  Though high redundancy rate of a tight frame can improve performance in
applications, as the dimension increases, it also makes the computational cost
skyrocket and the storage of frame coefficients increase exponentially. This
seriously restricts the usefulness of such tight frames for problems in
moderately high dimensions such as video processing in dimension three.
Inspired by the directional tensor product complex tight framelets ${TP-CTF}_m$
with $m\ge 3$ in [14,18] and their impressive performance for image processing
in [18,30] in this paper we introduce a directional tensor product complex
tight framelet ${TP-CTF}^!_6$ (called reduced ${TP-CTF}_6$) with low
redundancy. Such ${TP-CTF}_6^!$ is a particular example of tight framelet
filter banks with mixed sampling factors. The ${TP-CTF}^!_6$ in $d$ dimensions
not only offers good directionality but also has the low redundancy rate
$\frac{3^d-1}{2^d-1}$ (e.g., the redundancy rates are $2,
2\mathord{\frac{2}{3}}, 3\mathord{\frac{5}{7}}, 5\mathord{\frac{1}{3}}$ and
$7\mathord{\frac{25}{31}}$ for dimension $d=1,..., 5$, respectively). Moreover,
our numerical experiments on image/video denoising and inpainting show that the
performance using our proposed ${TP-CTF}^!_6$ is often comparable or sometimes
better than several state-of-the-art frame-based methods which have much higher
redundancy rates than that of ${TPCTF}^!_6$.
