Breast ultrasound tomography is an emerging imaging modality to reconstruct the sound speed, density, and ultrasound attenuation of the breast in addition to ultrasound reflection/beamforming images for breast cancer detection and characterization. We recently designed and manufactured a new synthetic-aperture breast ultrasound tomography prototype with two parallel transducer arrays consisting of a total of 768 transducer elements. The transducer arrays are translated vertically to scan the breast in a warm water tank from the chest wall/axillary region to the nipple region to acquire ultrasound transmission and reflection data for whole-breast ultrasound tomography imaging. The distance of these two ultrasound transducer arrays is adjustable for scanning breasts with different sizes. We use our breast ultrasound tomography prototype to acquire phantom and in vivo patient ultrasound data to study its feasibility for breast imaging. We apply our recently developed ultrasound imaging and tomography algorithms to ultrasound data acquired using our breast ultrasound tomography system. Our in vivo patient imaging results demonstrate that our breast ultrasound tomography can detect breast lesions shown on clinical ultrasound and mammographic images.

Ultrasound tomography has great potential to provide quantitative estimations of physical properties of breast tumors for accurate characterization of breast cancer. We design and manufacture a new synthetic-aperture breast ultrasound tomography system with two parallel transducer arrays. The distance of these two transducer arrays is adjustable for scanning breasts with different sizes. The ultrasound transducer arrays are translated vertically to scan the entire breast slice by slice and acquires ultrasound transmission and reflection data for whole-breast ultrasound imaging and tomographic reconstructions. We use the system to acquire patient data at the University of New Mexico Hospital for clinical studies. We present some preliminary imaging results of in vivo patient ultrasound data. Our preliminary clinical imaging results show promising of our breast ultrasound tomography system with two parallel transducer arrays for breast cancer imaging and characterization.

Ultrasound transmission tomography usually generates low-resolution breast images. We improve sound-speed reconstructions using ultrasound waveform tomography with both transmission and reflection data. We validate the improvement using computer-generated synthetic-aperture ultrasound transmission and reflection data for numerical breast phantoms. Our tomography results demonstrate that using both transmission and reflection data in ultrasound waveform tomography greatly enhances the resolution and accuracy of tomographic reconstructions compared to ultrasound waveform tomography using either transmission data or reflection data alone. To verify the capability of our novel ultrasound waveform tomography, we design and manufacture a new synthetic-aperture breast ultrasound tomography system with two parallel transducer arrays for clinical studies. The distance of the two transducer arrays is adjustable for accommodating different sizes of the breast. The parallel transducer arrays also allow us to easily scan the axillary region to evaluate the status of axillary lymph nodes and detect breast cancer in the axillary region. However, synthetic-aperture ultrasound reflection data acquired by firing each transducer element sequentially are usually much weaker than transmission data, and have much lower signal-to-noise ratios than the latter. We develop a numerical virtual-point-source method to enhance ultrasound reflection data using synthetic-aperture ultrasound data acquired by firing each transducer element sequentially. Synthetic-aperture ultrasound reflection data for a breast phantom obtained using our numerical virtual-point-source method reveals many coherent ultrasound reflection waveforms that are weak or invisible in the original synthetic-aperture ultrasound data. Ultrasound waveform tomography using both transmission and reflection data together with numerical virtual-point-source method has great potential to produce high-resolution tomographic reconstructions in clinical studies of breast ultrasound tomography.

