Expectation-Maximization based approach to 3D reconstruction from single-waveform multispectral Lidar data

Quentin Legros, Sylvain Meignen, Stephen McLaughlin, Yoann Altmann

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Abstract

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 (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. A new observation model based on a mixture model 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.

Original languageEnglish
JournalIEEE Transactions on Computational Imaging
Early online date29 May 2020
DOIs
Publication statusE-pub ahead of print - 29 May 2020

Keywords

  • 3D imaging
  • Bayesian estimation
  • Expectation-Maximization
  • Multispectral imaging
  • singlephoton Lidar

ASJC Scopus subject areas

  • Signal Processing
  • Computer Science Applications
  • Computational Mathematics

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