Thomas Robins

Bayesian methods are a popular research direction for inverse problems. There are a variety of techniques available to solve Bayes’ equation, each with their own strengths and limitations. Here, we discuss stochastic variational inference (SVI), which solves Bayes’ equation using gradient-based methods. This is important for applications which are time-limited (e.g. medical tomography) or where solving the forward problem is expensive (e.g. adjoint methods). To evaluate the use of SVI in both these contexts, we apply it to ultrasound tomography of the brain using full-waveform inversion (FWI). FWI is a computationally expensive adjoint method for solving the ultrasound tomography inverse problem, and we demonstrate that SVI can be used to find a no-cost estimate of the pixel-wise variance of the sound-speed distribution using a mean-field Gaussian approximation. In other words, we show experimentally that it is possible to estimate the pixel-wise uncertainty of the sound-speed reconstruction using SVI and a common approximation which is already implicit in other types of iterative reconstruction. Uncertainty estimates have a variety of uses in adjoint methods and tomography. As an illustrative example, we focus on the use of uncertainty for image quality assessment. This application is not limiting; our variance estimator has effectively no computational cost and we expect that it will have applications in fields such as non-destructive testing or aircraft component design where uncertainties may not be routinely estimated.

Ultrasound computed tomography techniques have the potential to provide clinicians with 3-D, quantitative and high-resolution information of both soft and hard tissues such as the breast or the adult human brain. Their practical application requires accurate modeling of the acquisition setup: the spatial location, orientation, and impulse response (IR) of each ultrasound transducer. However, the existing calibration methods fail to accurately characterize these transducers unless their size can be considered negligible when compared with the dominant wavelength, which reduces signal-to-noise ratios below usable levels in the presence of high-contrast tissues such as the skull. In this article, we introduce a methodology that can simultaneously estimate the location, orientation, and IR of the ultrasound transducers in a single calibration. We do this by extending spatial response identification (SRI), an algorithm that we have recently proposed to estimate transducer IRs. Our proposed methodology replaces the transducers in the acquisition device with a surrogate model whose effective response matches the experimental data by fitting a numerical model of wave propagation. This results in a flexible and robust calibration procedure that can accurately predict the behavior of the ultrasound acquisition device without ever having to know where the real transducers are or their individual IR. Experimental results using a ring acquisition system show that SRI produces calibrations of significantly higher quality than standard methodologies across all transducers, both in transmission and in reception. Experimental full-waveform inversion (FWI) reconstructions of a tissue-mimicking phantom demonstrate that SRI generates more accurate reconstructions than those produced with standard calibration techniques.

Ultrasound breast imaging is a promising alternative to conventional mammography because it does not expose women to harmful ionising radiation and it can successfully image dense breast tissue. However, conventional ultrasound imaging only provides morphological information with limited diagnostic value. Ultrasound computed tomography (USCT) uses energy in both transmission and reflection when imaging the breast to provide more diagnostically relevant quantitative tissue properties, but it is often based on time-of-flight tomography or similar ray approximations of the wave equation, resulting in reconstructed images with low resolution. Full-waveform inversion (FWI) is based on a more accurate approximation of wave-propagation phenomena and can consequently produce very high resolution images using frequencies below 1 megahertz. These low frequencies, however, are not available in most USCT acquisition systems, as they use transducers with central frequencies well above those required in FWI. To circumvent this problem, we designed, trained, and implemented a two-dimensional convolutional neural network to artificially generate missing low frequencies in USCT data. Our results show that FWI reconstructions using experiment data after the application of the proposed method successfully converged, showing good agreement with X-ray CT and reflection ultrasound-tomography images.

Environmental Health Perspectives is an Open Access journal published by the National Institute of Environmental Health Sciences. Environmental Health Perspectives is an Open Access journal published by the National Institute of Environmental Health Sciences.

Environmental Health Perspectives is an Open Access journal published by the National Institute of Environmental Health Sciences. Environmental Health Perspectives is an Open Access journal published by the National Institute of Environmental Health Sciences.