Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion

Abstract

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.