Minimization problems and associated flows related to weighted p energy and total variation

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 L-2 to the minimizer as t --> infinity.