Robust detection of illicit items using X-ray inspection methods has gained increasing importance in recent years due to the large volume of cargo crossing borders. Viewing this as an anomaly detection problem in which contraband items are anomalous relative to expected cargo, we propose a selfsupervised learning framework consisting of an encoderdecoder-classifier model, a multi-component loss function, and training strategy to extract discriminative features tailored for detection of the presence or absence of anomalies in X-ray cargo images. Our framework addresses the challenges posed by limited labeled data and provides a model with the ability to detect anomalies. Additionally, we created a dataset encompassing diverse cargo scenarios with and without anomalies providing a rigorous evaluation environment for anomaly detection problems. We explore the performance of our framework on our dataset and two other datasets, demonstrating robustness even in testing with complex novel anomalies significantly different from those encountered during training.

We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. GLMs have been difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using conjugate auxiliary variable methods. We define a new class of GLMs for categorical data called categorical-from-binary (CB) models. Each CB model has a likelihood that is bounded by the product of binary likelihoods, suggesting a natural posterior approximation. This approximation makes inference straightforward and fast; using well-known auxiliary variables for probit or logistic regression, the product of binary models admits conjugate closed-form variational inference that is embarrassingly parallel across categories and invariant to category ordering. Moreover, an independent binary model simultaneously approximates multiple CB models. Bayesian model averaging over these can improve the quality of the approximation for any given dataset. We show that our approach scales to thousands of categories, outperforming posterior estimation competitors like Automatic Differentiation Variational Inference (ADVI) and No U-Turn Sampling (NUTS) in the time required to achieve fixed prediction quality.

Many time series can be modeled as a sequence of segments representing high-level discrete states, such as running and walking in a human activity application. Flexible models should describe the system state and observations in stationary ``pure-state'' periods as well as transition periods between adjacent segments, such as a gradual slowdown between running and walking. However, most prior work assumes instantaneous transitions between pure discrete states. We propose a dynamical Wasserstein barycentric (DWB) model that estimates the system state over time as well as the data-generating distributions of pure states in an unsupervised manner. Our model assumes each pure state generates data from a multivariate normal distribution, and characterizes transitions between states via displacement-interpolation specified by the Wasserstein barycenter. The system state is represented by a barycentric weight vector which evolves over time via a random walk on the simplex. Parameter learning leverages the natural Riemannian geometry of Gaussian distributions under the Wasserstein distance, which leads to improved convergence speeds. Experiments on several human activity datasets show that our proposed DWB model accurately learns the generating distribution of pure states while improving state estimation for transition periods compared to the commonly used linear interpolation mixture models.

Two common problems in time series analysis are the decomposition of the data stream into disjoint segments that are each in some sense "homogeneous" - a problem known as Change Point Detection (CPD) - and the grouping of similar nonadjacent segments, a problem that we call Time Series Segment Clustering (TSSC). Building upon recent theoretical advances characterizing the limiting distribution-free behavior of the Wasserstein two-sample test (Ramdas et al. 2015), we propose a novel algorithm for unsupervised, distribution-free CPD which is amenable to both offline and online settings. We also introduce a method to mitigate false positives in CPD and address TSSC by using the Wasserstein distance between the detected segments to build an affinity matrix to which we apply spectral clustering. Results on both synthetic and real data sets show the benefits of the approach.

In recent years, CubeSats have emerged as a platform of intense interest for a wide range of applications, including remote sensing. Of specific interest in this paper are data processing challenges associated with the MIT's Microwave Atmospheric Satellite (MicroMAS). Due to the motion of MicroMAS and the geometry of the data acquisition process, measurements are not collected on a regular grid of spatial locations as required by most applications. Thus, a fundamental problem in processing these data is that of interpolation. The problem is further complicated by the fact that MicroMAS collects data from several frequencies at a single location. A baseline algorithm that can be used to solve this multi-frequency scattered data interpolation problem is to fit data from each frequency via independent Gaussian Process (GP) and apply standard GP regression to estimate unknown data on the regular grid for each frequency separately. However, this approach ignores the correlation between frequencies. From the covariance structure in the aforementioned Independent Multiple output GP Regression (IMGPR) algorithm, we proposed a Correlated Multiple output GP Regression (CMGPR) algorithm which replaces a set of delta vectors with parameterized weight vectors learned from the dataset. To test the effectiveness of our proposed algorithms, we use NOAA's ATMS temperature data. According to the experimental results, the CMGPR algorithm performs better than the IMGPR.

With the recent development of CubeSats, several ultracompact, low cost, and rapidly deployable satellites have been developed for earth observation missions. Because of the geometry of the acquisition process, measurements are irregularly sampled, whereas in meteorological applications, data are preferred on a regular grid. This problem is further complicated by the fact that, due to CubeSats' compact sizes and constraints, such as limited power, errors occur in geolocation calibration, resulting in positional errors. In this letter, we analyze how the commonly used triangulation-based linear data interpolation scheme behaves under probabilistic models for the positional errors. The derived distribution of interpolation error caused by positional error is intractable even under a Gaussian distribution for positional errors. To address this problem, we developed an analytical closed-form solution to the first two moments of the interpolation error. Using models for positional errors motivated by our prior work, experimental results show that, compared with the first-order linear model, the second-order one provides a better approximation in terms of the mean and variance, which is very close to that is obtained using more computationally intensive Monte Carlo simulations. This model also allows for the closed-form calculation of mean squared interpolation error, which can be of use in the context of system design where the impact of positional errors on remote sensing products must be considered.

In this paper, we develop machine learning approaches for estimating quantitative features (or metrics) characterizing subsurface zones of chemical contamination, focusing on problems involving dense nonaqueous-phase liquid (DNAPL). Source zone characterization, a necessary first step in the development of a remediation strategy, is challenging due to practical constraints associated with the data available for processing. Our methods focus on the use of manifold regression techniques for estimating source zone metrics related to the distribution of contaminant mass in highly saturated pool regions, as well as more diffuse ganglia regions, based on downgradient measurements of dissolved contaminant concentration at a defined time. We use manifold methods for jointly representing labeled training data composed of known source zone metrics, as well as features derived from the corresponding dissolved concentration data sets. We then propose a new integrated approach to the problems of 1) robustly embedding test data (downgradient dissolved concentration) into the manifold when the source zone metrics are not available and 2) constructing a regression function operating directly in the manifold space for source zone metric estimation. The utility of the approach is enhanced by the explicit incorporation of physical constraints associated with the metrics into the problem formulation. Results based upon simulated data demonstrate the potential effectiveness of the manifold regression approaches, as well as significant improvement in performance relative to the case where the algorithmic components are designed serially.

