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Volume 28, Issue 3
Separation of Scales in Elasticity Imaging: A Numerical Study

Habib Ammari, Pierre Garapon & François Jouve

DOI: 10.4208/jcm.2009.12-m1001

J. Comp. Math., 28 (2010), pp. 354-370.

Published online: 2010-06

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  • Abstract

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.

  • Keywords

Elastography, multi-scale imaging, anomaly reconstruction.

  • AMS Subject Headings

35R30, 74L15, 92C55.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-354, author = {Habib Ammari, Pierre Garapon and François Jouve}, title = {Separation of Scales in Elasticity Imaging: A Numerical Study}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {3}, pages = {354--370}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.12-m1001}, url = {http://global-sci.org/intro/article_detail/jcm/8524.html} }
TY - JOUR T1 - Separation of Scales in Elasticity Imaging: A Numerical Study AU - Habib Ammari, Pierre Garapon & François Jouve JO - Journal of Computational Mathematics VL - 3 SP - 354 EP - 370 PY - 2010 DA - 2010/06 SN - 28 DO - http://doi.org/10.4208/jcm.2009.12-m1001 UR - https://global-sci.org/intro/article_detail/jcm/8524.html KW - Elastography, multi-scale imaging, anomaly reconstruction. AB -

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.

Habib Ammari, Pierre Garapon and François Jouve. (2010). Separation of Scales in Elasticity Imaging: A Numerical Study. Journal of Computational Mathematics. 28 (3). 354-370. doi:10.4208/jcm.2009.12-m1001
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