  Tensor completion aims to recover the missing entries of a partially observed
tensor by exploiting its low-rank structure, and has been applied to visual
data recovery. In applications where the data arrives sequentially such as
streaming video completion, the missing entries of the tensor need to be
dynamically recovered in a streaming fashion. Traditional streaming tensor
completion algorithms treat the entire visual data as a tensor, which may not
work satisfactorily when there is a big change in the tensor subspace along the
temporal dimension, such as due to strong motion across the video frames. In
this paper, we develop a novel patch tracking-based streaming tensor ring
completion framework for visual data recovery. Given a newly incoming frame,
small patches are tracked from the previous frame. Meanwhile, for each tracked
patch, a patch tensor is constructed by stacking similar patches from the new
frame. Patch tensors are then completed using a streaming tensor ring
completion algorithm, and the incoming frame is recovered using the completed
patch tensors. We propose a new patch tracking strategy that can accurately and
efficiently track the patches with missing data. Further, a new streaming
tensor ring completion algorithm is proposed which can efficiently and
accurately update the latent core tensors and complete the missing entries of
the patch tensors. Extensive experimental results demonstrate the superior
performance of the proposed algorithms compared with both batch and streaming
state-of-the-art tensor completion methods.