Remediation of subsurface contamination by volatile organic compounds requires knowledge of the distribution of the contamination within the formation. To avoid the need for extensive sampling of the subsurface, here we present a Markov random field modeling approach where organic phase saturation is conditioned on the heterogeneous permeability of the domain. Estimation of the model parameters is accomplished using a Newton-type method in the context of a tractable pseudo-likelihood approximation to the true maximum likelihood objective function. Monte-Carlo analysis of samples drawn from this model indicate the potential utility of the approach for quantification of uncertainty for remediation design and assessment.

With their greatly reduced sizes, low development cost and rapid construction times, CubeSats have emerged as a platform of intense interest for a wide range of applications, including remote sensing. However, due to their compact form factor, performance tradeoffs relative to larger existing platforms have been encountered. Of specific interest in this paper are data processing challenges associated with the Micro-MAS platform. In meteorological applications, the radiometer samples are preferred on a regularly spaced grid for generating subsequent scientific products such as vertical temperature and water vapor profiles, or fusing with other gridded datasets. However, in reality, MicroMAS radiometer samples are not regularly spaced, and are expected to have geolocation errors comparable in magnitude to the beam-width [10]. In this work, we present a joint maximum a posteriori (MAP) estimation approach to determine both sample locations as well as brightness temperature on a regular spatial grid given irregularly sampled data corrupted by noise and uncertainty in sample locations. The performance of this approach is tested on Advanced Technology Microwave Sounder (ATMS) data which demonstrates significant improvement both qualitatively and quantitatively compared with traditional estimation methods.

Active contour techniques have been widely employed for medical image segmentation. Significant effort has been focused on the use of training data to build prior statistical models applicable specifically to problems where the objects of interest are embedded in cluttered background. Usually, the training data consist of whole shapes of certain organs or structures obtained manually by clinical experts. The resulting prior models enforce segmentation accuracy uniformly over the entire structure or structures to be identified. In this paper, we consider a new coupled prior shape model which is demonstrated to provide high accuracy, specifically in the region of the interest where precision is most needed for the application of the segmentation of the femur and tibia in magnetic resonance (MR) images. Experimental results for the segmentation of MR images of human knees demonstrate that the combination of the new coupled prior shape and a directional edge force provides the improved segmentation performance. Moreover, the new approach allows for equivalent accurate identification of bone marrow lesions, a promising biomarker related to osteoarthritis, to the current state of the art but requires significantly less manual interaction.

We present a reduced complexity algorithm for time-lapse Electrical Resistivity Tomography (ERT) based on an extended Kalman filter. The key idea of the fast algorithm is an efficient representation of state covariance matrix at each step as a weighted combination of the system noise covariance matrix and a low-rank perturbation term. We propose an efficient algorithm for updating the weights and the basis of the low-rank perturbation. The overall computational cost at each iteration is O(Nnm) and storage cost O(N), where N is the number of grid points, and nmis the number of measurements. The performance of this algorithm is demonstrated on a challenging application of monitoring the CO2plume using synthetic ERT data.

In this paper we develop three manifold regression approaches for estimating quantitative metrics characterizing subsurface zones contaminated by Dense Non-Aqueous Phase Liquids (DNAPLs) based on sparse down-gradient concentration data. We are particularly interested in estimating source zone characteristics related to the distribution of contaminant mass in highly saturated pool regions as well as more diffuse ganglia areas regions. Source zone characterization, a necessary first step in the development of any remediation strategy, is challenging due to practical constraints associated with the data available for processing. We use manifold methods for jointly representing labeled training data comprised of known metrics as well as features derived from the corresponding data sets. We then employ an integrated approach to the problems of (a) robustly embedding the sparse test data into the manifold when the metrics are not available and (b) constructing a regression function operating directly in manifold space for metric estimation. The utility of the approach is enhanced by the explicit incorporation of a physical constraint associated with the metrics into the problem formulation. We apply our manifold regression approaches to a simulated data set whose the hydraulic conductivity fields were generated using a Transition Probability Markov Chain (TP/MC) model. Using densely sampled concentration data for training but sparsely sampled data for testing, the results demonstrate the potential of our approaches.

The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a tensor-based iterative algorithm that simultaneously reconstructs the X-ray attenuation distribution for each energy. We use a multilinear image model rather than a more standard stacked vector representation in order to develop novel tensor-based regularizers. In particular, we model the multispectral unknown as a three-way tensor where the first two dimensions are space and the third dimension is energy. This approach allows for the design of tensor nuclear norm regularizers, which like its 2D counterpart, is a convex function of the multispectral unknown. The solution to the resulting convex optimization problem is obtained using an alternating direction method of multipliers approach. Simulation results show that the generalized tensor nuclear norm can be used as a standalone regularization technique for the energy selective (spectral) computed tomography problem and when combined with total variation regularization it enhances the regularization capabilities especially at low energy images where the effects of noise are most prominent.

This paper presents several strategies for spectral de-noising of hyperspectral images and hypercube reconstruction from a limited number of tomographic measurements. In particular we show that the non-noisy spectral data, when stacked across the spectral dimension, exhibits low-rank. On the other hand, under the same representation, the spectral noise exhibits a banded structure. Motivated by these features we show that the de-noised spectral data and the unknown spectral noise and the respective bands can be simultaneously estimated through the use of a low-rank and simultaneous sparse minimization operation without prior knowledge of the noisy bands. This result is novel for for hyperspectral imaging applications. In addition, we show that imaging for the Computed Tomography Imaging Systems (CTIS) can be improved under limited angle tomography by using low-rank penalization. For both of these cases we exploit the recent results in the theory of low-rank matrix completion using nuclear norm minimization.

Remediation of sites polluted by hazardous chemicals such as dense non-aqueous phase liquids (DNAPLs) represents an important environmental problem due to the large scale threat these releases pose to water supplies throughout the world. Successful cleanup and restoration relies on methods to characterize the source zone structure prior to remediation and subsequently to monitor the corresponding dissolved chemical levels. This paper develops and implements a new model-based approach to DNAPL source zone characterization based on the joint inversion of hydrological and geophysical data. To model the interaction of groundwater with the contaminant source zone, a fully three dimensional (3D) flow and transport model is used to provide the downstream contaminant concentrations associated to the source zone saturation distribution. As the geophysical modality we utilize electrical resistance tomography (ERT) where electric potential measurements related to the electrical properties of the medium are obtained cross gradient to the water flow direction. The inversion technique is based on the parametric level set method (PaLS) which provides for the recovery of the geometric profiles of the low and high saturation regions (corresponding to the ganglia and the pooling regions) and low order characterizations of the spatial variability within each region. The performance of our proposed algorithm is examined and discussed through the reconstruction of some challenging source zone architectures.

Large-scale contamination of ground water due to improper disposal of hazardous chemicals poses a global threat to drinking water supplies. Effective restoration and remediation of such sites relies upon a knowledge of the contaminant's distribution within the subsurface. Obtaining a detailed map of the existing distribution is usually not feasible; rather partial knowledge in terms of certain metrics that characterize the distribution has recently been shown to be sufficient for planning and monitoring remediation strategies. In this work we explore the prediction of a representative metric based upon down-gradient concentration profiles using a classification framework where each class represents a particular sub-range of the metric. Initial experiments show that our proposed model can be used effectively for predicting the metric.

