  Recently, the transform-based tensor representation has attracted increasing
attention in multimedia data (e.g., images and videos) recovery problems, which
consists of two indispensable components, i.e., transform and characterization.
Previously, the development of transform-based tensor representation mainly
focuses on the transform aspect. Although several attempts consider using
shallow matrix factorization (e.g., singular value decomposition and negative
matrix factorization) to characterize the frontal slices of transformed tensor
(termed as latent tensor), the faithful characterization aspect is
underexplored. To address this issue, we propose a unified Deep Tensor
Representation (termed as DTR) framework by synergistically combining the deep
latent generative module and the deep transform module. Especially, the deep
latent generative module can faithfully generate the latent tensor as compared
with shallow matrix factorization. The new DTR framework not only allows us to
better understand the classic shallow representations, but also leads us to
explore new representation. To examine the representation ability of the
proposed DTR, we consider the representative multi-dimensional data recovery
task and suggest an unsupervised DTR-based multi-dimensional data recovery
model. Extensive experiments demonstrate that DTR achieves superior performance
compared to state-of-the-art methods in both quantitative and qualitative
aspects, especially for fine details recovery.
