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Seminar abstract

Solving Constrained Total-Variation Image Restoration and Reconstruction Problems via Alternating Direction Methods

Michael Ng
Department of Mathematics
Hong Kong Baptist University

Abstract :

In this paper, we study alternating direction methods for solving constrained total-variation image restoration and reconstruction problems. Alternating direction methods can be implementable variants of the classical augmented Lagrangian method for optimization problems with separable structures and linear constraints. The proposed framework allows us to solve problems of image restoration, impulse noise removal, inpainting and image cartoon+texture decomposition. As the constrained model is employed, we only need to input the noise level and the estimation of the regularization parameter is not required in these imaging problems. Experimental results for such imaging problems are presented to illustrate the effectiveness of the proposed method. We show that the alternating direction method is very efficient for solving image restoration and reconstruction problems.


Michael Ng is a Professor in the Department of Mathematics at the Hong Kong Baptist University. He obtained his B.Sc. degree in 1990 and M.Phil. degree in 1992 at the University of Hong Kong, and Ph.D. degree in 1995 at Chinese University of Hong Kong. Michael is the Programme Director of the MSc Programme on Operational Research and Business Statistics and Director of the Centre for Mathematical Imaging and Vision (CMIV), Executive Director of the Institute for Computational Mathematics (ICM) at Hong Kong Baptist University. He is also the Engineering Panel Member of the Hong Kong Research Grants Council starting from 2009. Michael has published and edited 5 books, published more than 200 journal papers. He currently serves on the editorial boards of several international journals.
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