Characterization of sites contaminated by chemicals such as trichloroethylene, perchloroethylene, and other dense non-aqueous phase liquids (DNAPLs) is a necessary first step in the design and implementation of successful remediation strategies. In this paper, we develop a machine learning-based approach for estimating characteristics of a source zone related to the distribution of contaminant mass in highly saturated pool regions and more diffuse ganglia based on observations of down-gradient concentration images. After extracting a set of morphological features from training images, Laplacian Eigenmaps is employed to embed these features with the known source zone metric in a low dimensional manifold. A spectral regression scheme is used to embed the test data into the same manifold after which a Bayesian approach is employed to estimate the associated metric as well as a confidence interval. Results based upon simulated data demonstrate the potential effectiveness of the overall approach.

Adjoint field methods are both elegant and efficient for calculating sensitivity information required across a wide range of physics-based inverse problems. In this letter, we provide a unified approach to the derivation of such methods for problems whose physics are provided by Poisson's equation. Unlike existing approaches in the literature, we consider in detail and explicitly the role of general boundary conditions in the derivation of the associated adjoint-field-based sensitivities. We highlight the relationship between the adjoint field computations required for both gradient decent and Gauss-Newton approaches to image formation. Our derivation is based on standard results from vector calculus coupled with transparent manipulation of the underlying partial different equations, thereby making the concepts employed in this letter easily adaptable to other systems of interest.

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, which maps changes in the electrical properties of a domain to their respective variations in boundary data. Using perturbation theory the transform is approximated to yield a high-order misfit function which is then used to derive a regularized inverse problem. In particular, we consider the nonlinear problem to second-order accuracy; hence our approximation method improves upon the local linearization of the forward mapping. The inverse problem is approached using Newton's iterative algorithm, and results from simulated experiments are presented. With a moderate increase in computational complexity, the method yields superior results compared to those of regularized linear regression and can be implemented to address the nonlinear inverse problem.

Dual-energy computerized tomography has gained great interest because of its ability to characterize the chemical composition of a material rather than simply providing relative attenuation images as in conventional tomography. The purpose of this paper is to introduce a novel polychromatic dual-energy processing algorithm, with an emphasis on detection and characterization of piecewise constant objects embedded in an unknown cluttered background. Physical properties of the objects, particularly the Compton scattering and photoelectric absorption coefficients, are assumed to be known with some level of uncertainty. Our approach is based on a level-set representation of the characteristic function of the object and encompasses a number of regularization techniques for addressing both the prior information we have concerning the physical properties of the object and the fundamental physics-based limitations associated with our ability to jointly recover the Compton scattering and photoelectric absorption properties of the scene. In the absence of an object with appropriate physical properties, our approach returns a null characteristic function and, thus, can be viewed as simultaneously solving the detection and characterization problems. Unlike the vast majority of methods that define the level-set function nonparametrically, i.e., as a dense set of pixel values, we define our level set parametrically via radial basis functions and employ a Gauss-Newton-type algorithm for cost minimization. Numerical results show that the algorithm successfully detects objects of interest, finds their shape and location, and gives an adequate reconstruction of the background.

We address the problem of automatic 3D segmentation of a stack of electron microscopy sections of brain tissue. Unlike previous efforts, where the reconstruction is usually done on a section-to-section basis, or by the agglomerative clustering of 2D segments, we leverage information from the entire volume to obtain a globally optimal 3D segmentation. To do this, we formulate the segmentation as the solution to a fusion problem. We first enumerate multiple possible 2D segmentations for each section in the stack, and a set of 3D links that may connect segments across consecutive sections. We then identify the fusion of segments and links that provide the most globally consistent segmentation of the stack. We show that this two-step approach of pre-enumeration and posterior fusion yields significant advantages and provides state-of-the-art reconstruction results. Finally, as part of this method, we also introduce a robust rotationally-invariant set of features that we use to learn and enumerate the above 2D segmentations. Our features outperform previous connectomic-specific descriptors without relying on a large set of heuristics or manually designed filter banks.

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results in a significantly lower dimensional problem, which bypasses many difficulties with traditional level set methods, such as regularization, reinitialization, and use of signed distance function. Moreover, we show that from a computational point of view, low order representation of the problem paves the way for easier use of Newton and quasi-Newton methods. Specifically for the purposes of this paper, we parameterize the level set function in terms of adaptive compactly supported radial basis functions, which, used in the proposed manner, provide flexibility in presenting a larger class of shapes with fewer terms. Also they provide a “narrow-banding” advantage which can further reduce the number of active unknowns at each step of the evolution. The performance of the proposed approach is examined in three examples of inverse problems, i.e., electrical resistance tomography, X-ray computed tomography, and diffuse optical tomography.

Fluorescence molecular tomography (FMT) allows in vivo localization and quantification of fluorescence biodistributions in whole animals. The ill-posed nature of the tomographic reconstruction problem, however, limits the attainable resolution. Improvements in resolution and overall imaging performance can be achieved by forming image priors from geometric information obtained by a secondary anatomical or functional high-resolution imaging modality such as X-ray computed tomography or magnetic resonance imaging. A particular challenge in using image priors is to avoid the use of assumptions that may bias the solution and reduced the accuracy of the inverse problem. This is particularly relevant in FMT inversions where there is not an evident link between secondary geometric information and the underlying fluorescence biodistribution. We present here a new, two step approach to incorporating structural priors into the FMT inverse problem. By using the anatomic information to define a low dimensional inverse problem, we obtain a solution which we then use to determine the parameters defining a spatially varying regularization matrix for the full resolution problem. The regularization term is thus customized for each data set and is guided by the data rather than depending only on user defined a priori assumptions. Results are presented for both simulated and experimental data sets, and show significant improvements in image quality as compared to traditional regularization techniques.

The ability to constrain the geometry of deformable models for image segmentation can be useful when information about the expected shape or positioning of the objects in a scene is known a priori. An example of this occurs when segmenting neural cross sections in electron microscopy. Such images often contain multiple nested boundaries separating regions of homogeneous intensities. For these applications, multiphase level sets provide a partitioning framework that allows for the segmentation of multiple deformable objects by combining several level set functions. Although there has been much effort in the study of statistical shape priors that can be used to constrain the geometry of each partition, none of these methods allow for the direct modeling of geometric arrangements of partitions. In this paper, we show how to define elastic couplings between multiple level set functions to model ribbon-like partitions. We build such couplings using dynamic force fields that can depend on the image content and relative location and shape of the level set functions. To the best of our knowledge, this is the first work that shows a direct way of geometrically constraining multiphase level sets for image segmentation. We demonstrate the robustness of our method by comparing it with previous level set segmentation methods.

