TY - JOUR
T1 - Multiplicative noise removal in imaging
T2 - An exp-model and its fixed-point proximity algorithm
AU - Lu, Jian
AU - Shen, Lixin
AU - Xu, Chen
AU - Xu, Yuesheng
N1 - Funding Information:
The authors would like to thank Dr. Hyenkyun Woo for providing the source codes of both m V model and TwL- m V model, Dr. You-wei Wen for the HNW model, and Dr. Tieyong Zeng for the DZ model. Jian Lu and Chen Xu were supported in part by the National Natural Science Foundation of China under grants 61373087 , 11201312 , 61472257 , by the Natural Science Foundation of Guangdong, China under grants 2015A030313550 , 2015A030313557 , by the Foundation for Distinguished Young Teachers in Higher Education of Guangdong, China under grant Yq2013144 and by the Specialized Research Fund for the Doctoral Program of Higher Education of China under grant 20134408110001 . Lixin Shen and Yuesheng Xu were supported in part by the US National Science Foundation under grants DMS-1522332 and DMS-1115523 , by Guangdong Provincial Government of China through the “Computational Science Innovative Research Team” program and by the National Natural Science Foundation of China under grants 11071286 , 91130009 , 11171354 and 61375006 .
Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - We propose a variational model for restoration of images corrupted by multiplicative noise. The proposed model formulated in the logarithm transform domain of the desirable images consists of a data fitting term, a quadratic term, and a total variation regularizer. The data fitting term results directly from the presence of the multiplicative noise and the quadratic term reflects the statistics of the noise. We show that the proposed model is strictly convex under a mild condition. The solution of the model is then characterized in terms of the fixed-point of a nonlinear map described by the proximity operator of a function involved in the model. Based on the characterization, we present a fixed-point proximity algorithm for solving the model and analyze its convergence. Our numerical results indicate that the proposed model compares favorably to several existing state-of-the-art models with better results in terms of the peak signal-to-noise ratio of the denoised images and the CPU time consumed.
AB - We propose a variational model for restoration of images corrupted by multiplicative noise. The proposed model formulated in the logarithm transform domain of the desirable images consists of a data fitting term, a quadratic term, and a total variation regularizer. The data fitting term results directly from the presence of the multiplicative noise and the quadratic term reflects the statistics of the noise. We show that the proposed model is strictly convex under a mild condition. The solution of the model is then characterized in terms of the fixed-point of a nonlinear map described by the proximity operator of a function involved in the model. Based on the characterization, we present a fixed-point proximity algorithm for solving the model and analyze its convergence. Our numerical results indicate that the proposed model compares favorably to several existing state-of-the-art models with better results in terms of the peak signal-to-noise ratio of the denoised images and the CPU time consumed.
KW - Exp-model
KW - Fixed-point proximity algorithm
KW - Multiplicative noise
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U2 - 10.1016/j.acha.2015.10.003
DO - 10.1016/j.acha.2015.10.003
M3 - Article
AN - SCOPUS:84951096746
SN - 1063-5203
VL - 41
SP - 518
EP - 539
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 2
ER -