Title:

Multiscale PDE Models for Image Processing

Abstract:

In this talk, I will present multiscale variational models for
the wavelet inpainting problems,  which aims to filling in missing or
damaged wavelet coefficients in image reconstruction.  The problem is
motaviated by error concealment in image processing and communications.
And it is closely related to the classical image inpainting, with the
difference being that the inpainting regions are in the wavelet domain.
This brings new challenges to the reconstructions.  The new variational
models, especially total variation minimization in conjunction
with wavelets lead to PDE's, in the wavelet domain and can be solved
numerically. The proposed models have effective and automatic control
over geometric features of the inpainted images including sharp edges,
even in the presence of substantial loss of wavelet coefficients,
including in the low frequencies. This work is jointly with Tony Chan
(UCLA), Jackie Shen (Barclays), and Yang Wang (Michigan State).