Nonlinear Learnable Triple-Domain Transform Tensor Nuclear Norm for Hyperspectral Image Super-Resolution

Tensor Nuclear Norm (TNN) has been widely employed as a regularization term for hyperspectral image super-resolution (HSISR). However, conventional TNN constraints based on Discrete Fourier Transform (DFT) often suffer from rank estimation biases and an inability to effectively capture complex spectral-spatial correlations, limiting their efficacy in HSISR. To address these challenges, we propose a Nonlinear Learnable Triple-domain (NLT) transform framework that integrates nonlinear transform, DFT, and self-learning adaptation. This multi-stage process promotes singular value concentration, improving low-rank approximation and rank estimation accuracy. Building upon this framework, we develop an NL-transform-oriented tensor product, a truncated singular value decomposition (TSVD) operation, and a novel tensor nuclear norm (NLTN) tailored for HSISR. By incorporating spectral subspace estimation and clustering-based patch grouping, our approach effectively leverages spatial-spectral correlations and non-local self-similarities, leading to enhanced reconstruction quality. To further mitigate singular value over-penalization, we introduce a logarithmic-based generalized NLTNN (GNLTN) and formulate an optimization strategy based on the alternating direction method of multipliers (ADMM). Extensive experiments demonstrate that our method significantly outperforms existing approaches in terms of fusion accuracy and visual fidelity, setting new benchmarks for hyperspectral image super-resolution. The code is available at https://github.com/xuhonghui96/GNLTN.