Robust Spectral Unmixing of Sparse Multispectral Lidar Waveforms Using Gamma Markov Random Fields

Abstract

This paper presents a new Bayesian spectral unmixing algorithm to analyse remote scenes sensed via sparse multispectral Lidar measurements. To a first approximation, in the presence of a target, each Lidar waveform consists of a main peak, whose position depends on the target distance and whose amplitude depends on the wavelength of the laser source considered (i.e, on the target reflectivity). Besides, these temporal responses are usually assumed to be corrupted by Poisson noise in the low photon count regime. When considering multiple wavelengths, it becomes possible to use spectral information in order to identify and quantify the main materials in the scene, in addition to estimation of the Lidar-based range profiles. Due to its anomaly detection capability, the proposed hierarchical Bayesian model, coupled with an efficient Markov chain Monte Carlo algorithm, allows robust estimation of depth images together with abundance and outlier maps associated with the observed 3D scene. The proposed methodology is illustrated via experiments conducted with real multispectral Lidar data acquired in a controlled environment. The results demonstrate the possibility to unmix spectral responses constructed from extremely sparse photon counts (less than 10 photons per pixel and band). 2 Multispectral Lidar, Depth imaging, Robust spectral unmixing, Anomaly detection, Markov Chain Monte Carlo.

Bayesian 3D Reconstruction of Subsampled Multispectral Single-Photon Lidar Signals

“…The proposed subsampling scheme was evaluated on a real MSL dataset [17]. The scene consists of L = 32 wavelengths sampled at regular intervals of 10 nm from 500 nm to 810 nm, N r = N c = 198 pixels and T = 4500 histogram bins.…”

A Hierarchical Bayesian Approach to Neutron Spectrum Unfolding With Organic Scintillators

“…This approach allows better mixing properties than more standard random walk alternative strategies. The interested reader is invited to consult [45] for additional details about Hamiltonian Monte Carlo sampling and [46] for an example of application to linear inverse problems involving Poisson noise. The marginal posterior mean φ is approximated by averaging the generated variables after having removed the first N bi iterations of the sampler which correspond to the burn-in period of the sampler.…”

Bayesian restoration of reflectivity and range profiles from subsampled single-photon multispectral Lidar data

“…In a similar fashion to [5], [10], [17], we simplify the problem by estimating sequentially Λ and T, using weak assumptions which can often be satisfied in practice. The two estimation steps are detailed in what follows.…”

“…convergence issues), the proposed method can also be used to provide a posteriori measures of uncertainty associated with each estimation step. The interested reader is invited to consult [10] for examples of use of such measures for ranging assessment.…”

“…Single-photon approaches have been used for demonstrations of multispectral depth imaging for target identification [8], [9], quantification [10] and for the measurement of the physiological parameters of foliage [11]. In most cases, range and spectral information was assumed to be available for each wavelength.…”