Imaging breast microcalcifications is crucial for early detection and diagnosis of breast cancer. It is challenging for current clinical ultrasound to image breast microcalcifications. However, new imaging techniques using data acquired with a synthetic-aperture ultrasound system have the potential to significantly improve ultrasound imaging. We recently developed a super-resolution ultrasound imaging method termed the phase-coherent multiple-signal-classification (PC-MUSIC). This signal subspace method accounts for the phase response of transducer elements to improve image resolution. In this paper, we investigate the clinical feasibility of our super-resolution ultrasound imaging method for detecting breast microcalcifications. We use our custom-built, real-time synthetic-aperture ultrasound system to acquire breast ultrasound data for 40 patients whose mammograms show the presence of breast microcalcifications. We apply our super-resolution ultrasound imaging method to the patient data, and produce clear images of breast calcifications. Our super-resolution ultrasound PC-MUSIC imaging with synthetic-aperture ultrasound data can provide a new imaging modality for detecting breast microcalcifications in clinic without using ionizing radiation.

xxx Although the Bayesian approach provides a complete solution to model-based analysis, it is often difficult to obtain closed-form solutions for complex models. However, numerical solutions to Bayesian modeling problems are now becoming attractive because of the advent of powerful, low-cost computers and new algorithms. We describe a general-purpose implementation of the Bayesian methodology on workstations that can deal with complex nonlinear models in a very flexible way. The models are represented by a data-flow diagram that may be manipulated by the analyst through a graphical-programming environment that is based on a fully object-oriented design. Maximum a posteriori solutions are achieved using a general optimization algorithm. A new technique for estimating and visualizing the uncertainties in specific aspects of the model is incorporated.

During the early 90s, I engaged in a productive and enjoyable collaboration with Robert Wagner and his colleague, Kyle Myers. We explored the ramifications of the principle that the quality of an image should be assessed on the basis of how well it facilitates the performance of appropriate visual tasks. We applied this principle to algorithms used to reconstruct scenes from incomplete and/or noisy projection data. For binary visual tasks, we used both the conventional disk detection and a new challenging task, inspired by the Rayleigh resolution criterion, of deciding whether an object was a blurred version of two dots or a bar. The results of human and machine observer tests were summarized with the detectability index based on the area under the ROC curve. We investigated a variety of reconstruction algorithms, including ART, with and without a nonnegativity constraint, and the MEMSYS3 algorithm. We concluded that the performance of the Raleigh task was optimized when the strength of the prior was near MEMSYS's default "classic" value for both human and machine observers. A notable result was that the most-often-used metric of rms error in the reconstruction was not necessarily indicative of the value of a reconstructed image for the purpose of performing visual tasks.

Properly accounting for ultrasound scattering from heterogeneities within the breast is essential for high-resolution ultrasound breast imaging. This requires a reflectivity image reconstruction method capable of accurately handling ultrasound scattering. We develop an optimized ultrasound-wave propagator for reflectivity image reconstruction using pulse-echo ultrasound signals. The method is based on a solution of one-way wave equation and recursive inward continuation of ultrasound wavefields in the frequency-space and frequency-wave number domains using a heterogeneous sound-speed model of the breast obtained from tomography. It minimizes ultrasound phase errors during wavefield inward continuation while maintaining the advantage of high computational efficiency. Pulse-echo ultrasound imaging tests for a numerical breast phantom demonstrate that our optimized method has the potential to improve the reliability and accuracy of ultrasound breast imaging.

Ultrasound reflection imaging is a promising imaging modality for detecting small, early-stage breast cancers. Properly accounting for ultrasound scattering from heterogeneities within the breast is essential for high-resolution and high-quality ultrasound breast imaging. We develop a globally optimized Fourier finite-difference method for ultrasound reflectivity image reconstruction. It utilizes an optimized solution of acoustic-wave equation and a heterogeneous sound-speed distribution of the breast obtained from tomography to reconstruct ultrasound reflectivity images. The method contains a finite-difference term in addition to the split-step Fourier implementation, and minimizes ultrasound phase errors during wavefield inward continuation while maintaining the advantage of high computational efficiency. The accuracy analysis indicates that the optimized method is much more accurate than the split-step Fourier method. The computational efficiency of the optimized method is one to two orders of magnitude faster than time-reversal imaging using a finite-difference time-domain wave-equation scheme. Our new optimized method can accurately handle ultrasound scattering from breast heterogeneities during reflectivity image reconstruction. Our numerical imaging examples demonstrate that the optimized method has the potential to produce high-quality and high-resolution ultrasound reflectivity images in combination with a reliable ultrasound sound-speed tomography method.

