  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.