This paper presents a new synthesis algorithm to produce flat-top main beams with arbitrary footprint for array elements placed in an arbitrary planar geometry. The general framework of the paper would encompass the patterns produced by circular aperture distribution. It is shown that for patterns generated by circular apertures some efficient simplifying facts based on properties of Bessel functions can be applied. The method shows a high performance in generating optimally flat-top patterns with detailed geometry footprints.

The 29 papers in this special issue were originally presented at the 2008 International Geoscience and Remote Sensing Symposium (IGARSS'08), held from July 6 to 11 in Boston, MA.

In this paper, we report new progress in developing the instrument and software platform of a combined X-ray mammography/diffuse optical breast imaging system. Particularly, we focus on system validation using a series of balloon phantom experiments and the optical image analysis of 49 healthy patients. Using the finite-element method for forward modeling and a regularized Gauss-Newton method for parameter reconstruction, we recovered the inclusions inside the phantom and the hemoglobin images of the human breasts. An enhanced coupling coefficient estimation scheme was also incorporated to improve the accuracy and robustness of the reconstructions. The recovered average total hemoglobin concentration (HbT) and oxygen saturation (SO2) from 68 breast measurements are 16.2 microm and 71%, respectively, where the HbT presents a linear trend with breast density. The low HbT value compared to literature is likely due to the associated mammographic compression. From the spatially co-registered optical/X-ray images, we can identify the chest-wall muscle, fatty tissue, and fibroglandular regions with an average HbT of 20.1+/-6.1 microm for fibroglandular tissue, 15.4+/-5.0 microm for adipose, and 22.2+/-7.3 microm for muscle tissue. The differences between fibroglandular tissue and the corresponding adipose tissue are significant (p < 0.0001). At the same time, we recognize that the optical images are influenced, to a certain extent, by mammographical compression. The optical images from a subset of patients show composite features from both tissue structure and pressure distribution. We present mechanical simulations which further confirm this hypothesis.

Voxel-based reconstructions in diffuse optical tomography (DOT) using a quadratic regularization functional tend to produce very smooth images due to the attenuation of high spatial frequencies. This then causes difficulty in estimating the spatial extent and contrast of anomalous regions such as tumors. Given an assumption that the target image is piecewise constant, we can employ a parametric model to estimate the boundaries and contrast of an inhomogeneity directly. In this paper, we describe a method to directly reconstruct such a shape boundary from diffuse optical measurements. We parameterized the object boundary using a spherical harmonic basis, and derived a method to compute sensitivities of measurements with respect to shape parameters. We introduced a centroid constraint to ensure uniqueness of the combined shape/center parameter estimate, and a projected Newton method was utilized to optimize the object center position and shape parameters simultaneously. Using the shape Jacobian, we also computed the Cramér-Rao lower bound on the theoretical estimator accuracy given a particular measurement configuration, object shape, and level of measurement noise. Knowledge of the shape sensitivity matrix and of the measurement noise variance allows us to visualize the shape uncertainty region in three dimensions, giving a confidence region for our shape estimate. We have implemented our shape reconstruction method, using a finite-difference-based forward model to compute the forward and adjoint fields. Reconstruction results are shown for a number of simulated target shapes, and we investigate the problem of model order selection using realistic levels of measurement noise. Assuming a signal-to-noise ratio in the amplitude measurements of 40 dB and a standard deviation in the phase measurements of 0.1 degrees , we are able to estimate an object represented with an eighth-order spherical harmonic model having an absorption contrast of 0.15 cm(-1) and a volume of 4.82 cm(3) with errors of less than 10% in object volume and absorption contrast. We also investigate the robustness of our shape-based reconstruction approach to a violation of the assumption that the medium is purely piecewise constant.

We considered the problem of sensor signal processing in the presence of positional uncertainty with application to classification of unexploded ordnance from observations of electromagnetic induction data. Our approach is based on the synthesis of random walk and Markov chain models for describing the correlated positional perturbations. Using this model, we develop an algorithm for the estimation of target parameters in which we minimize the maximum data misfit where the maximization is taken over the range of positional uncertainties supported by our model. The specific Markov nature of this model leads naturally to a low complexity estimation scheme based on the Viterbi algorithm. The results of using our Min- Max approach show significant improvement in final classification relative to the case where positional uncertainty is ignored.

The physics-based classification of unexploded ordnance (UXO) from electromagnetic induction (EMI) data is an exercise in nonlinear data inversion in which model parameters are extracted from a dataset by way of a physical model. Gradient-descent-based algorithms like Levenberg-Marquart (LM) suffer from local minima entrapment, but deliver rapid, accurate estimates when initialized near the global minima. Global optimizers, like particle swarm optimization (PSO) are less susceptible to this limitation. Here we consider an approach for parameter estimation based on a hybridization of PSO and Levenberg-Marquart. For purposes of initializing the LM procedure, we demonstrate that PSO applied to a reduced form of the physical model reaches a reliable initialization in one tenth the time of a coarse search of parameter space. Monte Carlo testing of the approach shows PSO initialized Levenberg-Marquardt estimation converging to the best-fit solution every time, as opposed to a randomly but reasonably initialized estimation. PSO as a stand alone approach provides less fit solutions on average than the PSO/Levenberg-Marquardt hybrid within the same computation time. We demonstrate these observations using both the simple, dipole model for the UXO problem as well as an enhanced form of this model capable of better capturing signal structure for large UXO-type objects.

Detection of dense non-aqueous phase liquids (DNAPLs) is a practical interesting problem in geophysics. This problem involves forward modeling, subsurface sensing and object reconstruction. An analytical forward model - HSBA - in the frequency domain containing dyadic Green's function solution to describe the cross-well radar sensing in infinite soil media is developed. First order Born approximation is employed to linearize this inverse scattering problem. The forward model is validated by both frequency domain computational models and laboratory experiments that are collected using cross-well radar method that uses broadband antennas in subsurface to illuminate the inhomogeneous field and receive scattered electromagnetic (EM) waves. A shape-based inversion algorithm is proposed for contaminant pool localization and reconstruction, in which the shape of the object is assumed priori and represented by a low- order differentiable parametric function. The characteristics of the object - location, size and dielectric contrast to the background medium - are obtained by an iterative non-linear optimization. The inversion method using synthesized data by numerical experiments gives promising preliminary results.

A new parameter-free graph morphology based segmentation algorithm is proposed to address the problem of partitioning a 3D triangular mesh into disjoint sub- eshes that correspond to the physical parts of the underlying object. Curvedness, which is a rotation and translation invariant shape descriptor, is computed at every vertex in the input triangulation. Iterative graph dilation and morphological filtering of the outlier curvedness values result in multiple, disjoint, maximally connected sub-meshes such that each sub-mesh contains a set of vertices with similar curvedness values, and vertices in disjoint sub-meshes have significantly different curvedness values. Experimental evaluations using the triangulations of a number of complex objects demonstrate the robustness and the efficiency of the proposed algorithm and the results prove that it compares well with a number of state-of-the-art mesh segmentation algorithms.

