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A COMBINED FIRST-ORDER AND SECOND-ORDER VARIATION APPROACH FOR MULTIPLICATIVE NOISE REMOVAL

Published online by Cambridge University Press:  22 December 2014

LE JIANG ,
JIN HUANG ,
JUN LIU  and
XIAO-GUANG LV
LE JIANG
Affiliation:
School of Science, Huaihai Institute of Technology, Lianyungang, Jiangsu, 222005, China email math_jiangle@126.com, xiaoguanglv@126.com School of Mathematical Sciences/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China email huangjin2345@126.com, sino.roy@163.com
JIN HUANG
Affiliation:
School of Mathematical Sciences/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China email huangjin2345@126.com, sino.roy@163.com
JUN LIU
Affiliation:
School of Mathematical Sciences/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China email huangjin2345@126.com, sino.roy@163.com
XIAO-GUANG LV*
Affiliation:
School of Science, Huaihai Institute of Technology, Lianyungang, Jiangsu, 222005, China email math_jiangle@126.com, xiaoguanglv@126.com
*
✉xiaoguanglv@126.com
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Abstract

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Denoising of images corrupted by multiplicative noise is an important task in various applications, such as laser imaging, synthetic aperture radar and ultrasound imaging. We propose a combined first-order and second-order variational model for removal of multiplicative noise. Our model substantially reduces the staircase effects while preserving edges in the restored images, since it combines advantages of the first-order and second-order total variation. The issues of existence and uniqueness of a minimizer for this variational model are analysed. Moreover, a gradient descent method is employed to solve the associated Euler–Lagrange equation, and several numerical experiments are given to show the efficiency of our model. In particular, a comparison with an existing model in terms of peak signal-to-noise ratio and structural similarity index is provided.

Keywords

68U10multiplicative noise removaldenoisingtotal variationEuler–Lagrange equationstructural similarity index
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 2 , October 2014 , pp. 116 - 137
Copyright
Copyright © 2014 Australian Mathematical Society 

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