Waveform inversion is a promising method for ultrasound computed tomography able to produce high-resolution images of human breast tissue. However, the computational complexity of waveform inversion remains a considerable challenge, and the costs per iteration are proportional to the number of emitting transducers. We propose a twofold strategy to accelerate the time-to-solution by identifying the optimal number and location of emitters using sequential optimal experimental design (SOED). SOED is a powerful tool to iteratively add the most informative transducer or remove redundant measurements, respectively. This approach simultaneously provides optimized transducer configurations and a cost-benefit curve that quantifies the information gain versus the computational cost.<p> </p>First, we propose a method to identify the emitters that provide reconstructions with minimal expected uncertainties. Using a Bayesian approach, model uncertainties and resolution can be quantified with the trace of the posterior covariance. By linearizing the wave equation, we can compute the posterior covariance using the inverse of the Gauss-Newton approximation of the Hessian. Furthermore, this posterior is independent of the breast model and the experimental data, thus enabling pre-acquisition experimental optimization. Then, for the post-acquisition inversion, we present an approach to select a subsample of sources that accurately approximates the full gradient direction in each iteration. We control the convergence of the angular differences between consecutive gradient directions by randomly adding new emitters into the subsample.<p> </p>We present synthetic studies in 2D and 3D that consider a ring-shaped and a semi-ellipsoidal scanning device, respectively. Numerical results suggest that the provided methods have the potential to identify redundancies from the corresponding cost-benefit curves. Furthermore, the gradient direction rapidly converges to the direction of the full gradient, which appears to be independent of the model and the emitter locations.
Waveform inversion for ultrasound computed tomography (USCT) is a promising imaging technique for breast cancer screening. However, the improved spatial resolution and the ability to constrain multiple parameters simultaneously demand substantial computational resources for the recurring simulations of the wave equation. Hence, it is crucial to use fast and accurate methods for numerical wave propagation, on the one hand, and to keep the number of required simulations as small as possible, on the other hand. We present an efficient strategy for acoustic waveform inversion that combines (i) a spectral-element continuous Galerkin method for solving the wave equation, (ii) conforming hexahedral mesh generation to discretize the scanning device, (iii) a randomized descent method based on mini-batches to reduce the computational cost for misfit and gradient computations, and (iv) a trust-region method using a quasi-Newton approximation of the Hessian to iteratively solve the inverse problem. This approach combines ideas and state-of-the-art methods from global-scale seismology, large-scale nonlinear optimization, and machine learning. Numerical examples for a synthetic phantom demonstrate the efficiency of the discretization, the effectiveness of the mini-batch approximation and the robustness of the trust-region method to reconstruct the acoustic properties of breast tissue with partial information.
We present methods to optimize the setup of a 3D ultrasound tomography scanner for breast cancer detection. This approach provides a systematic and quantitative tool to evaluate different designs and to optimize the con- figuration with respect to predefined design parameters. We consider both, time-of-flight inversion using straight rays and time-domain waveform inversion governed by the acoustic wave equation for imaging the sound speed. In order to compare different designs, we measure their quality by extracting properties from the Hessian operator of the time-of-flight or waveform differences defined in the inverse problem, i.e., the second derivatives with respect to the sound speed. Spatial uncertainties and resolution can be related to the eigenvalues of the Hessian, which provide a good indication of the information contained in the data that is acquired with a given design. However, the complete spectrum is often prohibitively expensive to compute, thus suitable approximations have to be developed and analyzed. We use the trace of the Hessian operator as design criterion, which is equivalent to the sum of all eigenvalues and requires less computational effort. In addition, we suggest to take advantage of the spatial symmetry to extrapolate the 3D experimental design from a set of 2D configurations. In order to maximize the quality criterion, we use a genetic algorithm to explore the space of possible design configurations. Numerical results show that the proposed strategies are capable of improving an initial configuration with uniformly distributed transducers, clustering them around regions with poor illumination and improving the ray coverage of the domain of interest.
Ultrasound tomography is a modality that can be used to image various characteristics of the breast, such as sound speed, attenuation, and reflectivity. In the considered setup, the breast is immersed in water and scanned along the coronal axis from the chest wall to the nipple region. To improve image visualization, it is desirable to remove the water background. To this end, the 3D boundary of the breast must be accurately estimated. We present an iterative algorithm based on active contours that automatically detects the boundary of a breast using a 3D stack of attenuation images obtained from an ultrasound tomography scanner. We build upon an existing method to design an algorithm that is fast, fully automated, and reliable. We demonstrate the effectiveness of the proposed technique using clinical data sets.
