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Multiplicative Noise Removal Based on Unbiased Box-Cox Transformation

Part of: Nonlinear algebraic or transcendental equations Distribution theory Parametric inference

Published online by Cambridge University Press:  06 July 2017

Yu-Mei Huang ,
Hui-Yin Yan  and
Tieyong Zeng
Yu-Mei Huang*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P.R. China
Hui-Yin Yan*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P.R. China
Tieyong Zeng*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong HKBU Institute of Research and Continuing Education, Shenzhen Virtual University Park, Shenzhen 518057, China
*
*Corresponding author. Email addresses:zeng@hkbu.edu.hk (T. Zeng), huangym@lzu.edu.cn (Y.-M. Huang), yanhy12@lzu.edu.cn (H.-Y. Yan)
*Corresponding author. Email addresses:zeng@hkbu.edu.hk (T. Zeng), huangym@lzu.edu.cn (Y.-M. Huang), yanhy12@lzu.edu.cn (H.-Y. Yan)
*Corresponding author. Email addresses:zeng@hkbu.edu.hk (T. Zeng), huangym@lzu.edu.cn (Y.-M. Huang), yanhy12@lzu.edu.cn (H.-Y. Yan)

Abstract

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Multiplicative noise removal is a challenging problem in image restoration. In this paper, by applying Box-Cox transformation, we convert the multiplicative noise removal problem into the additive noise removal problem and the block matching three dimensional (BM3D) method is applied to get the final recovered image. Indeed, BM3D is an effective method to remove additive Gaussian white noise in images. A maximum likelihood method is designed to determine the parameter in the Box-Cox transformation. We also present the unbiased inverse transform for the Box-Cox transformation which is important. Both theoretical analysis and experimental results illustrate clearly that the proposed method can remove multiplicative noise very well especially when multiplicative noise is heavy. The proposed method is superior to the existing methods for multiplicative noise removal in the literature.

Keywords

Multiplicative noise removalBox-Cox transformationmaximum likelihood estimationblock-matching three dimensional method (BM3D)

MSC classification

Secondary: 62E17: Approximations to distributions (nonasymptotic) 62F10: Point estimation 65H05: Single equations 68U10: Image processing

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 3 , September 2017 , pp. 803 - 828
Copyright
Copyright © Global-Science Press 2017 

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