We used kernel density estimation (KDE) methods to build a priori probability density functions (pdfs) for the vector of features that are used to classify unexploded ordnance items given electromagnetic-induction sensor data. This a priori information is then used to develop a new suite of estimation and classification algorithms. As opposed to the commonly used maximum-likelihood parameter estimation methods, here we employ a maximum a posteriori (MAP) estimation algorithm that makes use of KDE-generated pdfs. Similarly, we use KDE priors to develop a suite of classification schemes operating in both "feature" space as well as ldquosignal/datardquo space. In terms of feature-based methods, we construct a support vector machine classifier and its extension to support M-ary classification. The KDE pdfs are also used to synthesize a MAP feature-based classifier. To address the numerical challenges associated with the optimal data-space Bayesian classifier, we have used several approximation techniques, including Laplacian approximation and generalized likelihood ratio tests employing the priors. Using both simulations and real field data, we observe a significant improvement in classification performance due to the use of the KDE-based prior models.

This paper proposes a new inverse method for microwave-based subsurface sensing of lossy dielectric objects embedded in a dispersive lossy ground with an unknown rough surface. An iterative inversion algorithm is employed to reconstruct the geometry and dielectric properties of the half-space ground as well as that of the buried object. B-splines are used to model the shape of the object as well as the height of the rough surface. In both cases, the control points for the spline function represent the unknowns to be recovered. A single-pole rational transfer function is used to capture the dispersive nature of the background. Here, the coefficients in the numerator and denominator are the unknowns. The approach presented in this paper is based on the state-of-the-art semianalytic mode matching forward model, which is a fast and efficient algorithm to determine the scattered electromagnetic fields. Numerical experiments involving two-dimensional geometries and TM incident plane waves demonstrate the accuracy and reliability of this inverse method

We consider the problem of classifying buried objects using electromagnetic induction data collected in a setting where there are errors in sensor positioning. Using a series of decay constants (or equivalently, Laplace plane poles) as features for classification, our algorithm seeks to estimate these poles and, subsequently, to determine the type of object in the sensor field of view. In many practical scenarios, a set of data is often accompanied by domain knowledge that the location of the transmitters and/or receivers is only known to within some degree of accuracy (e.g., 10 cm in the along-track direction and 5-cm cross-track). Here, we develop an approach to the extraction of information from such data sets in which the quantitative positional bound information is used in the context of a min-max optimization strategy. Specifically, we look for the parameters of interest that minimize the maximum data residual, where the maximum error is computed over ellipsoids or polyhedra of possible sensor locations defined by the bound information. Our formulation admits data collection with independent or dependent positional uncertainty values at successive nominal collection locations. Our algorithms for solving this optimization problem are validated using simulated and measured data

We examine the problem of fluorescence molecular tomography using the normalized Born approximation, termed herein the Born ratio, from a statistical perspective. Experimentally verified noise models for received signals at the excitation and emission wavelengths are combined to generate a stochastic model for the Born ratio. This model is then utilized within a maximum likelihood framework to obtain an inverse solution based on a fixed point iteration. Results are presented for three experimental scenarios: phantom data with a homogeneous background, phantoms implanted within a small animal, and in vivo data using an exogenous probe.

Reconfigurable supercomputing is a new direction of research in the quest for novel high-performance architectures. A handful of products are available in this field, but no architecture has emerged as the clear winner in performance. Using the US Air Force Research Labs' Heterogeneous High Performance Cluster (HHPC), we have developed a successful reconfigurable supercomputing implementation of synthetic aperture radar (SAR) image formation using backprojection, a highly parallel algorithm. By studying the architectural features of the HHPC and hand-tuning the application to those features, we estimate that better than 1000x speedup over a single-node software-only solution is feasable. In particular, we consider the movement of data between nodes, the movement of data between host PC and FPGA board, and the use of on-board memories available to the FPGA for data storage. These results indicate that reconfigurable supercomputers are an excellent choice to tackle highly-parallel large-dataset problems.

A reconstruction algorithm to simultaneously estimate the shape and location of three-dimensional breast cancer tumor is presented and its utility is analyzed. The approach is based on a spherical harmonic decomposition to capture the shape of the tumor. We combine a gradient descent optimization method with a direct electromagnetic solver to determine the coefficients in the harmonic expansion as well as the coordinates of the center of the tumor. The results demonstrate the potential advantage of collecting data using a multiple-view/tomographic-type strategy. We show how the order of the harmonic expansion must be increased to capture increasingly "irregularly" shaped tumors and explore the resulting increase in the central processing unit (CPU) time required by the algorithm. Our approach shows accurate reconstruction of the tumor image regardless of the source polarization. This work demonstrates the promise of the algorithm when used on data corrupted with Gaussian noise and when perfect knowledge of the tumor electrical properties is not available.

In the context of object recognition from point cloud data, we present a thermodynamically-inspired graph theoretic algorithm to address the problem of matching the scene and the model point clouds, when the cardinalities of the two sets are orders of magnitude different. Such an approach determines a subset of points from the model that is structurally and spatially as similar as possible to the set of points in the scene. A new formulation for graph enthalpy characterizes the structural differences between point sets, which together with the existing notions of graph entropy quantifies the Gibbs' free energy. A two-scale approach is proposed, wherein, at the coarse scale, a set of points that comprise the model neighborhood around the scene is identified by minimization of entropy. At the fine scale, the desired correspondence is achieved by a refinement process, aimed at maximizing the Gibbs' free energy. The results demonstrate the robustness and efficiency of the approach.

A fast algorithm for reconstructing the profile of random rough surfaces using electromagnetic scattering data is presented. The algorithm is based on merging a fast forward solver and an efficient optimization technique. The steepest descent fast multipole method is used as the three-dimensional fast forward solver. A rapidly convergent descent method employing a "marching-on" strategy for processing multifrequency and multi-incidence angle data is introduced to minimize an underlying cost function. The cost function represents the error between true (synthetic) and simulated scattered field data. Several key issues that impact the accuracy in reconstructing the rough profile are examined in this work, e.g., the location and number of receivers, the incident and scattered directions, the surface roughness, and details regarding the manner in which sensitivity information is computed in the inversion scheme. The results show that using the multiple-incidence (one angle at a time) and the multifrequency (one frequency at a time) strategies lead to improve the profile reconstruction.

