THE REES DISTINGUISHED LECTURER SERIES

Dr. Tony Chan

Math Dept, Univ of California at Los Angeles

 

Image Processing: A new frontier for applied math

Thursday September 28, 2006

103 Gore Hall
4:00 - 5:00

Image processing has emerged recently as a popular area of research for applied mathematicians. In addition to the numerous applications, both classical and new mathematical techniques have found useful application in this area, including nonlinear PDE, level set techniques, total variation regularization, optimization methods, differential geometry, and techniques from computational fluid dynamics. The field presents many opportunities as well as challenges for applied mathematicians. I'll use examples from my own work to illustrate some of these ideas.

Variational PDE Techniques in Wavelet Based Image Processing

Friday September 29, 2006

103 Gore Hall
3:30 - 4:30

I will present an overview of our recent work on combining variational models and PDE techniques with wavelets and their applications in digital image processing. It is well known that wavelets have revolutionized the field of image processing. PDE based techniques, such as Mumford-Shah functional, Total Variation (TV) denoising and anisotropic diffusion, also have been enjoying remarkable success in the past decade. Our goal is to combine these two approaches to further improve the image processing performance. We have proposed variational models, especially TV minimization, in conjunction with wavelets for different problems such as image denoising, compression and wavelet inpainting. The models can have effective and automatic control over the geometries of salient features, such as sharp edges, in the images. Therefore, they can improve the performance of the traditional wavelet methods. The models usually lead to PDE's, which are Euler-Lagrange equations of the variational formulations, in the wavelet domain and can be solved numerically. (This talk is based on joint works with with Jackie Shen (Minnesota), Haomin Zhou (Georgia Tech), and Tie Zhou (PKU))

 

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