  Recently, tensor singular value decomposition (t-SVD) has emerged as a
promising tool for hyperspectral image (HSI) processing. In the t-SVD, there
are two key building blocks: (i) the low-rank enhanced transform and (ii) the
accompanying low-rank characterization of transformed frontal slices. Previous
t-SVD methods mainly focus on the developments of (i), while neglecting the
other important aspect, i.e., the exact characterization of transformed frontal
slices. In this letter, we exploit the potentiality in both building blocks by
leveraging the \underline{\bf H}ierarchical nonlinear transform and the
\underline{\bf H}ierarchical matrix factorization to establish a new
\underline{\bf T}ensor \underline{\bf F}actorization (termed as H2TF). Compared
to shallow counter partners, e.g., low-rank matrix factorization or its convex
surrogates, H2TF can better capture complex structures of transformed frontal
slices due to its hierarchical modeling abilities. We then suggest the
H2TF-based HSI denoising model and develop an alternating direction method of
multipliers-based algorithm to address the resultant model. Extensive
experiments validate the superiority of our method over state-of-the-art HSI
denoising methods.
