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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. [ABSTRACT FROM PUBLISHER]

With their greatly reduced sizes, low development cost, and rapid construction time, CubeSats have merged as a platform of considerable interest for a wide range of applications, including remote sensing. Many applications require the interpolation of sensor data into a regularly spaced grid for the development of downstream scientific products. This problem is complicated for CubeSat platforms due to potentially significant uncertainties associated with the spatial position of the satellite. In this paper, we present a probabilistic approach to the data interpolation problem in which we estimate both the platform location and data samples on a regular grid given observations corrupted by noise and location error. Our approach is based on a Gaussian process model to connect the measured data to the values on the grid. Two statistical models for positional uncertainties are considered, one based on an assumption of independent errors and another motivated by positional errors associated with a specific platform of interest, the MicroMAS radiometer. In each case, the maximum a posteriori estimate of the positions and the data is generated using an optimized Gaussian process regression (OGPR) method resulting in two algorithms: OGPR-IID and OGPR-PCA. The performance of this approach is tested on both simulated data and advanced technology microwave sounder data where significant improvements both qualitatively and quantitatively relative to traditional interpolation methods are observed. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

Patch-based methods have attracted significant attention in recent years within the field of image processing for a variety of problems including denoising, inpainting, and super-resolution interpolation. Despite their prevalence for processing 2-D signals, they have received little attention in the 1-D signal processing literature. In this letter, we explore application of one such method, the nonlocal means (NLM) approach, to the denoising of biomedical signals. Using ECG as an example, we demonstrate that a straightforward NLM-based denoising scheme provides signal-to-noise ratio improvements very similar to state of the art wavelet-based methods, while giving \sim3\times or greater reduction in metrics measuring distortion of the denoised waveform. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

We propose a new shape-based inversion algorithm to identify an anomaly embedded in an inhomogeneous layered geometry. We apply our approach to microwave breast imaging where the geometry consists of several inhomogeneous layers and the potential tumor is embedded in the innermost layer. In addition to the tumor identification, we estimate the irregular transition layer between the breast inner layers. Our inversion algorithm is based on a low-dimensional parametric form of the relevant geometries, and uses multiple-frequency multi-source data to estimate the unknowns. Several numerical examples are provided to evaluate the effectiveness of our approach and demonstrate its robustness both to the initial choice of parameter values and uncertainty in the complex dielectric properties of the media even with the complex geometry and the simplified inverse model. [ABSTRACT FROM AUTHOR]

Intracranial aneurysms are localized, abnormal arterial dilatations with a variable risk of rupture, leading to medical conditions associated with high morbidity and mortality. Predicting their risk of rupture, especially for incidental asymptomatic aneurysms, is a challenging task. The size of the aneurysm sac is traditionally used to assess the risk, but shape analysis has emerged as a promising differentiator of rupture likelihood. The centroid–radii model (CRM) is introduced here to describe both the size and the shape of the aneurysms, and determine rupture status. The entropy of CRM is proposed as an aneurysm descriptor which is easy to compute, robust to noise and segmentation, and accurate in rupture status discrimination. Analysis is performed on 154 patient-derived saccular aneurysms. The aneurysms are further classified as sidewall and bifurcation, and the shape analysis is performed separately on the two subtypes. Using the entropy of CRM resulted in 80.3% and 70.5% classification accuracy of status rupture in sidewall and bifurcation aneurysms, respectively. When compared to the accuracy of some commonly used size and shape indexes, the entropy of the CRM proved to be a more accurate single index associated with rupture in intracranial aneurysms, for both sidewall and bifurcation subtypes. [ABSTRACT FROM AUTHOR]

We consider the estimation of a Gaussian random vector x observed through a linear transformation H and corrupted by additive Gaussian noise with a known covariance matrix, where the covariance matrix of x is known to lie in a given region of uncertainty that is described using bounds on the eigenvalues and on the elements of the covariance matrix. Recently, two criteria for minimax estimation called difference regret (DR) and ratio regret (RR) were proposed and their closed form solutions were presented assuming that the eigenvalues of the covariance matrix of x are known to lie in a given region of uncertainty, and assuming that the matrices HT Cw-1 and Cx are jointly diagonalizable, where Cw and Cx denote the covariance matrices of the additive noise and of x respectively. In this work we present a new criterion for the minimax estimation problem which we call the generalized difference regret (GDR), and derive a new minimax estimator which is based on the GDR criterion where the region of uncertainty is defined not only using upper and lower bounds on the eigenvalues of the parameter's covariance matrix, but also using upper and lower bounds on the individual elements of the covariance matrix itself. Furthermore, the new estimator does not require the assumption of joint diagonalizability and it can be obtained efficiently using semidefinite programming. We also show that when the joint diagonalizability assumption holds and when there are only eigenvalue uncertainties, then the new estimator is identical to the difference regret estimator. The experimental results show that we can obtain improved mean squared error (MSE) results compared to the MMSE, DR, and RR estimators. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A fast method for computing the acoustic field of ultrasound transducers is presented with application to rectangular elements that are cylindrically focused. No closed-form solutions exist for this case but several numerical techniques have been described in the ultrasound imaging literature. Our motivation is the rapid calculation of imaging kernels for physics-based diagnostic imaging for which current methods are too computationally intensive. Here, the surface integral defining the acoustic field from a baffled piston is converted to a 3-D spatial coavolution of the element surface and the Green's function. A 3-D version of the overlap-save method from digital signal processing is employed to obtain a fast computational algorithm based on spatial Fourier transforms. Further efficiency is gained by using a separable approximation to the Green's function through singular value decomposition and increasing the effective sampling rate by polyphase filtering. The tradeoff between accuracy and spatial sampling rate is explored to determine appropriate parameters for a specific transducer. Comparisons with standard tools such as Field II are presented, where nearly 2 orders of magnitude improvement in computation speed is observed for similar accuracy. [ABSTRACT FROM AUTHOR]

