# CMIV Workshop on Matrix Computation

## 15 January 2018 Hong Kong Baptist University

Time:
14:15-17:30
Venue:
FSC1217, Fong Shu Chuen Building,
Ho Sin Hang Campus, Hong Kong Baptist University

 Speakers: Chen Xiao Shan, South China Normal University, China Guo Xueping, East China Normal University, China Jia Zhigang, Jiangsu Normal University, China Wen You-Wei, Hunan University, China Zhang Wenxing, University of Electronic Science and Technology of China, China

 Program 2:15-2:50 Jia Zhigang A Structure-Preserving Algorithm for General Quaternion Eigenvalue Problems Abstracts: TBC 2:50-3:25 Chen Xiao Shan Noda Iterations for Generalized Eigenproblems Following Perron-Frobenius Theory Abstracts: In this paper, we investigate the generalized eigenvalue problem $A{\bf x}=\lambda B {\bf x}$ arising from economic models. Under certain conditions, there is a simple generalized eigenvalue $\rho(A, B)$ in the interval $(0, 1)$ with a positive eigenvector. Based on the Noda iteration, a modified Noda iteration (MNI) and a generalized Noda iteration (GNI) are proposed for finding the generalized eigenvalue $\rho(A, B)$ and the associated unit positive eigenvector. It is proved that the GNI method always converges and has a quadratic asymptotic convergence rate. So GNI has a similar convergence behavior as MNI. The efficiency of these algorithms is illustrated by numerical examples. 3:25-3:45 Break 3:45-4:20 Guo Xueping The SOR-like Methods for Saddle Point Problems Abstracts: TBC 4:20-4:55 Wen You-Wei Rank Minimization with Applications to Image Noise Removal Abstracts: Rank minimization problem has a wide range of applications in different areas. However, since this problem is NP-hard and non-convex, the frequently used method is to replace the matrix rank minimization with nuclear norm minimization. Nuclear norm is the convex envelope of the matrix rank and it is more computationally tractable. Matrix completion is a special case of rank minimization problem. In this paper, we consider directly using matrix rank as the regularization term instead of nuclear norm in the cost function for matrix completion problem. The solution is analyzed and obtained by a hard-thresholding operation on the singular values of the observed matrix. Then by exploiting patch-based nonlocal self-similarity scheme, we apply the proposed rank minimization algorithm to remove white Gaussian additive noise in images. Gamma multiplicative noise is also removed in logarithm domain. The experimental results illustrate that the proposed algorithm can remove noises in images more efficiently than nuclear norm can do. And the results are also competitive with those obtained by using the existing state-of-the-art noise removal methods in the literature. 4:55-5:30 Zhang Wenxing Lattice-based Patterned Fabric Inspection by Using Total Variation with Sparsity and Low-Rank Representations Abstracts: In this talk, we study an image decomposition model for patterned fabric inspection. It is important to represent fabric patterns effectively so that fabric defects can be separated. One concern is that both patterned fabric (e.g., star- or box-patterned fabrics) and fabric defects contain mainly low frequency components. The main idea of this paper is to use the convolution of a lattice with a Dirac comb to characterize a patterned fabric image so that its repetitive components can be effectively represented in the image decomposition model. We formulate a model with total variation, sparsity and low-rank terms for patterned fabric inspection. The total variation term is used to regularize defective image, and the sparsity and the low-rank terms are employed to control Dirac comb function. The proposed model can be solved efficiently via a convex programming solver. Our experimental results for different types of patterned fabrics show that the proposed model can inspect defects at a higher accuracy compared with some classical methods in the literature.

Host:
Centre for Mathematical Imaging and Vision, Hong Kong Baptist University