Primal-dual methods in total variation regularized L1 and L2 functionals arising in image denoising - Neri, Marrick C.
Forthedenoising of block images using the nonsmooth L2 TV-model, a new method based on the algorithm introduced by Chambolle [8] and on the primal-dual active set strategy due to Hinterm¨uller and Stadler [28] is introduced. The active set technique aims at decomposing the image into edges (active sets) and ﬂat zones (inactive sets, which we call islands). The data reconstruction on the islands is based on an averaging technique reﬂecting the statistics of the noise. Utilizing the primal and a corresponding dual variable in the island detection stabilizes the algorithm. The dual update is based onthe strategiesin[8] and[28]. Numericaltests showthatthe methodishighly eﬃcient in removing the noise, in restoring edges, and in the reconstruction of ﬂat image features. This paper also includes a method of VU decomposition constructed to solve the L2 TV-model. This method partitions the solution into a smooth part ? the U-subspace ? and nondiﬀerentiable part ? the V-subspace. We also construct a primal-dual active set method for the nonsmooth regularized L1 TV-model. The proposed method is eﬀective in removing impulse noise, random noise, and outliers. Finally, we perform introductory explorations of modiﬁed versions of the L1 and L2 TV-models with the Laplacian in the regularization term.