Peter D. Scott

Digital Decoding Of In-Line Holograms

Digitally sampled in-line holograms may be linearly filtered to reconstruct a representation of the original object distribution, thereby decoding the information contained in the hologram. The decoding process is performed by digital computation rather than optically. Substitution of digital for optical decoding has several advantages, including selective suppression of the twin-image artifact, elimination of the far-field requirement, and automation of the data reduction and analysis process. The proposed filter is a truncated series expansion of the inverse of that operator that maps object opacity function to hologram intensity. The first term of the expansion is shown to be equivalent to conventional (optical) reconstruction, with successive terms increasingly sup-pressing the twin image. The algorithm is computationally efficient, requiring only a single fast Fourier transform pair.

Object recognition using multilayer Hopfield neural network

An object recognition approach based on concurrent coarse-and-fine matching using a multilayer Hopfield neural network is presented. The proposed network consists of several cascaded single-layer Hopfield networks, each encoding object features at a distinct resolution, with bidirectional interconnections linking adjacent layers. The interconnection weights between nodes associating adjacent layers are structured to favor node pairs for which model translation and rotation, when viewed at the two corresponding resolutions, are consistent. This interlayer feedback feature of the algorithm reinforces the usual intralayer matching process in the conventional single-layer Hopfield network in order to compute the most consistent model-object match across several resolution levels. The performance of the algorithm is demonstrated for test images containing single objects, and multiple occluded objects. These results are compared with recognition results obtained using a single-layer Hopfield network.

Uncertainty propagation for nonlinear dynamic systems using Gaussian mixture models

A Gaussian-mixture-model approach is proposed for accurate uncertainty propagation through a general nonlinear system. The transition probability density function is approximated by a finite sum of Gaussian density functions for which the parameters (mean and covariance) are propagated using linear propagation theory. Two different approaches are introduced to update the weights of different components of a Gaussian-mixture model for uncertainty propagation through nonlinear system. The first method updates the weights such that they minimize the integral square difference between the true forecast probability density function and its Gaussian-sum approximation. The second method uses the Fokker-Planck-Kohnogorov equation error as feedback to adapt for the amplitude of different Gaussian components while solving a quadratic programming problem. The proposed methods are applied to a variety of problems in the open literature and are argued to be an excellent candidate for higher-dimensional uncertainty-propagation problems.

Adaptive Gaussian Sum Filter for Nonlinear Bayesian Estimation

A nonlinear filter is developed by representing the state probability density function by a finite sum of Gaussian density kernels whose mean and covariance are propagated from one time-step to the next using linear system theory methods such as extended Kalman filter or unscented Kalman filter. The novelty in the proposed method is that the weights of the Gaussian kernels are updated at every time-step, by solving a convex optimization problem posed by requiring the Gaussian sum approximation to satisfy the Fokker-Planck-Kolmogorov equation for continuous-time dynamical systems and the Chapman-Kolmogorov equation for discrete-time dynamical systems. The numerical simulation results show that updating the weights of different mixture components during propagation mode of the filter not only provides us with better state estimates but also with a more accurate state probability density function.

Foveal machine vision systems

A class of machine vision systems is proposed, called foveal vision systems. These systems, modeled after advanced biological vision, feature space-variant (variable-resolution) imager topologies and a closed-loop system architecture. The imager topology is characterized by resolution which is high at the center of the sampling lattice and which decreases with distance from the center. The central axis is controlled by feedback from higher-level algorithms, allowing the allocation of sampling resources to the region(s) of interest and resulting in greater relevant information from the imager yet permitting considerable reduction in data. Preliminary investigations have demonstrated reductions in data structure size and computations of several orders of magnitude relative to conventional implementations. The savings factors increase with field-of-view and resolution.<<ETX>>

