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A fast method is described for computing the acoustic field of ultrasound transducers with application to rectangular elements that are cylindrically focused. The efficiency is gained by using a separable approximation to the Green's function and the tradeoff between accuracy and spatial sampling rate is analyzed for determining appropriate parameters for a specific transducer.

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 (S[O.sub.2]) from 68 breast measurements are 16.2 [micro]m 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 [+ or -] 6.1 [micro]m for fibroglandular tissue, 15.4 [+ or -] 5.0 [micro]m for adipose, and 22.2 [+ or -] 7.3 [micro]m 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 mammographicai 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. Index Terms--Breast imaging, multimodality imaging, tomograhy.

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 Cramer-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 ad-joint 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.sup.-1] and a volume of 4.82 [cm.sup.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. Index Terms--optical tomography, image reconstruction, inverse problems, shape-based imaging.

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. Index Terms--Bounded-data uncertainty, dynamic programming, electromagnetic induction (EMI), min--max optimization, object classification, parameter estimation, positional uncertainty, subsurface sensing.

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. Index Terms--B-splines, dispersive media, ground-penetrating radar (GPR), inversion methods, nonlinear optimization, rough surface, subsurface sensing.

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. Index Terms--Breast cancer imaging, electromagnetic scattering, shape reconstruction problems, steepest descent gradient method.

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. Index Terms--Fast algorithms, inverse scattering, optimization techniques, profile reconstruction, rough surface scattering.

Optimized versions of frequency-wavenumber (F-K) migration methods are introduced to better focus ground-penetrating radar {{;PR} 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. Index Terms--Complex-velocity frequency-wavenumber (F-K) migration, dispersive medium, frequency-wavenumber (F-K) migration, minimum entropy optimization, Tikhonov regularization, varimax norm.

The problem of how to locate an object in an image when size and rotation are not known is investigated and discussed.

An approach is proposed for estimating dynamic magnetic resonance imaging (MRI) sequences. The approach is based on two complimentary strategies: an adaptive framework for estimating the MRI images themselves; and an adaptive technique for tailoring MRI system excitations for each data acquisition.

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. Index Terms--Analysis of variance (ANOVA), array signal processing, GPR mine detection, sequential detection, transient signal analysis.

We address the problem of optimally choosing the conductivity ([Sigma]) profile of a perfectly-matched-layer absorbing boundary condition (PML ABC) with prescribed number of layers so as to minimize reflections for a wide range of incidence angles and for a narrow (CW) or broad frequency-band. A new one-dimensional (1-D), frequency-domain description of 2-D PML performance is developed, validated and used in PML-[Sigma] profile optimization. An exhaustive search for PML-[Sigma] profiles that minimize reflections over a prescribed wide angle-range is carried out. Our procedure yields PML-[Sigma] profiles with better performance than previously reported values, for given number of layers. Index Terms - Perfectly-matched-layer (PML).

An efficient, wavelet domain algorithm for the calculation of error variance information for a wide class of linear inverse problems posed in a maximum a posteriori estimation framework has been developed. The algorithm is based on the permutation and partitioning of the Fisher information matrix to maximize a diagonal dominance criterion. It was shown that this diagonal approximation allows for the accurate recovery of the error variances.

We present an efficient, stable, recursive T-matrix algorithm to calculate the scattered field from a heterogeneous collection of spatially separated objects. The algorithm is based on the use of higher order multipole expansions than those typically employed in recursive T-matrix techniques. The use of these expansions introduces instability in the recursions developed in [5] and [6], specifically in the case of near-field computations. By modifying the original recursive algorithm to avoid these instabilities, we arrive at a flexible and efficient forward solver appropriate for a variety of scattering calculations. The algorithm can be applied when the objects are dielectric, metallic, or a mixture of both. We verify this method for cases where the scatterers are electrically small (fraction of a wavelength) or relatively large (12[Lambda]). While developed for near-field calculation, this approach is applicable for far-field problems as well. Finally, we demonstrate that the computational complexity of this approach compares favorably with comparable recursive algorithms. Index Terms - Elecromagnetic scattering.

The application of multiscale and stochastic techniques to the solution of a linearized inverse scattering problem is presented. This approach allows for the explicit and easy handling of many difficulties associated with problems of this type. Regularization is accomplished via the use of a multiscale prior stochastic model which offers considerable flexibility for the incorporation of prior knowledge and constraints. We use the relative error covariance matrix (RECM), introduced in [28], as a tool for quantitatively evaluating the manner in which data contribute to the structure of a reconstruction. Given a set of scattering experiments, the RECM is used for understanding and analyzing the process of data fusion and allows us to define the space-varying optimal scale for reconstruction as a function of the nature (resolution, quality, and distribution of observation points) of the available measurement sets. Examples of our multiscale inversion algorithm are presented using the Born approximation of an inverse electrical conductivity problem formulated so as to illustrate many of the features associated with inverse scattering problems arising in fields such as geophysical prospecting and medical imaging.

An adaptive two-pass rank order filter to remove impulse noises in highly corrupt images is presented. The working process of this adaptive filter based on the standard median filter, center-weighted median filter (CWMF), adaptive weighted median filter, lower-upper-middle (LUM) filter and soft-decision rank-order-mean (SD-ROM) filter, by analyzing the spatial distribution of estimated impulse noise is discussed.

The electromagnetic scattering from a three-dimensional (3-D) shallow object buried under a two-dimensional (2-D) random rough dielectric surface is analyzed in this work. 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 in this work. 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 buried anti-personnel mine. Significant polarization dependency is observed for the PEC object signature compared with that of the penetrable object, which can be used in target discrimination. Moreover, fields scattered above the rough ground experience significantly more distortion than fields transmitted into the ground. Index Terms--Buried-target, computational electromagnetics, fast multipole method (FMM), mine detection, rough surface scattering.

In this paper, we 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 DOA's, a set of crossings, condensed around expected object locations, are obtained. To process this spatial crossing pattern, we 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, we demonstrate the usefulness and performance of this approach for typical background electrical properties and signal to noise ratios. Index Terms--Array processing, hypothesis testing, subsurface object detection.

The problem of characterizing the geometric structure of an object buried in an inhomogeneous halfspace of unknown composition is considered. We develop a nonlinear inverse scattering algorithm based on a low-dimensional parameterization of the unknown object and the background. In particular, we 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. We 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. We demonstrate the performance of our approach via extensive numerical simulation involving two-dimensional (2-D), [TM.sub.z] scattering geometries. Our results indicate a strong ability to localize and estimate the shape of the object even in the presence of an unknown and inhomogeneous background. Index Terms--B-splines, clutter models, inverse scattering, mine detection, shape-based methods.

Research into the problem of reduced-order magnetic resonance imaging (MRI) acquisition is presented. It was possible to develop a problem formulation, linked analysis, and a computational technique to identify a set of excitation and reconstruction vectors for efficient MRI acquisition of an arbitrarily shaped region of interest.

An algorithm for the detection, localization and characterization of anomalous structures in a region that has scattered radiation along its boundary was developed based on a full nonlinear scattering model. Part of the algorithm is a method for incorporating prior geometric information associated to the anomaly detection problem. Experimental results showed that the algorithm is capable of obtaining high detection and low false alarm rates even in very noisy environments.