Gap Filling in Satellite Time Series: In Search of Simple Yet Reliable Reconstruction Methods

Complete and temporally consistent satellite image time series are essential for many Earth observation applications. This study formulates gap filling as a post-mask reconstruction problem and introduces two transparent operators that require neither external supervised training nor area-specific fine-tuning. Hypercomplex Bases (HCB) reconstruct missing observations directly from the spectro-temporal structure of the observed time series, whereas HELIX additionally exploits land-cover information through analytically estimated class-specific seasonal guidance. Reconstruction fidelity is first examined under spatially heterogeneous clustered cloud/shadow missingness, where unaffected observations from the same acquisition remain available. HCB and HELIX retain low spectral-angle deviations of 7.9° and 8.2°, respectively, together with comparatively limited spatial- and temporal-gradient changes and without the pronounced structural artefacts observed for several learned baselines. To isolate temporal reconstruction under common support conditions, a complementary complete-date benchmark removes entire acquisitions and systematically varies temporal support across seven study areas, all five main K¨oppen–Geiger climate groups, two years, 30 controlled gap scenarios, four spectral bands, and eleven land-cover classes. In this benchmark, HELIX achieves the lowest aggregate MAE (688.4 DN), MedAE (188 DN), RMSE (1636.4 DN), and mean SAM (7.38°), while HCB follows with an MAE of 879.4 DN, MedAE of 262 DN, RMSE of 1782.4 DN, and mean SAM of 7.88°. Both remain stable under interpolation-like and extrapolation-like configurations with one-sided temporal support. HCB provides strong reconstruction and spectral fidelity at low computational cost without ancillary semantic information, whereas HELIX complements it through semantic seasonal constraints that improve radiometric accuracy. The two approaches therefore represent complementary transparent operating points for robust and auditable reconstruction of masked optical satellite time series.