Bayesian restoration of reflectivity and range profiles from subsampled single-photon multispectral lidar data

In this paper, we investigate the recovery of range and spectral profiles associated with remote three-dimensional scenes sensed via single-photon multispectral Lidar (MSL). We consider different spatial/spectral sampling strategies and compare their performance for similar overall numbers of detected photons. For a regular spatial grid, the first strategy consists of sampling all the spatial locations of the grid for each of the wavelengths. Conversely, the three other strategies consist, for each spatial location, of acquiring a reduced number of wavelengths, chosen randomly or in a deterministic manner. We propose a fully automated computational method, adapted for the different sampling strategies in order to recover the target range profile, as well as the reflectivity profiles associated with the different wavelengths. The performance of the four sampling strategies is illustrated using a single photon MSL system with four wavelengths. The results presented demonstrate that although the first strategy usually provides more accurate results, the subsampling strategies do not exhibit a significant performance degradation, particularly for extremely photonstarved data (down to one photon per pixel on average).