Gregory E. Newstadt

Two-Stage Multiscale Search for Sparse Targets

We consider the problem of energy constrained and noise-limited search for targets that are sparsely distributed over a large area. We propose a multiscale search algorithm that significantly reduces the search time of the adaptive resource allocation policy (ARAP) introduced in [Bashan 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 rescanned. 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.

Parameter Estimation in Spherical Symmetry Groups

This letter 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 group-invariant extension of the Von Mises Fisher (VMF) distribution is obtained. The G-invariant VMF is parameterized by location and scale parameters that specify the distributions 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.

Robust spectral unmixing for anomaly detection

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-the-art algorithms, showing lower reconstruction and detection errors.

Moving target inference with bayesian models in SAR imagery

This work combines the physical, kinematic, and statistical properties of targets, clutter, and sensor calibration as manifested in multichannel synthetic aperture radar (SAR) imagery into a unified Bayesian structure that simultaneously estimates 1) clutter distributions and nuisance parameters, and 2) target signatures required for detection/inference. A Monte Carlo estimate of the posterior distribution is provided that infers the model parameters directly from the data with little tuning of algorithm parameters. Performance is demonstrated on both measured/synthetic wide-area datasets.

Detection/Tracking of moving targets with synthetic aperture radars

In this work, the problem of detecting and tracking targets with synthetic aperture radars is considered. A novel approach in which prior knowledge on target motion is assumed to be known for small patches within the field of view. Probability densities are derived as priors on the moving target signature within backprojected SAR images, based on the work of Jao.1 Furthermore, detection and tracking algorithms are presented to take advantage of the derived prior densities. It was found that pure detection suffered from a high false alarm rate as the number of targets in the scene increased. Thus, tracking algorithms were implemented through a particle filter based on the Joint Multi-Target Probability Density (JMPD) particle filter2 and the unscented Kalman filter (UKF)3 that could be used in a track-before-detect scenario. It was found that the PF was superior than the UKF, and was able to track 5 targets at 0.1 second intervals with a tracking error of 0.20 ± 1.61m (95% confidence interval).

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

This paper presents a new Bayesian spectral unmixing algorithm to analyze 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 three-dimensional 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).

Adaptive search for sparse dynamic targets

We consider the problem of energy constrained and noise-limited search for targets that are sparsely distributed over a large area. We propose a multiple-stage search algorithm that accounts for complex time-varying target behavior such as transitions among neighboring cells and varying target amplitudes. This work extends the adaptive resource allocation policy (ARAP) introduced in [Bashan et al, 2008] to policies with T ≫ 2 stages. The proposed search strategy is driven by minimization of a surrogate function for energy constrained mean-squared error within locations containing targets. Exact optimization of the multi-stage objective function is infeasible, but myopic optimization yields a closed-form solution. We extend the myopic solution with non-myopic considerations that save a percentage of resources for exploring the scene at large. Empirical evidence suggests that the non-myopic policy performs significantly better than the myopic solution in terms of estimation error, probability of detection, and robustness to model mismatch. Moreover, the provided search policy has low computational complexity compared to state-of-the-art dynamic programming solutions.

Adaptive search for dynamic targets under resource constraints

Previous work on resource constrained adaptive search for sparse static targets has produced two-stage allocation policies with desirable properties. For example, for large asymptotic SNR, such policies converge to the true region of interest (ROI) and attain optimal energy allocations relative to exhaustive search. This work investigates the problem of extending previous allocation policies to T ≫ 2 stages, with particular emphasis on cases where the SNR for any particular stage is considerably less than the asymptotic SNR. Furthermore, a new formulation is given that can account for non-static targets, including a dynamic transition model for target location and a population model to account for targets that leave or enter the scene. Under this formulation, a dynamic adaptive resource allocation policy (D-ARAP) is proposed that performs well and has low computational cost. It is shown that this policy provides significant gains over an exhaustive search policy in both static and dynamic target cases with near optimal performance as T → ∞. Moreover, D-ARAP is shown to be more robust than a greedy (myopic) policy when there are outliers or when targets may be obscured for periods of time.

Robust spectral unmixing of multispectral Lidar waveforms

This paper presents a new Bayesian spectral unmixing algorithm to analyse remote scenes sensed via multispectral Lidar measurements. To a first approximation, each Lidar waveform consists of the temporal signature of the observed target, which depends on the wavelength of the laser source considered and which is corrupted by Poisson noise. When the number of spectral bands is large enough, it becomes possible to identify and quantify the main materials in the scene, on top of the estimation of classical Lidar-based range profiles. Thanks 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.

Coercive region-level registration for multi-modal images

We propose a coercive approach to simultaneously register and segment multi-modal images which share similar spatial structure. Registration is done at the region level to facilitate data fusion while avoiding the need for interpolation. The algorithm performs alternating minimization of an objective function informed by statistical models for pixel values in different modalities. Hypothesis tests are developed to determine whether to refine segmentations by splitting regions. We demonstrate that our approach has significantly better performance than the state-of-the-art registration and segmentation methods on microscopy images.