Abstract: Matrix completion has been a significant signal acquisition manner in recent years.This paper extends matrix completion to the nonnegative tensor situation and designs an algorithm to nonnegative tensor completion.In this algorithm the nonnegative tensor completion problem is transformed into solving a series of nonnegative matrix completion problems and nonnegative least-squares method are employed to solve these problems.As the spatial and temporal structure is sufficiently utilized，the proposed nonnegative tensor completion algorithm has better recovery performance compared to nonnegative matrix completion algorithm.The experimental results demonstrate the superiority of the proposed method.

Key words: nonnegative tensor completion, matrix completion, nonnegative matrix completion, nonnegative least-squares

摘要： 近年来矩阵补全已成为一种重要的信号采集方式。将矩阵补全推广到非负张量情形，并提出了非负张量补全算法。该算法先将非负张量补全问题转化为交替求解一系列非负矩阵补全问题，再使用非负最小二乘方法求解这些问题。由于充分利用了数据的空时结构，所提的非负张量补全算法比非负矩阵补全算法有更好的恢复性能。实验结果证实了该方法的优越性。

关键词: 非负张量补全, 矩阵补全, 非负矩阵补全, 非负最小二乘