Entropy-Guided Heteroscedasticity Modeling for Fast Zero-Shot Remote Sensing Image Fusion

Hyperspectral pansharpening (HyPan) and hyperspectral-multispectral image fusion (HMIF) reconstruct a high-resolution hyperspectral image (HR-HSI) from a low-resolution hyperspectral image (LR-HSI) and a high-spatial-resolution panchromatic or multispectral observation (PAN/MSI), a fundamental and highly ill-posed inverse problem in remote sensing. We address the zero-shot setting, in which the result must be obtained from the input observation pair alone without any external training data, and focus on optimization-based zero-shot methods, which optimize an untrained network directly on the input observations and stay faithful to the physical observation model. Uniformly weighting their spatial and spectral fidelity terms is, however, problematic: the spatial term is mainly informative at edges and fine structures, while the flat background that dominates remote sensing scenes dilutes these sparse constraints, and the spectral term is dominated by low-frequency content, so the two objectives drive the network in conflicting directions and the optimization settles at a sub-optimal compromise. We propose a fast zero-shot optimization framework with entropy-guided heteroscedasticity modeling: an information gate computed from the local Shannon entropy down-weights uninformative regions and strengthens genuine high-frequency structure, aligning the two objectives, and a two-stage schedule first anchors the spectral manifold and then refines spatial details. On HyPan and HMIF benchmarks, our method improves spectral fidelity and spatial sharpness over state-of-the-art methods, reconstructing an image in about 17 seconds without any external training data.