In this paper, we present a novel Bayesian approach for estimating spectral and range profiles from single-photon Lidar waveforms associated with single surfaces in the photon-limited regime. In contrast to classical multispectral Lidar signals, we consider a single Lidar waveform per pixel, whereby a single detector is used to acquire information simultaneously at multiple wavelengths. A new observation model based on a mixture of distributions is developed. It relates the unknown parameters of interest to the observed waveforms containing information from multiple wavelengths. Adopting a Bayesian approach, several prior models are investigated and a stochastic Expectation-Maximization algorithm is proposed to estimate the spectral and depth profiles. The reconstruction performance and computational complexity of our approach are assessed, for different prior models, through a series of experiments using synthetic and real data under different observation scenarios. The results obtained demonstrate a significant speed-up without significant degradation of the reconstruction performance when compared to existing methods in the photon-starved regime.
翻译:在本文中,我们展示了一种新颖的巴伊西亚方法,用于估计光子限制系统中单光子李达尔波形与单一表面相联的光谱和范围剖面图;与古典多光谱利达尔信号不同,我们考虑采用单一的利达尔波形像素,即使用单一的探测器同时获取多波长信息;开发了一种基于分布混合的新观测模型;将未知的兴趣参数与包含多波长信息的观测波形联系起来;采用巴伊西亚方法,对以前的若干模型进行调查,并提议采用一种随机预期-最大化算法来估计光谱和深度剖面图;对不同的前模型,通过在不同的观测情景下使用合成和真实数据进行一系列实验,评估我们方法的重建绩效和计算复杂性;获得的结果表明,与光子-星系中的现有方法相比,重建绩效在不显著退化的情况下大大加快。