Summary: Separation of Scales in Elasticity Imaging: A Numerical
In magnetic resonance elastography, one seeks to reconstruct the shear modulus
from measurements of the displacement field in the whole body. In this paper, we
present an optimization approach which solves the problem by simply minimizing a dis-
crepancy functional. In order to recover a complex anomaly in a homogenous medium,
we first observe that the information contained in the wavefield should be decomposed
into two parts, a "near-field" part in the region around the anomaly and a "far-field"
part in the region away from the anomaly. As will be justified both theoretically and
numerically, separating these scales provides a local and precise reconstruction.
Extensive work has been carried out in the past decade to image the elastic properties
of human soft tissues by inducing motion. This broad field, called elasticity imaging or
elastography, is based on the initial idea that shear elasticity can be correlated with the
pathology of tissues.
There are several techniques that can be classified according to the type of mechanical