  The problem of incomplete data is common in signal processing and machine
learning. Tensor completion algorithms aim to recover the incomplete data from
its partially observed entries. In this paper, taking advantages of high
compressibility and flexibility of recently proposed tensor ring (TR)
decomposition, we propose a new tensor completion approach named tensor ring
weighted optimization (TR-WOPT). It finds the latent factors of the incomplete
tensor by gradient descent algorithm, then the latent factors are employed to
predict the missing entries of the tensor. We conduct various tensor completion
experiments on synthetic data and real-world data. The simulation results show
that TR-WOPT performs well in various high-dimension tensors. Furthermore,
image completion results show that our proposed algorithm outperforms the
state-of-the-art algorithms in many situations. Especially when the missing
rate of the test images is high (e.g., over 0.9), the performance of our
TR-WOPT is significantly better than the compared algorithms.
