Department of Mathematics & Statistics Calendar Week of September 14-18, 2009 Tuesday, September 15, 2009 3:30 PM *No* *Faculty Meeting* 459 MSC Wednesday, September 16, 2009 11:30 AM *Stat Seminar 459 MSC Maria Rizzo, BGSU "Distance Correlation" Wednesday, September 16, 2009 3:30 PM *Algebra Seminar 445 MSC Rieuwert J. Blok, BGSU "Graphs of Groups" Wednesday, September 16, 2009 3:30 PM *Ed Seminar 459 MSC Group Discussion "Lesson Study: Teaching Students How to interpret their solution" Thursday, September 17, 2009 3:30 PM *Grad Student Seminar 459 MSC Steve Dinda, BGSU "Bioinformatics II" Thursday, September 17, 2009 4:00 PM Advisory Committee Meeting 400 MSC Friday, September 18, 2009 3:30 PM *COLLOQUIUM 459 MSC Dr. Yao Lu, University of Michigan "Integral Equation Models for Image Restoration: High Accuracy Methods and Fast Algorithms" Abstract: Discrete models are consistently used as practical models for image restoration. They are piecewise constant approximations of the true physical (continuous) model, and hence, inevitably impose bottleneck model errors. We propose to work directly with the continuous model for image restoration aiming at suppressing the model errors caused by the discrete models. A systematic study is introduced in this talk for the continuous out-of-focus image models which can be formulated as an integral equation of the first kind. The resulting integral equation is regularized by the Lavrentiev method and the Tikhonov method. We develop fast multiscale algorithms having high accuracy to solve the regularized integral equations of the second kind. Numerical experiments show that the methods based on the continuous model perform much better than those based on discrete models, in terms of PSNR values and visual quality of the reconstructed images.
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