Full-Scale Regression Modeling of Spatial Details for Single-/Multiplatform Hypersharpening

Whenever the sharpening band is not unique, the hypersharpening paradigm extends traditional pansharpening to any m-to-n fusion task, by integrating spatial information from multiple sources. The m-to-n fusion task is recast into multiple 1-to-n pansharpening problems by appropriately selecting or synthesizing a set of high-resolution (HR) bands to sharpen the set of low-resolution (LR) bands. The synthesis generates each of the sharpening bands as a linear combination of the available HR bands. The spectral coefficients of each synthetic band can be estimated using a multivariate linear regression (MLR) that matches the LR band to be sharpened. A different combination of the HR bands is assimilated to each LR band. Here, we propose a novel hypersharpening instance that directly combines high-pass spatial details, rather than lowpass image components. In general, fusion methods optimize their parameters at reduced scale, assuming a scale-invariance property. Instead, we introduce an estimation strategy that allows the fusion parameters to be directly retrieved at the full spatial scale. Starting from an iterative process, we derive an asymptotic closed-form solution and establish its convergence conditions. Three case studies involving as many real datasets—Sentinel-2, Environmental Mapping and Analysis Program (EnMAP), and WorldView-3—demonstrate performance improvements at reduced and full resolutions, obtained without any parametric optimization by the user, confirming the effectiveness and versatility of the proposed solution in single- and multiplatform fusion scenarios featuring diverse spatial resolutions, spectral bands, and resolution ratios.