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...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.展开更多
基金partially supported by the ANR project EchoScan (AN-06-Blan-0089)
文摘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.
