Low rank variational tensor recovery for multi-linear inverse problems

In this work we consider the recovery of a tensor with a known low-dimensional structure with respect to variation along one or more of it's dimensions. We consider the n-rank of the tensor variation as a low rank measure and formulate a convex tensor recovery problem. A numerical method based on convex set projection is developed. As an example application the proposed method is used to de-noise noise corrupted MRI data.