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.

本研究考虑在张量完成问题中学习非负低秩张量，并使用对偶理论提出了一种新颖的分解方法，分解将非负约束与低秩约束解耦。所得问题是流形上的优化问题，并提出了 Riemannian 共轭梯度的变种来解决它。实验结果表明，所提出的方法优于许多最先进的张量完成算法。