COMPRESSED SENSING OF CANOPY HEIGHT: DENSE LABEL FREE RECONSTRUCTION FROM SPARSE LIDAR FOOTPRINTS AND SATELLITE OPTICS

Dense canopy height maps are normally learned from wall to wall airborne LiDAR, which does not exist over most tropical forests, while spaceborne profiling LiDAR such as GEDI delivers only a sparse set of 25m footprints. We cast canopy mapping as a compressed sensing problem: the unknown is the dense canopy height field, the measurements are the relative height metrics of a few footprints (a nonlinear, quantile type operator), and the optical image is side information. On a small open benchmark (593/80/240 patches of SPOT 6/7 imagery and LiDAR HD canopy height from France, split by tile) with a GEDI like footprint simulator, we show that (i) classical sparse reconstruction from footprints alone -Delaunay and thin plate interpolation, total variation inpainting stalls at 4.2-4.3m MAE at 253 footprints/km2 (3.9–4.1m at about 500); (ii) a network trained only from footprints, by track-wise measurement splitting and an operator-aware loss on four height metrics per footprint, never sees a dense label yet reaches 3.61±0.04m, against 3.15±0.02m for the same network trained with dense LiDAR; the operatoraware loss is essential (naive disk-mean or centre-pixel supervision gives a +3.6m bias and 1.1m higher MAE); (iii) conditioning on the footprints available at inference through an optical-similarity (“optical-kriging”) attention module brings the footprint-trained model to 3.23m at 63 and 3.08m at 253 footprints/km2, i.e. on par with the dense-label optical model, while the same module trained with dense labels improves from 3.15 to 2.56m (−19%). We also report negative results (data-consistency projection, test-time adaptation) and the (small) sensitivity to footprint geolocation error and noise. The whole study fits on two commodity GPUs.