In this paper, we present an adaptive two-pass rank order filter to remove impulse noise in highly corrupted images. When the noise ratio is high, rank order filters, such as the median filter for example, can produce unsatisfactory results. Better results can be obtained by applying the filter twice, which we call two-pass filtering. To further improve the performance, we develop an adaptive two-pass rank order filter. Between the passes of filtering, an adaptive process is used to detect irregularities in the spatial distribution of the estimated impulse noise. The adaptive process then selectively replaces some pixels changed by the first pass of filtering with their original observed pixel values. These pixels are then kept unchanged during the second filtering. In combination, the adaptive process and the second filter eliminate more impulse noise and restore some pixels that are mistakenly altered by the first filtering. As a final result, the reconstructed image maintains a higher degree of fidelity and has a smaller amount of noise. The idea of adaptive two-pass processing can be applied to many rank order filters, such as a center-weighted median filter (CWMF), adaptive CWMF, lower-upper-middle filter, and soft-decision rank-order-mean filter. Results from computer simulations are used to demonstrate the performance of this type of adaptation using a number of basic rank order filters.

The nonlinearized reconstruction of geometry and electrical characteristics of homogeneous obstacles buried in a half-space is investigated. The sources and sensors are placed in the other homogeneous half-space. To solve this non linear and ill-posed problem, an adaptive scheme based on the use of B-spline basis is proposed. The proposed numerical results show the possibilities of this inversion scheme.

Optimized versions of frequency-wavenumber (F-K) migration methods are introduced to better focus ground-penetrating radar (GPR) data in applications of shallow subsurface object localization, e.g., landmine remediation. Migration methods are based on the wave equation and operate by backpropagating the received data into the earth so as to localize buried objects. Traditional F-K migration is based on an underlying assumption that the wavefields propagate in a homogeneous medium. The presence of a rough air-ground interface in the GPR case degrades the localization ability. To overcome this problem in the context of the F-K algorithm, we introduce lateral variations in the velocity of waves in the medium. An optimization approach is employed to choose that velocity function that results in a well-focused image where an entropy-like criterion is used to quantify the notion of focus. Extension of the basic method to lossy medium is also described. The utility of these techniques is demonstrated using field data from a number of GPR systems.

Medical image processing in general and computerized tomography (CT) in particular can benefit greatly from hardware acceleration. This application domain is marked by computationally intensive algorithms requiring the rapid processing of large amounts of data. To date, reconfigurable hardware has not been applied to this important area. For efficient implementation and maximum speedup, fixed-point implementations are required. The associated quantization errors must be carefully balanced against the requirements of the medical community. Specifically, care must be taken so that very little error is introduced compared to floating-point implementations and the visual quality of the images is not compromised. In this paper, we present an FPGA implementation of the parallel-beam backprojection algorithm used in CT for which all of these requirements are met. We explore a number of quantization issues arising in backprojection and concentrate on minimizing error while maximizing efficiency. Our implementation shows significant speedup over software versions of the same algorithm, and is more flexible than an ASIC implementation. Our FPGA implementation can easily be adapted to both medical sensors with different dynamic ranges as well as tomographic scanners employed in a wider range of application areas including nondestructive evaluation and baggage inspection in airport terminals.

We introduce a multiscale texture image segmentation algorithm based on wavelet packets and graphs. Wavelet packets are used to generate scale-space features with strong discriminating power. A graph-theoretic approach to clustering is employed starting at the coarsest scale and working to the finest. We begin with the construction of a fully connected, weighted, undirected graph among all coarse scale pixels. The weights are determined from the wavelet packet generated features. Segmentation is achieved by constructing a minimum spanning tree for this graph, which is subsequently partitioned into sub trees by breaking "inconsistent" edges. Each sub tree corresponds to a different texture. Segment information is recursively passed to the next finer scale where we introduce a novel approach to constructing complete graphs for only a subset of pixels thereby improving the speed of the method with negligible performance degradation. We demonstrate the performance of our algorithm on synthetic images as well as on high-resolution infrared imagery.

We address inverse medium problems characterized by low-sensitivity observation data. A new level-set based method to recover the structure of piecewise homogeneous media is proposed. We make two contributions to this area of research. First, we capitalize on the flexibility in specifying the level-set velocity function in a way which counteracts the low sensitivity characteristic of the problem. The new approach speeds convergence while keeping the level set function smooth. Second, extending the current state of the art in the use of level sets for known binary media, we describe a simple and efficient implementation for N-ary media problems. We restrict our application examples to the electrical resistance tomography (ERT) problem, however, the proposed approaches are applicable to a variety of inverse problems involving shape reconstruction. We demonstrate the utility of our approach through a series of simulations using synthetic ERT data. Despite the ill-posed nature of the ERT problem, the simulation results show quite accurate estimations of the locations, sizes and shapes of multiple spatial inhomogeneities.

In this paper, we present an adaptive two-pass median filter to remove impulsive noise. In two-pass median filtering, an image contaminated by impulsive noise is processed by a median filter twice. Median filtering is a non-reversible process, i.e., useful information discarded by the filter cannot be recovered. This behavior becomes more apparent in two-pass median filtering. To correct this problem, between the two filtering processes we introduce an adaptive process to selectively replace some pixels by their original values based on the spatial distribution of estimated impulsive noise. Compared with standard median filtering and two-pass median filtering, better results are obtained in terms of visual appreciation and mean squared error. We use examples to demonstrate the performance of the method.

We present an adaptive difference of Gaussians (ADOG) method to improve landmine detection from ground penetrating radar (GPR) imagery. GPR is widely used for a variety of subsurface sensing problems including landmine detection and localization. In most all applications, specular reflection from the air-ground interface is the most significant source of interference often eclipsing the returns from the buried object. From an image processing viewpoint, the specular reflection constitutes a sharp edge and the landmine reflected signals are more smooth and of low spatial frequency. As an edge-preserving method, the ADOG keeps the specular reflection intact and removes the object reflected signals. Then by subtracting the ADOG output from the original image, we eliminate the specular reflection and obtain an image with enhanced object reflected signals. Using the difference image, we can obtain better result in detecting buried objects. Results from applying our algorithm on a landmine detection application are used to demonstrate the performance of the method.

Here we consider the use of model-based methods for the detection of buried objects from a sequence of synthetic aperture images obtained by a radar sensor moving linearly down a track. The scattering physics of the underlying sensing modality cause the relevant target signatures to change in a complex yet predictable manner from one image to the next. To arrive at a tractable processing scheme that exploits these motion-induced changes, we develop a flexible parametric model capable of capturing the full variation of these signatures. A detection scheme based on a principal components analysis of estimated model vectors is then derived. Results are demonstrated using field data from a forward-looking sensor.

