Cascade-Transform-Based Tensor Nuclear Norm for Hyperspectral Image Super-Resolution

Recent advancements in tensor nuclear norm (TNN) have led to promising solutions for hyperspectral image super-resolution (HSISR), which produces enriched outputs by fusing low-resolution hyperspectral images (LRHSIs) with high-resolution multispectral images (HRMSIs). However, current TNN, mainly reliant on the discrete Fourier transform (DFT), still suffers from mirroring boundary effects and singleton domain limitation. As a relief, we propose cascade-transform-based tensor nuclear norm (CTNN) with two variants for HSISR, featuring new definitions and algebraic structures for tensor product and TNN operations. The first variant processes tubal elements derived from DFT as inputs in the discrete cosine transform (DCT) domain, allowing for more nuanced feature extraction. The second learns adaptive matrices from the data in each iteration update and links them with a fixed DFT matrix to dynamically update the transform domain, preventing rank estimation bias. Furthermore, the nonconvex form of the proposed CTNN is applied to three modes of each spectral subspace similarity cube, termed log-sum-based full-scale CTNN (LFCTNN), capturing the global low-rank structure of LRHSI and the nonlocal similarities present in HRMSI. Experimental evaluations on various remote sensing datasets indicate that our approach exceeds existing state-of-the-art methods. The code is available at https://github.com/xuhonghui96/LFCTNN.