H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization

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: 1) the low-rank enhanced transform and 2) the accompanying low-rank characterization of transformed frontal slices. Previous t-SVD methods mainly focus on the developments of 1), 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 hierarchical nonlinear transform (HSI) and the hierarchical matrix factorization (HMF) to establish a new tensor factorization (termed as H2TF). Compared with shallow counter partners, e.g., low-rank matrix factorization (MF) 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 (SOTA) HSI denoising methods.