  Existing digital sensors capture images at fixed spatial and spectral
resolutions (e.g., RGB, multispectral, and hyperspectral images), and each
combination requires bespoke machine learning models. Neural Implicit Functions
partially overcome the spatial resolution challenge by representing an image in
a resolution-independent way. However, they still operate at fixed, pre-defined
spectral resolutions. To address this challenge, we propose Spatial-Spectral
Implicit Function (SSIF), a neural implicit model that represents an image as a
function of both continuous pixel coordinates in the spatial domain and
continuous wavelengths in the spectral domain. We empirically demonstrate the
effectiveness of SSIF on two challenging spatio-spectral super-resolution
benchmarks. We observe that SSIF consistently outperforms state-of-the-art
baselines even when the baselines are allowed to train separate models at each
spectral resolution. We show that SSIF generalizes well to both unseen spatial
resolutions and spectral resolutions. Moreover, SSIF can generate
high-resolution images that improve the performance of downstream tasks (e.g.,
land use classification) by 1.7%-7%.