We utilize data from Hopkinson-bar experiments and quasi-static compression experiments to characterize uncertainties for parameters governing the Preston-Tonks-Wallace (PTW) [1] plastic deformation model for a variety of materials. This particular plastic deformation model is designed to be valid over a range of input conditions, which include strain, strain rate and temperature. However, because of variations between experimental samples, measurement variation, as well as slight inadequacies in the model, no single parameter setting gives a good match to all of the experimental data for a given material. These deficiencies need to be taken into account when assessing the uncertainties in the model parameters. In this paper, we use a Bayesian hierarchical model to account for the variations in the experimental data. This modeling approach results in parameter estimates for each material, along with uncertainty estimates, which are the main focus of this paper. The results are summarized in the table below. Parameter Al Be DU Ta U-6Nb θ 0.0364 0.0268 0.0465 0.0124 0.0974 (0.011) (0.00756) (0.0219) (0.00558) (0.0497) κ 0.415 0.197 0.136 0.711 0.503 (0.137) (0.112) (0.064) (0.156) (0.113) −log(γ) 10.3 11.2 14.7 11.5 6.32 (4.0) (5.74) (3.03) (1.77) (4.16) y0 0.0113 0.00165 0.00534 0.00939 0.00665 (0.00323) (0.000248) (0.000766) (0.00129) (0.00351) y∞ 0.0058 0.000938 0.00236 0.00136 0.000724 (0.000239) (0.000283) (0.000934) (0.00028) (0.000522) s0 0.0295 0.0169 0.0123 0.0168 0.0707 (0.0118) (0.00978) (0.00327) (0.00554) (0.0228) s∞ 0.00781 0.00337 0.00485 0.00295 0.00646 (0.000411) (0.00148) (0.00165) (0.00062) (0.000495)

Least-squares data analysis is based on the assumption that the normal (Gaussian) distribution appropriately characterizes the likelihood, that is, the conditional probability of each measurement d, given ameasured quantity y, p(d/y). On the other hand, there is ample evidence in nuclear physics of significant disagreements among measurements, which are inconsistent with the normal distribution, given their stated uncertainties. In this study the histories of 99 measurements of the lifetimes of five elementary particles are examined to determine what can be inferred about the distribution of their values relative to their stated uncertainties. Taken as a whole, the variations in die data are somewhat larger than their quoted uncertainties would indicate. These data strongly support using a Student t distribution for the likelihood function instead of a normal. The most probable value for the order of the t distribution is 2.6 +/- 0.9. It is shown that analyses based on long-tailed t-distribution likelihoods gracefully cope with outlying data.

Purpose: To improve resolution and reduce speckle in ultrasound breast images by accounting for ultrasound scattering from breast heterogeneities during reflectivityimage reconstruction.Method and Materials: X‐ray mammography often fails to detect cancers in dense breasts, while breast ultrasound has the potential to detect them. Breast heterogeneities, particularly in dense breasts, generate significant ultrasound scattering. Properly handling ultrasound scattering is critical for reliable cancer detection and diagnosis in dense breasts. Ultrasoundwave propagation in the breast is governed by the acoustic‐wave equation in heterogeneous media, which can be decomposed into two one‐way wave equations describing wave propagation in opposite directions. A split‐step Fourier solution of a one‐way wave equation is used for backpropagation of reflected ultrasoundwaves. The backpropagation consists of two steps: one phase‐shift step in the frequency‐wavenumber domain, and another phaseshift step in the frequency‐space domain. During the backpropagation of ultrasound wavefields, heterogeneous breast sound‐speed models obtained from transmission ultrasound tomography are used to approximately account for ultrasoundwavescattering. The reflectivityimaging method based on the split‐step Fourier propagator is applied to computer‐generated ultrasound data and in‐vivo ultrasound breast data acquired using a ring transducer array. The ultrasoundimages are compared with those obtained using a uniform sound‐speed model.Results: Comparison of ultrasoundreflectivityimages obtained using heterogeneous breast sound‐speed models with those obtained with a uniform model shows that ultrasound scattering of breast heterogeneities needs to be taken into account to obtain high‐resolution and high‐quality breast images.Conclusion: Using heterogeneous sound‐speed models for ultrasoundwave backpropagation during reflectivityimage reconstruction significantly improves image resolution and reduces speckle. The resolution and quality of ultrasoundreflectivityimages are further enhanced with increasing accuracy and resolution of transmission ultrasound tomography.