For women with dense breast tissue, who are at much higher risk for developing breast cancer, the performance of mammography is at its worst. Consequently, many early cancers go undetected when they are the most treatable. Improved cancer detection for women with dense breasts would decrease the proportion of breast cancers diagnosed at later stages, which would significantly lower the mortality rate. The emergence of whole breast ultrasound provides good performance for women with dense breast tissue, and may eliminate the current trade-off between the cost effectiveness of mammography and the imaging performance of more expensive systems such as magnetic resonance imaging. We report on the performance of SoftVue, a whole breast ultrasound imaging system, based on the principles of ultrasound tomography. SoftVue was developed by Delphinus Medical Technologies and builds on an early prototype developed at the Karmanos Cancer Institute. We present results from preliminary testing of the SoftVue system, performed both in the lab and in the clinic. These tests aimed to validate the expected improvements in image performance. Initial qualitative analyses showed major improvements in image quality, thereby validating the new imaging system design. Specifically, SoftVue’s imaging performance was consistent across all breast density categories and had much better resolution and contrast. The implications of these results for clinical breast imaging are discussed and future work is described.
Photoacoustic tomography (PAT) is a hybrid imaging method, which combines ultrasonic and optical imaging modalities, in order to overcome their respective weaknesses and to combine their strengths. It is based on the reconstruction of optical absorption properties of the tissue from the measurements of a photoacoustically generated pressure field. Current methods consider laser excitation, under thermal and stress confinement assumptions, which leads to the generation of a propagating pressure field. Conventional reconstruction tech niques then recover the initial pressure field based on the boundary measurements by iterative reconstruction algorithms in time- or Fourier-domain. Here, we propose an application of a new sensing principle that allows for efficient and non-iterative reconstruction algorithm for imaging point absorbers in PAT. We consider a closed volume surrounded by a measurement surface in an acoustically homogeneous medium and we aim at recovering the positions and the amount of heat absorbed by these absorbers. We propose a two-step algorithm based on proper choice of so-called sensing functions. Specifically, in the first step, we extract the projected positions on the complex plane and the weights by a sensing function that is well-localized on the same plane. In the second step, we recover the remaining z-location by choosing a proper set of plane waves. We show that the proposed families of sensing functions are sufficient to recover the parameters of the unknown sources without any discretization of the domain. We extend the method for sources that have joint-sparsity; i.e., the absorbers have the same positions for different frequencies. We evaluate the performance of the proposed algorithm using simulated and noisy sensor data and we demonstrate the improvement obtained by exploiting joint sparsity.
We study the use and impact of a dictionary in a tomographic reconstruction setup. First, we build two different
dictionaries: one using a set of bases functions (Discrete Cosine Transform), and the other that is learned using
patches extracted from training images, similar to the image that we would like to reconstruct. We use K-SVD as
the learning algorithm. These dictionaries being local, we convert them to global dictionaries, ready to be applied
on whole images, by generating all possible shifts of each atom across the image. During the reconstruction, we
minimize the reconstruction error by performing a gradient descent on the image representation in the dictionary
space. Our experiments show promising results, allowing to eliminate standard artifacts in the tomographic
reconstruction, and to reduce the number of measurements required for the inversion. However, the quality of
the results depends on the convergence of the learning process, and on the parameters of the dictionaries (number
of atoms, convergence criterion, atom size, etc.). The exact influence of each of these remains to be studied.
