Stochastic EM algorithm for fast analysis of single waveform multi-spectral Lidar data

This paper addresses the problem of estimating spectral and range profiles from single-photon Lidar waveforms associated with single surfaces in presence of an unknown background. A single Lidar waveform per pixel is considered, whereby a single detector is used to acquire information simultaneously at multiple wavelengths. A novel Bayesian approach is developed to perform the estimation of model parameters in a reduced computational time. This is achieved by transforming an EM-based algorithm recently proposed into a stochastic EM algorithm, which is computationally more attractive. The reconstruction performance and computational complexity of our approach are assessed through a series of experiments using synthetic data under different observation scenarios. The obtained results demonstrate a significant speed-up compared to the state-of-the-art method, without significant degradation of the estimation quality.