In this article, we present a new algorithm for fast, online 3D reconstruction of dynamic scenes using times of arrival of photons recorded by single-photon detector arrays. One of the main challenges in 3D imaging using single-photon lidar in practical applications is the presence of strong ambient illumination which corrupts the data and can jeopardize the detection of peaks/surface in the signals. This background noise not only complicates the observation model classically used for 3D reconstruction but also the estimation procedure which requires iterative methods. In this work, we consider a new similarity measure for robust depth estimation, which allows us to use a simple observation model and a non-iterative estimation procedure while being robust to mis-specification of the background illumination model. This choice leads to a computationally attractive depth estimation procedure without significant degradation of the reconstruction performance. This new depth estimation procedure is coupled with a spatio-temporal model to capture the natural correlation between neighboring pixels and successive frames for dynamic scene analysis. The resulting online inference process is scalable and well suited for parallel implementation. The benefits of the proposed method are demonstrated through a series of experiments conducted with simulated and real single-photon lidar videos, allowing the analysis of dynamic scenes at 325 m observed under extreme ambient illumination conditions.

This paper addresses the problem of estimating the instantaneous frequency (IF) and amplitude of the modes composing a non-stationary multi-component signal in the presence of noise. A novel observation model for the signal spectrogram is developed within a Bayesian framework to handle intricate configurations involving noise or overlapping components. The model parameters are estimated using a stochastic variant of the Expectation-Maximization algorithm, bypassing the computationally expensive joint parameter estimation from the posterior distribution. We then design an algorithm for instantaneous amplitude and frequency estimation that accounts for overlap and amplitude variations of the components. To assess the performance of the proposed method, we conduct experiments on both real-world and simulated signals, involving separated or crossing modes. The benefits of our method in terms of efficiency compared with several state-of-the art techniques appear to be significant in that latter case, but also when the amplitude of the components are varying across time.

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.

This paper addresses the problem of disentangling nonoverlapping multicomponent signals from their observation being possibly contaminated by external additive noise. We aim to extract and to retrieve the elementary components (also called modes) present in an observed nonstationary mixture signal. To this end, we propose a new pseudo-Bayesian algorithm to perform the estimation of the instantaneous frequency of the signal modes from their time-frequency representation. In a second time, a detection algorithm is developed to restrict the time region where each signal component behaves, to enhance quality of the reconstructed signal. We finally deal with the presence of noise in the vicinity of the estimated instantaneous frequency by introducing a new reconstruction approach relying on nonbinary band-pass synthesis filters. We validate our methods by comparing their reconstruction performance to state-of-the-art approaches through several experiments involving both synthetic and real-world data under different experimental conditions.

Non-stationary multicomponent signals are ubiquitous in real-world applications. They can be modeled as a super-imposition of amplitude- and frequency-modulated components so-called the modes, which require dedicated techniques to be efficiently analyzed and disentangled. State-of-the-art methods use specific assumptions and paradigms which can produce very different results in specific use cases. Hence, this paper aims to present and discuss the advantages and the limitations of several promising recent approaches respectively applied to signal denoising, mode retrieval and instantaneous frequency estimation through a comparative evaluation benchmark. Our numerical experiments show the specific scenarios where each method is the more adapted in terms of quality of mode separation and reconstruction while also considering the computational efficiency.