Invited Session Thu.3.H 1028

Thursday, 15:15 - 16:45 h, Room: H 1028

Cluster 21: Sparse optimization & compressed sensing [...]

Variational signal processing -- algorithms and applications


Chair: Junfeng Yang



Thursday, 15:15 - 15:40 h, Room: H 1028, Talk 1

Wenxing Zhang
On variational image decomposition model for blurred images with missing pixel values

Coauthors: Michael K Ng, Xiaoming Yuan


In this talk, we develop a decomposition model to restore blurred images with missing pixel values. Our assumption is that the true image is the superposition of cartoon and texture parts. We use the total variation (TV) norm to regularize the cartoon part and its dual norm to regularize the texture part, respectively. We recommend an efficient numerical algorithm based on the variable splitting method to solve the problem. Theoretically, the existence of minimizer to the energy functional and the convergence of the algorithm are guaranteed. In contrast to recently developed methods for deblurring images, this algorithm not only gives the restored image, but also gives a decomposition of cartoon and texture parts. These two parts can be further used in segmentation and inpainting problems. Numerical comparisons between this algorithm and some state-of-the-art methods are also reported.



Thursday, 15:45 - 16:10 h, Room: H 1028, Talk 2

Junfeng Yang
Convergence of a class of stationary iterative methods for saddle point problems

Coauthors: Xin Liu, Yin Zhang


The alternating direction method (ADM) was originally proposed in the 1970s. In the literature, very restrictive conditions, such as convexity of the objective function over the entire domain and separability into exactly two blocks, have been imposed to guarantee convergence of the ADM. Moreover, the convergence rate of ADM remains unclear. In this paper, we carry out a unified study on the convergence of a class of stationary iterative methods, which includes the ADM as a special case, for quadratic programming problems with linear equality constraints or linear saddle point problems. We establish global and q-linear convergence results without assuming convexity of the objective function and in the absence of separability of variables. Some numerical results are presented to support our findings, and extension to nonlinear saddle point problems is also discussed.


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