Minimization Problems and Associated Flows Related to Weighted p Energy and Total Variation

Abstract

Motivated by the problem of edge preserving regularization in image restoration, in this paper we investigate the relations between weighted p energy based and total variation based minimization problems and their associated flows. We prove that the weighted total variation based minimization and its associated flow in a weakened formulation can be approximated by the weighted p energy based minimization and its associated flows, respectively. Moreover, we show that the flow of the weighted total variation based minimization converges weakly in BV and strongly in L2 to the minimizer as $t\rightarrow \infty$.