Commun. Comput. Phys., 13 (2013), pp. 1066-1092.


The Convex Relaxation Method on Deconvolution Model with Multiplicative Noise

Yumei Huang 1, Michael Ng 2, Tieyong Zeng 2*

1 School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
2 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.

Received 31 August 2011; Accepted (in revised version) 9 March 2012
Available online 21 September 2012
doi:10.4208/cicp.310811.090312a

Abstract

In this paper, we consider variational approaches to handle the multiplicative noise removal and deblurring problem. Based on rather reasonable physical blurring-noisy assumptions, we derive a new variational model for this issue. After the study of the basic properties, we propose to approximate it by a convex relaxation model which is a balance between the previous non-convex model and a convex model. The relaxed model is solved by an alternating minimization approach. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed method.

AMS subject classifications: 52A40, 65K10, 65K15, 90C26

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Key words: Alternating minimization, convergence, deblurring, multiplicative noise, non-convex model.

*Corresponding author.
Email: zeng@hkbu.edu.hk (T. Zeng)
 

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