Hierarchical Progressive Transform With Learnable Prior for Hyperspectral Image Super-Resolution

Hyperspectral image super-resolution (HSI-SR) aims to reconstruct a high-resolution HSI (HR-HSI) by fusing a low-resolution HSI (LR-HSI) with a high-resolution multispectral image (HR-MSI). Tensor Nuclear Norm (TNN) regularization exploits transform domains to capture the low-rank structure of HSIs. However, existing methods face a fundamental rigidity-flexibility trade-off: fixed transforms offer stability but lack adaptability, while data-driven transforms provide flexibility but suffer from optimization instability. To address this, we propose a novel HSI-SR model based on a Log-sum-based full-scale Learnable TNN (LLTNN) regularizer. The core of our framework is the Hierarchical Progressive Transform (HPT) operator, which establishes a principled dual-layer scheme. The explicit layer employs fixed multi-domain transforms to provide a robust structural anchor, while the implicit layer introduces a data-driven adaptive transform that captures scene-specific correlations which fixed bases cannot model. This explicit-to-implicit design yields more compact low-rank representations than single-domain or simple cascade methods. The full-scale framework imposes low-rankness jointly across all three tensor modes with a non-convex log-sum penalty to preserve essential features while suppressing noise. Extensive experiments on simulated and real-world datasets demonstrate that our method achieves state-of-the-art performance compared with existing approaches. The code is available at https://github.com/Tuzhihui/LLTNN_code.