Wavelets and Multiscale PDE Models for Image Processing
Speaker:Prof. Haomin Zhou
School of Mathematics
Georgia Institute of Technology
Date & Time:15 Nov 2010 (Monday) 14:30 - 15:30
Venue:J314
Organized by:Department of Mathematics

Abstract

In this talk, I will review some wavelet based multiscale variational models for image processing such as denoising. In particular, I will focus on the wavelet inpainting problem, which aims to filling in missing or damaged wavelet coefficients in image reconstruction. The problem is motivated by error concealment in image processing and communications. And it is closely related to the classical image inpainting problem, with the difference being that the inpainting regions are in the wavelet domain. This brings new challenges to the reconstructions.The variational models, especially the total variation minimization in conjunction with wavelets, lead to PDE's in the wavelet domain and can be solved numerically. These models have automatic control over geometric features of the inpainted images including sharp edges. The numerical examples show that the models can effectively recover the missing or damaged information, even in the presence of substantial loss of wavelet coefficients, including in the low frequencies.

Biography

Prof. Hao-Min Zhou, Associate Professor of the School of Mathematics, Georgia Institute of Technology. His areas of research interest are numerical analysis and scientific computing, computations of partial differential equations and stochastic differential equations, wavelets and PDE based image processing, level set methods and random dynamical systems.