Expectation-Maximization Based Approach to 3D Reconstruction From Single-Waveform Multispectral Lidar Data

Abstract

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.

Robust and Guided Bayesian Reconstruction of Single-Photon 3D Lidar Data: Application to Multispectral and Underwater Imaging

“…The proposed algorithm is validated on real multispectral Lidar data of a static lego target (see Fig. 11 (left) for a reference acquired at 40 ms acquisition time per pixel) [23]. This data has 200×200 pixels, T = 1500 bins (a bin represents 2ps) and L = 4 wavelengths acquired at 473, 532, 589 and 640 nm.…”

A Bayesian model averaging method for software reliability modeling and assessment

“…The EM algorithm is a frequently-used method for the MLE, especially when dealing with the problem of missing data. 31,32 By calculating the posterior probability of the model using the EM algorithm, the complexity of the MLE algorithm is reduced. 33,34 In this paper, we denote 𝑌 = 𝑚(𝑡) is the observed data, and the complete data 𝑋 = (𝑌, 𝑍) is obtained by combining the observed data generated by the random variable 𝑌 and the unobserved variable 𝑍 = 𝑧 𝑛𝑙 .…”

“…The EM algorithm is a frequently‐used method for the MLE, especially when dealing with the problem of missing data 31,32 . By calculating the posterior probability of the model using the EM algorithm, the complexity of the MLE algorithm is reduced 33,34 …”

Robust and Guided Bayesian Reconstruction of Single-Photon 3D Lidar Data: Application to Multispectral and Underwater Imaging

“…for ∈ {1, • • • , L}, where w norm is a normalization constant ensuring ,n w ( ) n,n = 1, the coefficient ζ is easily fixed based on physical considerations related to the impulse response width and it is weighted by q ( ) to account for the multi-resolution effect. In (14), the product over promotes lower scales data if their weights are high.…”