We present an optimized frequency-wavenumber (F-K) migration method to localize buried objects such as landmines in lossy medium. F-K migration has been proposed to find the location of a buried object using ground penetrating radar (GPR) data. This approach makes use of a wave equation in the Fourier domain to back-propagate the received wavefield. For GPR applications however, standard F-K migration assumes that the ground surface is flat and the medium is loss-free which are not true in reality. When implemented in the Fourier domain, the wave equation becomes the Helmholtz equation. It is then straightforward to incorporate a complex index of refraction in the Helmholtz equation to describe wave phenomenon in lossy medium. We generalize F-K migration to the case of rough ground surface and lossy medium. In the framework of Tikhonov regularization, we develop an algorithm that optimally alters the wave propagation velocity and the complex index of refraction to take into account of the ground roughness and lossy medium. In the process of searching the optimal velocity and complex index of refraction, the algorithm is constrained to produce an image of minimum entropy. By minimizing the entropy of the resulting image, better results are obtained in terms of enhanced mainlobe, suppressed sidelobes, and reduced noise. We use examples from field data to demonstrate the performance of our method.

In detection of landmines using ground penetrating radar (GPR), the most significant interference is the specular reflection. Compared with the specular reflection, landmine scattered signals are of small amplitude and difficult to observe. Better detection results can be obtained if the specular reflection can be well separated from the landmine scattered signals. Difference of Gaussians (DOG) is an operation that generates a sharp image from an original image, i.e. in the case of a GPR image, it keeps the specular reflection intact. Therefore by subtracting the DOG output from an original GPR image, we are able to remove the specular reflection and enhance the landmine scattered signals. The DOG takes the difference between two Gaussian curves of zero means and different standard deviations and convolves with the original image. One advantage of the DOG is that the two standard deviations can be chosen properly to suit different applications. We develop an adaptive DOG (ADOG) to process GPR images to improve detection of buried landmines. In the ADOG, the two standard deviations of Gaussians are computed adaptively as a GPR image is scanned from the top to the bottom row. At each row, two windows are used to calculate the two standard deviations and the current row is convolved with the DOG. The output has an unchanged specular reflection while there is a reduced landmine scattered signal. The final image is obtained by subtracting the ADOG output from the original image to remove the specular reflection. The landmine scattered signal is greatly enhanced, allowing more accurate detection.

We propose using an adaptive filter to enhance ground penetrating radar (GPR) images. It is well known that GPR images are usually dominated by the specular ground reflection. The specular reflection makes the object scattered signals difficult to observe, so it first must be removed before more refined detection and classification processing can be employed. To remove the specular reflection, the biggest challenge is that, due to ground roughness, the reflection cannot be satisfactorily subtracted by some simple methods such as a moving-average filter. Using contrast stretch we can enhance the object reflect signal and then use standard background removal method to eliminate most of the specular reflection. During the contrast stretch, the GPR images may have "streaky" artifacts because of the background removal. To overcome this side-effect, we apply an adaptive filter to remove "streaky" artifacts. Using field data, we show that images of higher quality can be obtained by our method.

We introduce a combination of high-dimensional analysis of variance (HANOVA) and sequential probability ratio test (SPRT) to detect buried objects from an array ground-penetrating radar (GPR) surveying a region of interest in a progressive manner. Using HANOVA, we exploit the transient characteristic of GPR signals in the time domain to extract information about buried objects at fixed positions of the array. Based on the output of the HANOVA, the SPRT is employed to make detection decisions recursively as the array moves downtrack. The method is on-line implementable and of low computational complexity. Our approach is validated using field-data from two quite different GPR sensing systems designed for landmine detection applications.

In this paper, we examine the problem of locating an object in an image when size and rotation are unknown. Previous work has shown that with known geometric parameters, an image restoration method can be useful by estimating a delta function at the object location. When the geometric parameters are unknown, this method becomes impractical because the likelihood surface to be minimized across size and rotation has numerous local minima and areas of zero gradient. We propose a new approach where a smooth approximation of the template is used to minimize a well-behaved likelihood surface. A coarse-to-fine approximation of the original template using a diffusion-like equation is used to create a library of templates. Using this library, we can successively perform minimizations which are locally well-behaved. As detail is added to the template, the likelihood surface gains local minima, but previous estimates place us within a well-behaved "bowl" around the global minimum, leading to an accurate estimate. Numerical experiments are shown which verify the value of this approach for a wide range of values of the geometric parameters.

Dynamic magnetic resonance imaging (MRI) refers to the acquisition of a sequence of MRI images to monitor temporal changes in tissue structure. We present a method for the estimation of dynamic MRI sequences based on two complimentary strategies: an adaptive framework for the estimation of the MRI images themselves, and an adaptive method to tailor the MRI system excitations for each data acquisition. We refer to this method as the doubly adaptive temporal update method (DATUM) for dynamic MRI. Analysis of the adaptive image estimate framework shows that calculating the optimal system excitations for each new image requires complete knowledge of the next image in the sequence. Since this is not realizable, we introduce a linear predictor to aid in determining appropriate excitations. Simulated examples using real MRI data are included to illustrate that the doubly adaptive strategy can provide estimates with lower steady state error than previously proposed methods and also the ability to recover from dramatic changes in the image sequence.

The electromagnetic scattering from a three-dimensional (3D) shallow object buried under a two-dimensional (2D) random rough dielectric surface is analyzed. The buried object can be a perfect electric conductor (PEC) or can be a penetrable dielectric with size and burial depth comparable to the free-space wavelength. The random rough ground surface is characterized with Gaussian statistics for surface height and for surface autocorrelation function. The Poggio, Miller, Chang, Harrington, and Wu (PMCHW) integral equations are implemented and extended. The integral equation-based steepest descent fast multipole method (SDFMM), that was originally developed at UIUC, has been used and the computer code based on this algorithm has been successfully modified to handle the current application. The significant potential of the SDFMM code is that it calculates the unknown moment method surface electric and magnetic currents on the scatterer in a dramatically fast, efficient, and accurate manner. Interactions between the rough surface interface and the buried object are fully taken into account with this new formulation. Ten incident Gaussian beams with the same elevation angle and different azimuth angles are generated for excitation as one possible way of having multiple views of a given target. The scattered electric fields due to these ten incident beams are calculated in the near zone and their complex vector average over the multiple views is computed. The target signature is obtained by subtracting the electric fields scattered from the rough ground only from those scattered from the ground with the hurled anti-personnel mine.

The authors present an algorithm for the detection and localization of an unknown number of objects buried in a halfspace and present in the near field of a linear receiver array. To overcome the nonplanar nature of the wavefield over the array, the full array is divided into a collection of subarrays such that the scattered fields from objects are locally planar at each subarray. Using the multiple signal classification (MUSIC) algorithm, directions of arrival (DOA) of locally planar waves at each subarray are found. By triangulating these DOAs, a set of crossings, condensed around expected object locations, are obtained. To process this spatial crossing pattern, the authors develop a statistical model for the distribution of these crossings and employ hypotheses testing techniques to identify a collection of small windows likely to contain targets. Finally, the results of the hypothesis tests are used to estimate the number and locations of the targets. Using simulated data, they demonstrate the usefulness and performance of this approach for typical background electrical properties and signal to noise ratios.

