In this article, 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 (up to 100 times faster for four bands) without significant degradation of the reconstruction performance when compared to existing methods in the photon-starved regime.

中文翻译：

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基于期望最大化的单波形多光谱激光雷达数据 3D 重建方法

在本文中，我们提出了一种新颖的贝叶斯方法，用于从与光子限制范围内的单个表面相关的单光子激光雷达波形中估计光谱和距离轮廓。与经典的多光谱激光雷达信号相比，我们考虑每个像素的单个激光雷达波形，其中单个检测器用于同时获取多个波长的信息。开发了一种基于混合分布的新观测模型。它将感兴趣的未知参数与包含来自多个波长的信息的观测波形联系起来。采用贝叶斯方法，研究了几个先验模型，并提出了一种随机期望最大化算法来估计光谱和深度剖面。评估了我们方法的重建性能和计算复杂性，对于不同的先验模型，通过在不同观察场景下使用合成和真实数据进行的一系列实验。与光子匮乏区域中的现有方法相比，获得的结果证明了显着的加速（四个波段最多快 100 倍），而重建性能没有显着下降。