High resolution 3D ultrasonic breast imaging by time-domain full waveform inversion

Abstract

Ultrasound tomography (UST) scanners allow quantitative images of the human breast's acoustic properties to be derived with potential applications in screening, diagnosis and therapy planning. Time domain full waveform inversion (TD-FWI) is a promising UST image formation technique that fits the parameter fields of a wave physics model by gradient-based optimization. For high resolution 3D UST, it holds three key challenges: Firstly, its central building block, the computation of the gradient for a single US measurement, has a restrictively large memory footprint. Secondly, this building block needs to be computed for each of the 103-104 measurements, resulting in a massive parallel computation usually performed on large computational clusters for days. Lastly, the structure of the underlying optimization problem may result in slow progression of the solver and convergence to a local minimum. In this work, we design and evaluate a comprehensive computational strategy to overcome these challenges: Firstly, we exploit a gradient computation based on time reversal that dramatically reduces the memory footprint at the expense of one additional wave simulation per source. Secondly, we break the dependence on the number of measurements by using source encoding (SE) to compute stochastic gradient estimates. Also we describe a more accurate, TD-specific SE technique with a finer variance control and use a state-of-the-art stochastic LBFGS method. Lastly, we design an efficient TD multi-grid scheme together with preconditioning to speed up the convergence while avoiding local minima. All components are evaluated in extensive numerical proof-of-concept studies simulating a bowl-shaped 3D UST breast scanner prototype. Finally, we demonstrate that their combination allows us to obtain an accurate 442x442x222 voxel image with a resolution of 0.5mm using Matlab on a single GPU within 24 hours.

Ray-based inversion accounting for scattering for biomedical ultrasound computed tomography

“…Arguably, the choice of model that will achieve the most accurate results is the model that describes the physics of acoustic propagation most accurately. For this reason, there has been great interest recently in using so-called full-wave models that explicitly model the acoustic wave equation for heterogenous media [60,61,62,22,63,66,67]. As expected, these approaches have been shown to provide accurate and high resolution images, but a significant hurdle to the practical applicability of these is that the full-wave solvers are compute intensive.…”

“…Note that replacing the Hessian with the identity in the above equation will give the steepest descent search direction, which is equivalent to taking a first-order optimisation approach, in which the nonlinear objective function (38) is minimised using a search direction which uses only the information included in the gradient term in (41). First-order approaches [5] are currently in widespread use for full-wave inversion [60,61,62,63,67], because they do not require the additional expense of computing the Hessian. Here, however, the use of a second-order minimisation is the key to incorporating the effects of scattering in the inversion.…”

“…This paper is concerned with the latter challenge, image reconstruction. Approaches to UST reconstruction can be classified by (1) whether the inversion is linearised or nonlinear, (2) the nature of the forward model used, and (3) the data type used in the inversion. In terms of the data used, there are broadly two categories.…”

“…when the numerical model accurately represents the measurement scenario, these approaches have the potential to reconstruct accurate, high resolution images. This approach, for which there is a considerable literature in the seismic community [1], has begun to be explored in earnest for medical applications [20,60,59,61,62,21,63,66,64,67]. Full-wave approaches are discussed further in Sec.…”

Accurate and Robust Deep Learning Framework for Solving Wave-Based Inverse Problems in the Super-Resolution Regime

“…This exacerbates the already prohibitively expensive computational cost of these algorithms which require state-of-the-art computer clusters to even process the field data. Evidently, applications requiring real time reconstructions, such as biomedical imaging, radar, continuous monitoring for CO 2 sequestration and geothermal energy, etc, remain beyond the reach of such algorithms [41].…”