DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Carlos N. Rautenberg, Humboldt-Universität zu Berlin

**Title: ***
Optimal Parameter Selection for a Weighted Total Variation Model in Image Reconstruction
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**Abstract:**
A Weighted Total Variation (WTV) model in function space is introduced where the regularization parameter is spatially variant. We study the optimal selection of the regularization function over the Fenchel pre-dual formulation of the WTV model. A bilevel optimization problem is proposed for the automatic choice of the parameter, where the upper level problem comprises an objective based on local variance estimators and the lower level is a variational inequality. Such formulation arises in image reconstruction from the need to enhance details in certain regions while maintaining homogeneity of others. We address existence and approximation methods based on semi-linear equations, monotonicity techniques, and descent algorithms. We additionally show that the descent algorithm preserves regularity (in each step and asymptotically) of the regularization function. Several numerical tests, and comparison with other algorithms are provided.

**Time:** Friday, September 22, 2017, 1:30-2:30pm

**Place:** Exploratory Hall, Room 4106

Department of Mathematical Sciences

George Mason University

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Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491