Iterative TV-Regularization of Grey-Scale Images

Abstract

The TV-regularization method due to Rudin, Osher, and Fatemi is widely used in mathematical image analysis. We consider a nonstationary and iterative variant of this approach and provide a mathematical theory that extends the results of Radmoser et al. to the BV setting. While existence and uniqueness, a maximum–minimum principle, and preservation of the average grey value are not hard to prove, we also establish the convergence to a constant steady state and consider a large family of Lyapunov functionals. These properties allow us to interpret the iterated TV-regularization as a time-discrete scale-space representation of the original image.