A tensor-based nonlocal total variation model for multi-channel image recovery.

•We define a new nonlocal total variation using a tensor nuclear norm (TenNLTV) and this total variation can simultaneously exploit the local structural image regularity, the nonlocal image self-similarity, and the image channel correlation.•We present an image restoration model using the proposed TenNLTV. Then, an effective algorithm is designed for this framework using the variable-splitting strategy and the alternative direction methods of multipliers (ADMM).•A subproblem in our algorithm involves a two-order complex eigen system, and a closed-form solution is derived for this system, which can lead to an algorithm acceleration.•Extensive experimental results on several inverse imaging problems demonstrate that the proposed regularizer is systematically superior over other competing local and nonlocal total variation approaches, both quantitatively and visually.