When dealing with color imaging problems, one of the main issues is how to couple channels in order to enable joint directions of smoothing. We propose to consider the gradient of a multi-channel image as a tensor, the smoothness of which is measured by taking different norms along the different dimensions (pixels, derivatives, channels). The resulting regularization framework is called collaborative total variation (CTV). We analyze theoretical properties of a large number of CTV models and show which of them are best suited for image denoising and other inverse problems. This has been a project in collaboration with Prof. Daniel Cremers from the Technical University of Munich and Prof. Michael Moller from the University of Siegen.