By drawing an analogy between the logarithm of a probability distribution and a physical potential, it is natural to ask the question, "what is the effect of applying an external force on model parameters?" In Bayesian inference, parameters are frequently estimated as those that maximize the posterior, yielding the maximum a posteriori (MAP) solution, which corresponds to minimizing phi = -log(posterior). The uncertainty in the estimated parameters is typically summarized by the covariance matrix for the posterior distribution, C. I describe a novel approach to estimating specified elements of C in which one adds to phi a term proportional to a force, f, that is hypothetically applied to the parameters. After minimizing the augmented phi, the change in the parameters is proportional to Cf. By selecting the appropriate force, the analyst can estimate the variance in a quantity of special interest, as well as its covariance relative to other quantities. This technique allows one to replace a stochastic MCMC calculation with a deterministic optimization procedure. The usefulness of this technique is demonstrated with a few simple examples, as well as a more complicated one, namely, the uncertainty in edge localization in a tomographic reconstruction of an object's boundary from two projections.

We present an approach to uncertainty quantification for nuclear applications that combines the covariance evaluation of differential cross-section data and the error propagation from matching a criticality experiment using a neutron-transport calculation. We have studied the reduction in uncertainty of Pu-239 fission cross sections by using a one-dimensional neutron-transport calculation with the PARTISN code. The evaluation of (239)pu differential cross-section data is combined with a criticality measurement (Jezebel) using a Bayesian method. To quantify the uncertainty in such calculations, we generate a set of random samples of the cross sections, which represents the covariance matrix, and estimate the distribution of calculated quantities, such as criticality. We show that inclusion of the Jezebel data reduces uncertainties in estimating neutron multiplicity.

The evaluation of neutron cross sections as a function of energy is fraught with inconsistent measurements. I describe a Bayesian approach to deal with the inconsistencies by probabilistically modeling the possibility of discrepant data and data sets with long‐tailed likelihood functions. Systematic normalization uncertainties in each data set are included by considering the normalization to be a variable with specified uncertainty. By characterizing its uncertainty with a mixture of Cauchy and Gaussian distributions, data sets that disagree with the majority of others are given less weight in terms of normalization, but still provide useful information about the energy dependency of the cross sections. I demonstrate the approach with data sets of neutron fission cross sections for americium 243. Samples from the posterior obtained with the Markov Chain Monte Carlo technique are used to estimate the posterior mean and standard error.

We present an approach to uncertainty quantification for nuclear applications, which combines the covariance evaluation of differential cross-sections data and the error propagation from matching a criticality experiment using a neutron-transport calculation. We have studied the reduction in uncertainty of Pu fission cross sections by using a one-dimensional neutron-transport calculation with the PARTISN code. The evaluation of Pu differential cross-section data is combined with a criticality measurement (Jezebel) using a Bayesian method. To quantify the uncertainty in such calculations, we generate a set of random samples of the cross sections, which represents the covariance matrix, and estimate the distribution of calculated quantities, such as criticality. We show that inclusion of the Jezebel data reduces uncertainties in estimating neutron multiplicity.