Nonlinear models have recently shown interesting properties for spectral unmixing. This paper studies a generalized bilinear model and a hierarchical Bayesian algorithm for unmixing hyperspectral images. The proposed model is a generalization not only of the accepted linear mixing model but also of a bilinear model that has been recently introduced in the literature. Appropriate priors are chosen for its parameters to satisfy the positivity and sum-to-one constraints for the abundances. The joint posterior distribution of the unknown parameter vector is then derived. Unfortunately, this posterior is too complex to obtain analytical expressions of the standard Bayesian estimators. As a consequence, a Metropolis-within-Gibbs algorithm is proposed, which allows samples distributed according to this posterior to be generated and to estimate the unknown model parameters. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data.

Single-photon lidar has emerged as a prime candidate technology for depth imaging through challenging environments. Until now, a major limitation has been the significant amount of time required for the analysis of the recorded data. Here we show a new computational framework for real-time three-dimensional (3D) scene reconstruction from single-photon data. By combining statistical models with highly scalable computational tools from the computer graphics community, we demonstrate 3D reconstruction of complex outdoor scenes with processing times of the order of 20 ms, where the lidar data was acquired in broad daylight from distances up to 320 metres. The proposed method can handle an unknown number of surfaces in each pixel, allowing for target detection and imaging through cluttered scenes. This enables robust, real-time target reconstruction of complex moving scenes, paving the way for single-photon lidar at video rates for practical 3D imaging applications.

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data.

More to imaging than meets the eye: Traditional imaging techniques involve peering down a lens and collecting as much light from the target scene as possible. That requirement can set limits on what can be seen. Altmann et al. review some of the most recent developments in the field of computational imaging, including full three-dimensional imaging of scenes that are hidden from direct view (e.g., around a corner or behind an obstacle). High-resolution imaging can be achieved with a single-pixel detector at wavelengths for which no cameras currently exist. Such advances will lead to the development of cameras that can see through fog or inside the human body. Science , this issue p. eaat2298

The safety and success of autonomous vehicles (AVs) depend on their ability to accurately map and respond to their surroundings in real time. One of the most promising recent technologies for depth mapping is single-photon lidar (SPL), which measures the time of flight of individual photons. The long-range capabilities (kilometers), excellent depth resolution (centimeters), and use of low-power (eye-safe) laser sources renders this modality a strong candidate for use in AVs. While presenting unique opportunities, the remarkable sensitivity of single-photon detectors introduces several signal processing challenges. The discrete nature of photon counting and the particular design of the detection devices means the acquired signals cannot be treated as arising in a linear system with additive Gaussian noise. Moreover, the number of useful photon detections may be small despite a large data volume, thus requiring careful modeling and algorithmic design for real-time performance. This article discusses the main working principles of SPL and summarizes recent advances in signal processing techniques for this modality, highlighting promising applications in AVs as well as a number of challenges for vehicular lidar that cannot be solved by better hardware alone.

This paper presents a new Bayesian model and algorithm used for depth and reflectivity profiling using full waveforms from the time-correlated single-photon counting measurement in the limit of very low photon counts. The proposed model represents each Lidar waveform as a combination of a known impulse response, weighted by the target reflectivity, and an unknown constant background, corrupted by Poisson noise. Prior knowledge about the problem is embedded through prior distributions that account for the different parameter constraints and their spatial correlation among the image pixels. In particular, a gamma Markov random field (MRF) is used to model the joint distribution of the target reflectivity, and a second MRF is used to model the distribution of the target depth, which are both expected to exhibit significant spatial correlations. An adaptive Markov chain Monte Carlo algorithm is then proposed to perform Bayesian inference. This algorithm is equipped with a stochastic optimization adaptation mechanism that automatically adjusts the parameters of the MRFs by maximum marginal likelihood estimation. Finally, the benefits of the proposed methodology are demonstrated through a series of experiments using real data.