One of the most popular approaches to ill-posed image and signal reconstruction problems is to determine the reconstructed signal as the argument that minimizes a suitable convex energy functional consisting of a data fidelity and a regularization term. While this technique has been applied extremely successfully in various different fields, it introduces a certain bias or loss of contrast which can be avoided by using Bregman iteration as proposed by Osher et al. in 2005. In my talk I will propose an extension of the aforementioned Bregman iteration to images and signals with multiple channels. While the talk focuses on color image denoising using total variation regularization as an example, the proposed iterative procedure can potentially be used to improve any variational multichannel signal reconstruction method for which the different channels of the solution are expected to have a small Bregman distance.