Separation of Scales in Elasticity Imaging: A Numerical Study (Journal of Computational Mathematics, 2018)
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 discrepancy 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.