  Tensor completion refers to the task of estimating the missing data from an
incomplete measurement or observation, which is a core problem frequently
arising from the areas of big data analysis, computer vision, and network
engineering. Due to the multidimensional nature of high-order tensors, the
matrix approaches, e.g., matrix factorization and direct matricization of
tensors, are often not ideal for tensor completion and recovery. In this paper,
we introduce a unified low-rank and sparse enhanced Tucker decomposition model
for tensor completion. Our model possesses a sparse regularization term to
promote a sparse core tensor of the Tucker decomposition, which is beneficial
for tensor data compression. Moreover, we enforce low-rank regularization terms
on factor matrices of the Tucker decomposition for inducing the low-rankness of
the tensor with a cheap computational cost. Numerically, we propose a
customized ADMM with enough easy subproblems to solve the underlying model. It
is remarkable that our model is able to deal with different types of real-world
data sets, since it exploits the potential periodicity and inherent correlation
properties appeared in tensors. A series of computational experiments on
real-world data sets, including internet traffic data sets, color images, and
face recognition, demonstrate that our model performs better than many existing
state-of-the-art matricization and tensorization approaches in terms of
achieving higher recovery accuracy.