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 μm 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 for fibroglandular tissue, 15.4 ± 5.0 μm for adipose, and 2212 ± 7.3 μm 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. [ABSTRACT FROM AUTHOR]

Abstract-We propose a new approach to approximating the Chapman-Kolmogorov equation (CKE) for particle-based nonlinear filtering algorithms, using a new proposal distribution and the improved fast Gauss transform (IFGT) with tighter accuracy bounds. The new proposal distribution, used to obtain a Monte Carlo (MC) approximation of the CKE, is based on the proposal distribution found in the auxiliary marginal particle filter (AMPF). By using MC integration to approximate the integrals of the AMPF proposal distribution as well as the CKE, we demonstrate significant improvement in terms of both error and computation time. We consider the additive state noise case where the evaluation of the CKE is equivalent to performing kernel density estimation (KDE), thus fast methods such as the IFGT can be used. In practice, the IFGT demonstrates performance far better than that which is predicted by current error analysis, therefore the existing bounds are not useful for determining the IFGT parameters which in practice have to be chosen experimentally in order to obtain satisfactory compromise between accuracy and speed of the filtering algorithm. We provide in this paper much improved performance bounds for the IFGT, and which unlike the previous bound, are consistent with the expectation that the error decreases as the truncation order of the IFGT increases. The new bounds lead to a new definition of the IFGT parameters and give important insight into the effect that these parameters have on the error, therefore facilitating the choice of parameters in practice. The experimental results show that we can obtain similar error to the sequential importance sampling (SIS) particle filter, while using fewer particles. Furthermore the choice of the new LFGT parameters remains roughly the same for all the examples that we give. [ABSTRACT FROM AUTHOR]

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°, 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 cm³ with errors of less than 10% in object volume find 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. [ABSTRACT FROM AUTHOR]

A new parameter-free graph-morphology-based segmentation algorithm is proposed to address the problem of partitioning a 3D triangular mesh into disjoint submeshes 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 submeshes such that each submesh contains a set of vertices with similarcurvedness values, and vertices in disjoint submeshes 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. [ABSTRACT FROM AUTHOR]

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 "signal/data" 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. [ABSTRACT FROM AUTHOR]

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 mm-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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Focuses on the combination of minimum entropy image restoration with the frequency-wavenumber (F-K) migration approach to accurately localize subsurface objects using ground-penetrating radar (GPR). Analysis of the GPR operation and the standard F-K migration.

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. In this paper, 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 wellbehaved "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. [ABSTRACT FROM AUTHOR]

Dynamic magnetic resonance imaging (MRI) refers to the acquisition of a sequence of MRI images to monitor temporal changes in tissue structure. In this paper 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. [ABSTRACT FROM AUTHOR]

Introduces a combination of high-dimensional analysis of variance and sequential probability ratio test to detect buried objects from an array ground-penetrating radar. Examples of using the method in different situations; Field data from different radar configurations and test sites; Information on cross-track processing.

Presents information on a study which developed an approach for the problem of reduced-order magnetic resonance imaging (MRI) acquisition. Novel applications of MRI technology; Models; Examples; Summary.

Analyzes the electromagnetic scattering from a three-dimensional (3-D) shallow object buried under a two-dimensional random rough dielectric surface. Significant potential of the steepest descent fast multipole method; Interactions between the rough surface interface and the buried object; Cross section of 3-D object buried under the rough surface ground.

Presents 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 sensor array. Background on the multi, bistatic measurement scheme; Development of a subarray processing method for the detection; Examples; Conclusion.

Describes a low-order polynomial expansion method used in addressing object localization and characterization problems from scattered electric field data. Challenges associated with inverse scattering problems; Formulation of the scattering problem; Algorithms used to solve the inverse scattering problems; Effectiveness of algorithms used through numerical examples.

Presents information on a study focused on an algorithm for detection, localization and characterization of anomalous structures from observations of scattered electromagnetic fields. Overview of the detection methods; Description of the detection algorithm; Examples; Conclusions.

Presents information on a study which presented an efficient, wavelet domain algorithm for computing the error variances associated with a wide class of linear inverse problems posed in a maximum a posteriori (MAP) estimation framework. Problem formulation; Variance extraction of the study; Conclusion.

Presents a T-matrix algorithm for the calculation of the scattered field from a heterogenous collection of spatially separated objects. Basis for the algorithm method; Objects where the algorithm is beneficial to use; Development of a near-field calculation approach.