WaveDiffUR: A diffusion SDE-based solver for ultra magnification super-resolution in remote sensing images

Deep neural networks have recently achieved significant advancements in remote sensing superresolu-tion (SR). However, most existing methods are limited to low magnification rates (e.g., 2 or 4) due to the escalating ill-posedness at higher magnification scales. To tackle this challenge, we redefine high-magnification SR as the ultra-resolution (UR) problem, reframing it as solving a conditional diffusion stochastic differential equation (SDE). In this context, we propose WaveDiffUR, a novel wavelet-domain diffusion UR solver that decomposes the UR process into sequential sub-processes addressing conditional wavelet components. WaveDiffUR iteratively reconstructs low-frequency wavelet details (ensuring global consistency) and high-frequency components (enhancing local fidelity) by incorporating pre-trained SR models as plug-and-play modules. This modularity mitigates the ill-posedness of the SDE and ensures scalability across diverse applications. To address limitations in fixed boundary conditions at extreme magnifications, we introduce the cross-scale pyramid (CSP) constraint, a dynamic and adaptive framework that guides WaveDiffUR in generating fine-grained wavelet details, ensuring consistent and high-fidelity outputs even at extreme magnification rates.