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We utilize Full Waveform Inversion (FWI) framework to convert shear wave elastography (SWE) measurements on multiple planes to a single three-dimensional (3D) image of elasticity using gradient optimization to adjust the elasticity map until the mismatch between simulated and measured particle velocities is minimized. Several ideas are brought together to ensure the robustness and effectiveness of the proposed FWI: correlation-based matching between measurements and simulation, high-fidelity finite element simulation of 3D shear waves in incompressible elastic media, multi-resolution parametrization to help with convergence, multi-frequency continuation for finer resolution imaging, and multi-push illumination. With the help of in silico and phantom validation studies, the algorithm is shown to be effective in providing images outside the measurement plane, including reconstructing full 3D images from 2D. 

Abstract Objective. With the ultimate goal of reconstructing 3D elasticity maps from ultrasound particle velocity measurements in a plane, we present in this paper a methodology of inverting for 2D elasticity maps from measurements on a single line.Approach. The inversion approach is based on gradient optimization where the elasticity map is iteratively modified until a good match is obtained between simulated and measured responses. Full-wave simulation is used as the underlying forward model to accurately capture the physics of shear wave propagation and scattering in heterogeneous soft tissue. A key aspect of the proposed inversion approach is a cost functional based on correlation between measured and simulated responses.Main results. We illustrate that the correlation-based functional has better convexity and convergence properties compared to the traditional least-squares functional, and is less sensitive to initial guess, robust against noisy measurements and other errors that are common in ultrasound elastography. Inversion with synthetic data illustrates the effectiveness of the method to characterize homogeneous inclusions as well as elasticity map of the entire region of interest.Significance. The proposed ideas lead to a new framework for shear wave elastography that shows promise in obtaining accurate maps of shear modulus using shear wave elastography data obtained from standard clinical scanners. 

Based on a recently developed approximate wave-equation solver, we have developed a methodology to reduce the computational cost of seismic migration in the frequency domain. This approach divides the domain of interest into smaller subdomains, and the wavefield is computed using a sequential process to determine the downward- and upward-propagating wavefields — hence called a double-sweeping solver. A sequential process becomes possible using a special approximation of the interface conditions between subdomains. This method is incorporated into the least-squares migration framework as an approximate solver. The associated computational effort is comparable to one-way wave-equation approaches, yet, as illustrated by the numerical examples, the accuracy and convergence behavior are comparable to that of the full-wave equation.