  Recent approaches to the tensor completion problem have often overlooked the
nonnegative structure of the data. We consider the problem of learning a
nonnegative low-rank tensor, and using duality theory, we propose a novel
factorization of such tensors. The factorization decouples the nonnegative
constraints from the low-rank constraints. The resulting problem is an
optimization problem on manifolds, and we propose a variant of Riemannian
conjugate gradients to solve it. We test the proposed algorithm across various
tasks such as colour image inpainting, video completion, and hyperspectral
image completion. Experimental results show that the proposed method
outperforms many state-of-the-art tensor completion algorithms.
