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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.

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.

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 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.

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.

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.