Abstract

We address the issue of regularizing Osher and Rudin’s shock filter, used for image deblurring, in order to allow processes that are more robust against noise. Previous solutions to the problem suggested adding some sort of difiusion term to the shock equation. We analyze and prove some properties of coupled shock and difiusion processes. Finally we propose an original solution of adding a complex difiusion term to the shock equation. This new term is used to smooth out noise and indicate infiection points simultaneously. The imaginary value, which is an approximated smoothed second derivative scaled by time, is used to control the process. This results in a robust deblurring process that performs well also on noisy signals.