非负低秩张量补全的基于对偶公式及其在图像和视频补全中的应用
Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion
AI总结：
本文针对张量补全中忽略非负结构的问题，提出基于对偶理论的新颖分解，解耦非负与低秩约束，并采用黎曼共轭梯度变体求解，在图像和视频补全任务上优于现有方法。
摘要：
近期针对张量补全问题的方法常常忽略了数据的非负结构。我们考虑学习非负低秩张量的问题，并利用对偶理论，提出了一种新颖的此类张量分解方法。该分解将非负约束与低秩约束解耦。由此产生的问题是一个流形上的优化问题，我们提出了一种黎曼共轭梯度的变体来求解它。我们在彩色图像修复、视频补全和高光谱图像补全等多种任务上测试了所提出的算法。实验结果表明，所提出的方法优于许多最先进的张量补全算法。
英文摘要：
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.
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