We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework. We show the t-SVD is a specialization of the well-studied block-term decomposition for third-order tensors, and we present an algorithm under this model that can track changing free submodules from incomplete streaming 2-D data. The proposed algorithm uses principles from incremental gradient descent on the Grassmann manifold of subspaces to solve the tensor completion problem with linear complexity and constant memory in the number of time samples. We provide a local expected linear convergence result for our algorithm. Our empirical results are competitive in accuracy but much faster in compute time than state-of-the-art tensor completion algorithms on real applications to recover temporal chemo-sensing and MRI data under limited sampling.

翻译：我们提出一个新的快速流算法,用于利用强单值分解(t-SVD)代数框架来估算低水平低水平电压缺失的细数问题。我们展示t-SVD是三级电压的精心研究的分块分解的专业化,我们在此模型下提出一种算法,可以跟踪从不完整流流2-D数据中变化的免费子模块。提议的算法使用子空间格拉斯曼方块的递增梯度下降原则来解决线性复杂度高压完成问题和时间样本中恒定的内存问题。我们为我们的算法提供了一种当地预期线性趋同结果。我们的经验结果在准确性上具有竞争力,但在计算时间上比在有限的取样下恢复时间化学测量和磁共振成像数据的实际应用中,在最先进的电压分解算法方面,我们的经验结果比目前最先进的分解算法要快得多。