Invited Session Thu.3.MA 415

Thursday, 15:15 - 16:45 h, Room: MA 415

Cluster 19: PDE-constrained optimization & multi-level/multi-grid methods [...]

Variational methods in image processing and compressed sensing


Chair: Wotao Yin



Thursday, 15:15 - 15:40 h, Room: MA 415, Talk 1

Yiqiu Dong
A convex variational model for restoring blurred images with multiplicative noise

Coauthor: Tieyong Zeng


In this talk, we are concerned with a convex variational model for restoring blurred images with multiplicative noise. Based on the statistical property of the noise, a quadratic penalty technique is utilized in order to obtain a strictly convex model. For solving the optimization problem in the model, a primal-dual method is proposed. Numerical results show that this method can provide better performance of suppressing noise as well as preserving details in the image.



Thursday, 15:45 - 16:10 h, Room: MA 415, Talk 2

Hong Jiang
Surveillance video processing using compressive sensing

Coauthors: Wei Deng, Zuowei Shen


A compressive sensing method combined with decomposition of a matrix formed with image frames of a surveillance video into low rank and sparse matrices is proposed to segment the background and extract moving objects in a surveillance video. The video is acquired by compressive measurements, and the measurements are used to reconstruct the video by a low rank and sparse decomposition of matrix. The low rank component represents the background, and the sparse component is used to identify moving objects in the surveillance video. The decomposition is performed by an augmented Lagrangian alternating direction method. Experiments are carried out to demonstrate that moving objects can be reliably extracted with a small amount of measurements.



Thursday, 16:15 - 16:40 h, Room: MA 415, Talk 3

Tao Wu
A nonconvex TVq model in image restoration

Coauthor: Michael Hinterm├╝ller


A nonconvex variational model is introduced which contains lq-norm, q ∈ (0,1), of image gradient as regularization. Such a regularization is a nonconvex compromise between support minimization and convex total-variation model. In finite-dimensional setting, existence of minimizer is proven, a semismooth Newton solver is introduced, and its global and locally superlinear convergence is established. The potential indefiniteness of Hessian is handled by a trust-region based regularization scheme. Finally, the associated model in function space is discussed.


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