Polynomial-chaos-based Bayesian approach for state and parameter estimations

Two new recursive approaches have been developed to provide accurate estimates for posterior moments of both parameters and system states while making use of the generalized polynomial-chaos framework for uncertainty propagation. The main idea of the generalized polynomial-chaos method is to expand random state and input parameter variables involved in a stochastic differential/difference equation in a polynomial expansion. These polynomials are associated with the prior probability density function for the input parameters. Later, Galerkin projection is used to obtain a deterministic system of equations for the expansion coefficients. The first proposed approach provides means to update prior expansion coefficients by constraining the polynomial-chaos expansion to satisfy a specified number of posterior moment constraints derived from Bayes’s rule. The second proposed approach makes use of the minimum variance formulation to update generalized polynomial-chaos coefficients. The main advantage of the prop...

Unscented Kalman Filter/Smoother for a CBRN puff-based dispersion model

Fixed interval smoothing for systems with nonlinear process and measurement models is studied and applied to the assimilation of sensor data in a Chemical, Biological, Radiological or Nuclear (CBRN) incident scenario. A two-filter smoother that uses a Backward Sigma-Point Information Filter, and also a forward-backward Rauch-Tung-Striebel (RTS) smoothing form are re-derived using the weighted statistical linearization concept. Both methods are derived in the context of the Unscented Kalman Filter. The square root version of the resulting RTS Unscented Kalman Filter / Smoother is applied to a CBRN dispersion puff-based model with variable state dimension, and the data assimilation performance of the method is compared with a Particle Filter implementation.

The Covariance Least-Squares Algorithm for Spectral Estimation of Processes of Short Data Length

A new method for generating the autoregressive (AR) process parameters for spectral estimation is introduced. The method fits AR models to the data optimally in the sense of minimizing the sum of squares of the error covariance function within the model prediction region, and is thus designated as the Covariance Least-Squares (CLS) algorithm. This minimization is shown to be identical with minimizing the weighted average one-step, linear prediction errors with adaptive weights corresponding to the energy of the data within the prediction region. The CLS algorithm is compared to the Least-Squares (LS) algorithm [1], [2] by simulation and asymptotic properties. It is shown that the CLS method combines all the desirable properties of the comparison algorithm with improved robustness in the presence of nonstationarity, namely, additive transients and envelope modulation. It is also shown that the CLS algorithm provides asymptotically unbiased AR parameters, a property also shared by the comparison LS algorithm.

Foveal automatic target recognition using a multiresolution neural network

This paper presents a method for detecting and classifying a target from its foveal (graded resolution) imagery using a multiresolution neural network. Target identification decisions are based on minimizing an energy function. This energy function is evaluated by comparing a candidate blob with a library of target models at several levels of resolution simultaneously available in the current foveal image. For this purpose, a concurrent (top-down-and-bottom-up) matching procedure is implemented via a novel multilayer Hopfield neural network. The associated energy function supports not only interactions between cells at the same resolution level, but also between sets of nodes at distinct resolution levels. This permits features at different resolution levels to corroborate or refute one another contributing to an efficient evaluation of potential matches. Gaze control, refoveation to more salient regions of the available image space, is implemented as a search for high resolution features which will disambiguate the candidate blob. Tests using real two-dimensional (2-D) objects and their simulated foveal imagery are provided.

Data assimilation in variable dimension dispersion models using particle filters

Data assimilation in the context of puff based dispersion models is studied. A representative two dimensional Gaussian puff atmospheric dispersion model is used for the purpose of testing and comparing several data assimilation techniques. A continuous nonlinear observation model, and a quantized probabilistic nonlinear observation model, are used to simulate the measurements. The quantized model is used to simulate bar sensor readings of the concentration. Dispersion models usually lead to high dimensional space-gridded state space models. In the case of puff based dispersion models, this may be avoided by using puff parameters themselves as the states, but at the cost of introducing nonlinearity and variable dimensionality. The potential of sampling based techniques is discussed in this context, with a particular focus on the particle filter approach, for which variable state dimensionality creates no difficulties. The performance of particle filter is compared with that of the extended Kalman filter, and its advantages and limitations are illustrated.