Analytic sensing has recently been proposed for source localization from boundary measurements using a generalization
of the finite-rate-of-innovation framework. The method is tailored to the quasi-static electromagnetic
approximation, which is commonly used in electroencephalography. In this work, we extend analytic sensing
for physical systems that are governed by the wave equation; i.e., the sources emit signals that travel as waves
through the volume and that are measured at the boundary over time. This source localization problem is highly
ill-posed (i.e., the unicity of the source distribution is not guaranteed) and additional assumptions about the
sources are needed. We assume that the sources can be described with finite number of parameters, particularly,
we consider point sources that are characterized by their position and strength. This assumption makes
the solution unique and turns the problem into parametric estimation. Following the framework of analytic
sensing, we propose a two-step method. In the first step, we extend the reciprocity gap functional concept to
wave-equation based test functions; i.e., well-chosen test functions can relate the boundary measurements to
generalized measure that contain volumetric information about the sources within the domain. In the second
step-again due to the choice of the test functions - we can apply the finite-rate-of-innovation principle; i.e., the
generalized samples can be annihilated by a known filter, thus turning the non-linear source localization problem
into an equivalent root-finding one. We demonstrate the feasibility of our technique for a 3-D spherical geometry.
The performance of the reconstruction algorithm is evaluated in the presence of noise and compared with the
theoretical limit given by Cramer-Rao lower bounds.
Accurate calibration is a requirement of many array signal processing techniques. We investigate the calibration
of a transducer array using time delays. We derive a strategy based on the mean square error criterion and
discuss how time delays that are not available can be interpolated from existing ones. The proposed method is
made robust to noise and model mismatch by means of a novel iterative technique for distance matrix denoising.
The convergence of the method is proved. Finally, the accuracy of the proposed calibration algorithm is assessed
both in simulated scenarios and using experimental data obtained from an ultrasound scanner designed for breast
We present a bent ray reconstruction algorithm for an ultrasound tomography (UT) scanner designed for breast
screening. The scanner consists of a circular array of transmitters and receivers which encloses the object to be
imaged. By solving a nonlinear system of equations, the reconstruction algorithm estimates the sound speed of
the object using the set of travel-time measurements. The main difficulty in this inverse problem is to ensure the
convergence and robustness to noise. In this paper, we propose a gradient method to find a solution for which
the corresponding travel-times are closest to the measured travel-times in the least squares sense. To this end,
first the gradient of the cost function is derived using Fermat's Principle. Then, the iterative nonlinear conjugate
gradient algorithm solves the minimization problem. This is combined with the backtracking line search method
to efficiently find the step size in each iteration. This approach is guaranteed to converge to a local minimum
of the cost function where the convergence point depends on the initial guess. Moreover, the method has the
potential to easily incorporate regularity constraints such as sparsity as a priori information on the model. The method is tested both numerically and using in vivo data obtained from a UT scanner. The results confirm the stability and robustness of our approach for breast screening applications.
We present preliminary results obtained using a time domain wave-based reconstruction algorithm for an ultrasound
transmission tomography scanner with a circular geometry. While a comprehensive description of this type of algorithm has already been given elsewhere, the focus of this work is on some practical issues arising with this approach. In fact, wave-based reconstruction methods suffer from two major drawbacks which limit their application in a practical setting: convergence is difficult to obtain and the computational cost is prohibitive. We address the first problem by appropriate initialization using a ray-based reconstruction. Then, the complexity of the method is reduced by means of an efficient parallel implementation on graphical processing units (GPU). We provide a mathematical derivation of the wave-based method under consideration, describe some details of our implementation and present simulation results obtained with a numerical phantom designed for a breast cancer detection application. The source code of our GPU implementation is freely available on the web at www.usense.org.
A major limitation of thermal therapies is the lack of detailed thermal information needed to monitor the
therapy. Temperatures are routinely measured invasively with thermocouples, but only sparse measurements
can be made. Ultrasound tomography is an attractive modality for temperature monitoring because it is noninvasive,
non-ionizing, convenient and inexpensive. It capitalizes on the fact that the changes in temperature
cause the changes in sound speed. In this work we investigate the possibility of monitoring large temperature
changes, in the interval from body temperature to -40°C. The ability to estimate temperature in this interval is
of a great importance in cryosurgery, where freezing is used to destroy abnormal tissue. In our experiment, we
freeze locally a tissue-mimicking phantom using a combination of one, two or three cryoprobes. The estimation of
sound speed is a difficult task because, first, the sound is highly attenuated when traversing the frozen tissue; and
second, the sound speed to be reconstructed has a high spatial bandwidth, due to the dramatic change in speed
between the frozen and unfrozen tissue. We show that the first problem can be overcome using a beamforming
technique. As the classical reconstruction algorithms inherently smooth the reconstruction, we propose to solve
the second problem by applying reconstruction techniques based on sparsity.