  Tensor decompositions are powerful tools for analyzing multi-dimensional data
in their original format. Besides tensor decompositions like Tucker and CP,
Tensor SVD (t-SVD) which is based on the t-product of tensors is another
extension of SVD to tensors that recently developed and has found numerous
applications in analyzing high dimensional data. This paper offers a new
insight into the t-Product and shows that this product is a block convolution
of two tensors with periodic boundary conditions. Based on this viewpoint, we
propose a new tensor-tensor product called the $\star_c{}\text{-Product}$ based
on Block convolution with reflective boundary conditions. Using a tensor
framework, this product can be easily extended to tensors of arbitrary order.
Additionally, we introduce a tensor decomposition based on our
$\star_c{}\text{-Product}$ for arbitrary order tensors. Compared to t-SVD, our
new decomposition has lower complexity, and experiments show that it yields
higher-quality results in applications such as classification and compression.
