This paper is concerned with the problem of recovering third-order tensor data from limited samples. A recently proposed tensor decomposition (BMD) method has been shown to efficiently compress third-order spatiotemporal data. Using the BMD, we formulate a slicewise nuclear norm penalized algorithm to recover a third-order tensor from limited observed samples. We develop an efficient alternating direction method of multipliers (ADMM) scheme to solve the resulting minimization problem. Experimental results on real data show our method to give reconstruction comparable to those of HaLRTC (Liu et al., IEEE Trans Ptrn Anal Mchn Int, 2012), a well-known tensor completion method, in about the same number of iterations. However, our method has the advantage of smaller subproblems and higher parallelizability per iteration.

翻译：本文研究从有限样本中恢复三阶张量数据的问题。最近提出的张量分解方法（BMD）已被证明能有效压缩三阶时空数据。基于BMD，我们提出了一种按切片进行核范数惩罚的算法，用于从有限观测样本中恢复三阶张量。我们开发了一种高效的交替方向乘子法（ADMM）方案来求解由此产生的极小化问题。真实数据上的实验结果表明，我们的方法在迭代次数与HaLRTC（Liu等，IEEE Trans Ptrn Anal Mchn Int，2012，一种著名的张量补全方法）大致相同的情况下，其重建效果与之相当。然而，我们的方法具有子问题规模更小、每次迭代并行性更高的优势。