In synthetic aperture radar (SAR), images are formed by focusing the response of stationary objects to a single spatial location. On the other hand, moving targets cause phase errors in the standard formation of SAR images that cause displacement and defocusing effects. SAR imagery also contains significant sources of non-stationary spatially-varying noises, including antenna gain discrepancies, angular scintillation (glints) and complex speckle. In order to account for this intricate phenomenology, this work combines the knowledge of the physical, kinematic, and statistical properties of SAR imaging into a single unified Bayesian structure that simultaneously (a) estimates the nuisance parameters such as clutter distributions and antenna miscalibrations and (b) estimates the target signature required for detection/inference of the target state. Moreover, we provide a Monte Carlo estimate of the posterior distribution for the target state and nuisance parameters that infers the parameters of the model directly from the data, largely eliminating tuning of algorithm parameters. We demonstrate that our algorithm competes at least as well on a synthetic dataset as state-of-the-art algorithms for estimating sparse signals. Finally, performance analysis on a measured dataset demonstrates that the proposed algorithm is robust at detecting/estimating targets over a wide area and performs at least as well as popular algorithms for SAR moving target detection.

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.

Abstract-We consider the problem of energy constrained and noise-limited search for targets that are sparsely distributed over a large area. We propose a multi-scale search algorithm that significantly reduces the search time of the adaptive resource allocation policy (ARAP) introduced in [Bashan et all, 2008]. Similarly to ARAP, the proposed approach scans a Q-cell partition of the search area in two stages: first the entire domain is scanned and second a subset of the domain, suspected of containing targets, is re-scanned. The search strategy of the proposed algorithm is driven by maximization of a modified version of the previously introduced ARAP objective function, which is a surrogate for energy constrained target detection performance. We analyze the performance of the proposed multistage ARAP approach and show that it can reduce mean search time with respect to ARAP for equivalent energy constrained detection performance. To illustrate the potential gains of M-ARAP, we simulate a moving target indicator (MTI) radar system and show that M-ARAP achieves an estimation performance gain of 7 dB and a 85% reduction in scan time as compared to an exhaustive search. This comes within 1 dB of the previously introduced ARAP algorithm at a fraction of its required scan time.

This paper considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy a restricted finite mixture representation. When specialized to the case of distributions over the sphere that are invariant to the actions of a finite spherical symmetry group G, a groupinvariant extension of the Von Mises Fisher (VMF) distribution is obtained. The G-invariant VMF is parameterized by location and scale parameters that specify the distribution's mean orientation and its concentration about the mean, respectively. Using the restricted finite mixture representation these parameters can be estimated using an Expectation Maximization (EM) maximum likelihood (ML) estimation algorithm. This is illustrated for the problem of mean crystal orientation estimation under the spherically symmetric group associated with the crystal form, e.g., cubic or octahedral or hexahedral. Simulations and experiments establish the advantages of the extended VMF EM-ML estimator for data acquired by Electron Backscatter Diffraction (EBSD) microscopy of a polycrystalline Nickel alloy sample. 1

This paper is concerned with a joint Bayesian formulation for determining the endmembers and abundances of hyperspectral images along with sparse outliers which can lead to estimation errors unless accounted for. We present an inference method that generalizes previous work and provides a MCMC estimate of the posterior distribution. The proposed method is compared empirically to state-of-theart algorithms, showing lower reconstruction and detection errors.