  In this paper, we propose Plane Wave Elastography (PWE), a novel ultrasound
shear wave elastography (SWE) approach. Currently, commercial methods for SWE
rely on directional filtering based on the prior knowledge of the wave
propagation direction, to remove complicated wave patterns formed due to
reflection and refraction. The result is a set of decomposed directional waves
that are separately analyzed to construct shear modulus fields that are then
combined through compounding. Instead, PWE relies on a rigorous representation
of the wave propagation using the frequency-domain scalar wave equation to
automatically select appropriate propagation directions and simultaneously
reconstruct shear modulus fields. Specifically, assuming a homogeneous,
isotropic, incompressible, linear-elastic medium, we represent the solution of
the wave equation using a linear combination of plane waves propagating in
arbitrary directions. Given this closed-form solution, we formulate the SWE
problem as a nonlinear least-squares optimization problem which can be solved
very efficiently. Through numerous phantom studies, we show that PWE can handle
complicated waveforms without prior filtering and is competitive with
state-of-the-art that requires prior filtering based on the knowledge of
propagation directions.
