Commun. Comput. Phys.,
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Volume 4.


Lipschitz and Total-Variational Regularization for Blind Deconvolution

Yu-Mei Huang 1, Michael K. Ng 2*

1 Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong; and Department of Mathematics, Lanzhou University, Gansu, China.
2 Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.

Received 3 June 2007; Accepted (in revised version) 9 November 2007
Available online 27 February 2008

Abstract

In \cite{chan298}, Chan and Wong proposed to use total variational regularization for both images and point spread functions in blind deconvolution. Their experimental results show that the detail of the restored images cannot be recovered. In this paper, we consider images in Lipschitz spaces, and propose to use Lipschitz regularization for images and total variational regularization for point spread functions in blind deconvolution. Our experimental results show that such combination of Lipschitz and total variational regularization methods can recover both images and point spread functions quite well.

AMS subject classifications: 52B10, 65D18, 68U05, 68U07

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Key words: Lipschitz regularization, total variational regularization, blind deconvolution, texture, Poisson singular integral, alternating iterative algorithm.

*Corresponding author.
Email: ymhuang@math.hkbu.edu.hk (Y. M. Huang), mng@math.hkbu. edu.hk (M. K. Ng)
 

The Global Science Journal