  In this paper we present a novel iterative procedure for multichannel image
and data reconstruction using Bregman distances. With the motivation that
multiple channels sharing a common subgradient with respect to a suitable
regularization implies desirable properties such as a common edge set (and a
common direction of the normals to the level lines) in the case of the total
variation (TV), we propose to determine each iterate by regularizing each
channel with a weighted linear combination of Bregman distances to all other
image channels from the previous iteration. In this sense we generalize the
Bregman iteration proposed by Osher et al. to multichannel images. We prove the
convergence of the proposed scheme, analyze stationary points and present
numerical experiments on color image denoising, which show the superior
behavior of our approach in comparison to TV, TV with Bregman iterations on
each channel separately, and vectorial TV. Additionally, we propose to use the
infimal convolution of Bregman distances to different channels from the
previous iteration to obtain the independence of the sign and hence the
independence of the direction of the edge. While this work focuses on TV
regularization, the proposed scheme can potentially improve any variational
multichannel reconstruction method with a 1-homogeneous regularization.