Motivated by work in the area of dynamic magnetic resonance imaging (MRI), we develop a new approach to the problem of reduced-order MRI acquisition. Efforts in this field have concentrated on the use of Fourier and singular value decomposition (SVD) methods to obtain low-order representations of an entire image plane. We augment this work to the case of imaging an arbitrarily-shaped region of interest (ROI) embedded within the full image. After developing a natural error metric for this problem, we show that determining the minimal order required to meet a prescribed error level is in general intractable, but can be solved under certain assumptions. We then develop an optimization approach to the related problem of minimizing the error for a given order. Finally, we demonstrate the utility of this approach and its advantages over existing Fourier and SVD methods on a number of MRI images.

A common image processing problem is determining the location of an object using a template when the size and rotation of the target are unknown. Using a maximum likelihood formulation, localization is possible by computing a likelihood surface for a dense sampling of the size and rotation space. However, optimization is complicated by local minima and regions of small or zero gradient. We therefore demonstrate a technique which employs a library of templates starting from a smooth approximation and adding detail until the exact template is reached. Successively estimating the geometric parameters using these templates achieves the accuracy of the exact template while remaining within a well-behaved "bowl" in the search space which allows standard minimization techniques to be used.

We develop a new geometric curve evolution approach to tomographic reconstruction problems including multiple objects having different levels of intensity, and background with varying intensity. We use two contours to represent the boundaries of distinct object regions with different intensity levels and a set of basis functions and expansion coefficients to describe the background. By designing coupled "tomographic flows", the problem of estimating the two contours and intensity coefficients is recast into a curve evolution problem. A new "repelling" force between the two coupled curves is proposed for the reconstruction algorithms to accelerate convergence. The performance of the coupled curve evolution method is demonstrated via a Radon inversion example. The results show that our curve evolution method achieves improved shape reconstruction over comparable regularization techniques.

We introduce a sliding window adaptive RLS-like algorithm for filtering alpha-stable noise. Unlike previously introduced stochastic gradient-type algorithms, the new adaptation algorithm minimizes the L/sub p/ norm of the error exactly in a sliding window of fixed size. Therefore, it behaves much like the RLS algorithm in terms of convergence speed and computational complexity compared to previously introduced stochastic gradient-based algorithms, which behave like the LMS algorithm. It is shown that the new algorithm achieves superior convergence rate at the expense of increased computational complexity.

The problem of characterizing the geometric structure of an object buried in an inhomogeneous halfspace of unknown composition is considered. The authors develop a nonlinear inverse scattering algorithm based on a low-dimensional parameterization of the unknown object and the background. In particular, they use a low-order polynomial expansion to represent the spatial variations in the real and imaginary parts of the object and background complex permittivities. The boundary separating the target from the unknown background is described using a periodic, quadratic B-spline curve whose control points can be individually manipulated. They determine the unknown control point locations and contrast expansion coefficients using a greedy-type approach to minimize a regularized least-squares cost function. The regularizer used here is designed to constrain the geometric structure of the boundary of the object and is closely related to snake methods employed in the image processing community. They demonstrate the performance of their approach via extensive numerical simulation involving two-dimensional (2D), TM/sub z/ scattering geometries. Their results indicate a strong ability to localize and estimate the shape of the object even in the presence of an unknown and inhomogeneous background.

In this paper, we consider a wavelet based edge-preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e., edges in two dimensions or jumps in one dimension). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the local structure of the underlying image. In particular, we are able to adapt quite easily to scale-varying and orientation-varying features in the image while simultaneously retaining the edge preservation properties of the regularizer. We demonstrate a half-quadratic algorithm for obtaining the restorations from observed data.

In this paper, we present an algorithm for the detection, localization, and characterization of anomalous structures in an overall region of interest given observations of scattered electromagnetic fields obtained along the boundary of the region. Such anomaly detection problems are encountered in applications including medical imaging, radar signal processing, and geophysical exploration. The techniques developed in this work are based on a nonlinear scattering model relating the anomalous structures to the observed data. A sequence of M-ary hypothesis tests are employed first to localize anomalous behavior to large areas and then to refine these initial estimates to better characterize the true target structures. We introduce a method for the incorporation of prior information into the processing which reflects constraints relevant directly to the anomaly detection problem such as the number, shapes, and sizes of anomalies present in the region. The algorithm is demonstrated using a low-frequency, inverse conductivity problem found in geophysical applications.

We consider a wavelet-based edge preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e. edges in two dimensions or jumps in 1D). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the scale based structure of the underlying image. We demonstrate an efficient algorithm for obtaining the reconstructions from observed data and for choosing the multiple regularization parameters governing the priors.

A common problem in image processing is recovery of an image given noisy linear functionals of the original. While it has been shown that in certain situations, models possessing a 1/f-type power spectrum perform well as regularizers to stabilize these ill-posed inverse problems, the optimal parameters for the model are rarely known a priori. Previously, it was demonstrated that the expectation maximization (EM) algorithm can satisfactorily perform the estimation of the model parameters in the unblurred one-dimensional case. In this paper, we extend this analysis to the situation of two-dimensional objects and an environment which includes blurring. We show that again the EM algorithm performs well. In addition, we examine performance in terms of the variance of the estimates and bounds on these quantities.

One common problem in signal and image processing is the determination of a discrete representation of a signal given data corresponding to a noisy and blurred version of the unknown. We examine the performance degradation associated with the use of a two-parameter family of fractal-type statistical models in a linear least squares estimator (LLSE) when the model parameters do not match those of the actual process. These models are shown to perform well under various circumstances for estimating noisy and blurred 1/f type fractals and first order Gauss-Markov (FOGM) signals. In addition we demonstrate an effective means of bounding one of the model parameters as a function of the other so as to reduce the model to a single parameter.

Includes bibliographical references (p. 34-36).

A scale-recursive algorithm is presented for the detection and characterization of anomalous structures in a medium based upon observations of scattered radiation obtained along the boundary of the region. A nonlinear scattering model based upon Maxwell's equation is used to relate the anomalous structures to the measured fields. Decision- and estimation-theoretic techniques are employed to (a) identify large-scale areas in which such anomalies are present and (b) spatially refine these estimated regions to better localize the true anomalous structures. Examples are presented from a low-frequency inverse conductivity problem drawn from the field of geophysical signal processing.

Presents a multiscale, statistically-based algorithm for the detection and characterization of localized anomalies in a medium based upon observations of scattered energy obtained along the boundaries of the region. The authors use wavelet transform methods for lowering the computational complexity of the detection and estimation procedures and for providing efficient and physically meaningful models for the non-anomalous behavior of the medium. Determination of the structures of the anomalous areas is performed in a scale-recursive manner using a sequence of generalized, M-ary likelihood ratio tests to successively subdivide the region under consideration as a means of localizing anomalies both in space and scale. Examples of the approach are demonstrated using the Born approximation to a 2D inverse conductivity problem arising in geophysical prospecting applications.>