Performance Bounds for Reliability and Hallucination Risk in Remote-Sensing Super-Resolution

Kurzfassung

Remote-sensing super-resolution promises enhanced spatial detail, but its reliability is fundamentally limited by the ambiguity of the underlying ill-posed inverse problem. We address this challenge by utilizing computable performance bounds that characterize the achievable reconstruction accuracy independently of any specific reconstruction method and solely from the forward operator and the data (Gottschling et al., 2025). These bounds are derived from the null space of the forward operator, i.e., from the image content that is lost under the downsampling process.

We demonstrate the practical value of these bounds through a comprehensive evaluation across multiple quality measures, land-cover types, degradation settings, and super-resolution factors. We consider spatial and spectral metrics to analyze how theoretical performance limits depend on the evaluation criterion, scene characteristics, and degradation model, and how existing super-resolution methods perform relative to the derived lower and upper bounds. A particular contribution of this work is a systematic analysis of the relationship between zoom level and hallucinations. We show how the bounds evolve over a wider range of magnification factors and examine how increasing zoom affects both the frequency and spatial extent of hallucinated content.

We further compare the proposed bounds with uncertainty estimates from pretrained neural super-resolution models (Donike et al., 2025), allowing us to assess whether these uncertainty maps capture the task's fundamental ambiguity or primarily reflect model-specific effects. In addition, we study out-of-distribution samples and imagery from extreme events to better understand model behavior under distribution shift. In this setting, we investigate whether kernel sizes can help relate such cases to known in-distribution land-cover classes and thereby support a more principled interpretation of hallucination risk.

Overall, the evaluation highlights that, as reconstruction methods approach the theoretical performance range, the dominant factors shaping achievable accuracy shift from model choice to scene content, zoom level, and the intrinsic ambiguity of the inverse problem. This positions the proposed framework as a rigorous basis for analyzing reliability, uncertainty, and hallucination risk in super-resolution, with clear relevance for safe and trustworthy GeoAI.