SCALMU: Synthetically Trained Coupling of Adaptive Learned Multiplicative Updates for Hyperspectral–Multispectral Fusion

Hyperspectral–multispectral image (HSI–MSI) fusion aims to recover a high-resolution hyperspectral (HSI) image from a low-resolution HSI and a high-resolution multispectral (MSI) image. Classical methods such as coupled non-negative matrix factorization (CNMF) benefit from a strong physical interpretability but suffer from inferior results compared to their deep-learning counterparts. To address this limitation, we propose synthetically trained coupling of adaptive learned multiplicative updates (SCALMUs), a novel blind unrolled neural network architecture that integrates adaptive learnable matrices within the classical framework of CNMF multiplicative updates (MUs), improving its results. Due to its architectural proximity to CNMF, the resulting algorithm preserves physical interpretability and non-negativity constraints. To overcome the scarcity of supervised training data, we generate a synthetic HSI–MSI dataset using the dead leaves model and train SCALMU end-to-end under synthetic supervision. Experiments on several datasets show that SCALMU outperforms state-of-the-art (SOTA) methods and highlights the potential of blind fusion trained with synthetic data. The code is available at https://github.com/xinxinxu99/SCALMU.git