Title:

Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision

Abstract:

As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. We study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. We show that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. Multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the augmented Lagrange multiplier paradigm. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting.

Bio:

Lei Zhang (M’04, SM’14) received the B.Sc. degree in 1995 from Shenyang Institute of Aeronautical Engineering, Shenyang, P.R. China, the M.Sc. and Ph.D degrees in Control Theory and Engineering from Northwestern Polytechnical University, Xi’an, P.R. China, respectively in 1998 and 2001. From 2001 to 2002, he was a research associate in the Dept. of Computing, The Hong Kong Polytechnic University. From Jan. 2003 to Jan. 2006 he worked as a Postdoctoral Fellow in the Dept. of Electrical and Computer Engineering, McMaster University, Canada. In 2006, he joined the Dept. of Computing, The Hong Kong Polytechnic University, as an Assistant Professor. Since Sept. 2010, he has been an Associate Professor in the same department. His research interests include Computer Vision, Pattern Recognition, Image and Video Processing, and Biometrics, etc. Dr. Zhang has published more than 200 papers in those areas. By 2015, his publications have been cited more than 12,000 times in literature. Dr. Zhang is currently an Associate Editor of IEEE Trans. on Image Processing, IEEE Trans. on CSVT and Image and Vision Computing. He was awarded the 2012-13 Faculty Award in Research and Scholarly Activities. More information can be found in his homepage http://www4.comp.polyu.edu.hk/~cslzhang/.