov acceleration. It is found that the combination
of these methods is efficient and robust in the image restoration.<br/></p>