  Tensor data often suffer from missing value problem due to the complex
high-dimensional structure while acquiring them. To complete the missing
information, lots of Low-Rank Tensor Completion (LRTC) methods have been
proposed, most of which depend on the low-rank property of tensor data. In this
way, the low-rank component of the original data could be recovered roughly.
However, the shortcoming is that the detail information can not be fully
restored, no matter the Sum of the Nuclear Norm (SNN) nor the Tensor Nuclear
Norm (TNN) based methods. On the contrary, in the field of signal processing,
Convolutional Sparse Coding (CSC) can provide a good representation of the
high-frequency component of the image, which is generally associated with the
detail component of the data. Nevertheless, CSC can not handle the
low-frequency component well. To this end, we propose two novel methods,
LRTC-CSC-I and LRTC-CSC-II, which adopt CSC as a supplementary regularization
for LRTC to capture the high-frequency components. Therefore, the LRTC-CSC
methods can not only solve the missing value problem but also recover the
details. Moreover, the regularizer CSC can be trained with small samples due to
the sparsity characteristic. Extensive experiments show the effectiveness of
LRTC-CSC methods, and quantitative evaluation indicates that the performance of
our models are superior to state-of-the-art methods.
