A fast and exact algorithm of minimizing the Rudin-Osher-Fatemi functional in one dimension

Series: 
Applied and Computational Mathematics Seminar
Monday, October 12, 2009 - 13:00
1 hour (actually 50 minutes)
Location: 
Skiles 255
,  
University of Alabama (Department of Mathematics)
,  
Organizer: 
The Rudin-Osher-Fatemi (ROF) model is one of the most powerful and popular models in image denoising. Despite its simple form, the ROF functional has proved to be nontrivial to minimize by conventional methods. The difficulty is mainly due to the nonlinearity and poor conditioning of the related problem. In this talk, I will focus on the minimization of the ROF functional in the one-dimensional case. I will present a new algorithm that arrives at the minimizer of the ROF functional fast and exactly. The proposed algorithm will be compared with the standard and popular gradient projection method in accuracy, efficiency and other aspects.