TY - JOUR
T1 - An Efficient Variational Model for Multiplicative Noise Removal
AU - Liu , Min
AU - Lu , Xiliang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 125
EP - 140
PY - 2022
DA - 2022/02
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2021-0065 
UR - https://global-sci.org/intro/article_detail/nmtma/20224.html
KW - Multiplicative noise, variational model, alternating direction minimization.
AB - <p style="text-align: justify;">In this paper, an efficient variational model for multiplicative noise removal is proposed. By using a MAP estimator, Aubert and Aujol [SIAM J. Appl.
Math., 68(2008), pp. 925-946] derived a nonconvex cost functional. With logarithmic transformation, we transform the image into a logarithmic domain which makes
the fidelity convex in the transform domain. Considering the TV regularization term
in logarithmic domain may cause oversmoothness numerically, we propose the TV
regularization directly in the original image domain, which preserves more details
of images. An alternative minimization algorithm is applied to solve the optimization problem. The $z$-subproblem can be solved by a closed formula, which makes the
method very efficient. The convergence of the algorithm is discussed. The numerical
experiments show the efficiency of the proposed model and algorithm.</p>