Year: 2010
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 3 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2009.12-m1001
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 3 : pp. 354–370
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Elastography multi-scale imaging anomaly reconstruction.
-
A convex inversion framework for identifying parameters in saddle point problems with applications to inverse incompressible elasticity
Jadamba, Baasansuren | Khan, Akhtar A | Richards, Michael | Sama, MiguelInverse Problems, Vol. 36 (2020), Iss. 7 P.074003
https://doi.org/10.1088/1361-6420/ab8482 [Citations: 4] -
Handbook of Mathematical Methods in Imaging
Expansion Methods
Ammari, Habib | Kang, Hyeonbae2011
https://doi.org/10.1007/978-0-387-92920-0_11 [Citations: 11] -
Contingent derivatives and regularization for noncoercive inverse problems
Clason, Christian | Khan, Akhtar A. | Sama, Miguel | Tammer, ChristianeOptimization, Vol. 68 (2019), Iss. 7 P.1337
https://doi.org/10.1080/02331934.2018.1442448 [Citations: 8] -
A New Energy Inversion for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location
Doyley, M. M. | Jadamba, B. | Khan, A. A. | Sama, M. | Winkler, B.Numerical Functional Analysis and Optimization, Vol. 35 (2014), Iss. 7-9 P.984
https://doi.org/10.1080/01630563.2014.935859 [Citations: 11] -
On convex modified output least-squares for elliptic inverse problems: stability, regularization, applications, and numerics
Jadamba, Baasansuren | Khan, Akhtar A. | Sama, Miguel | Tammer, ChristianeOptimization, Vol. 66 (2017), Iss. 6 P.983
https://doi.org/10.1080/02331934.2017.1316270 [Citations: 4] -
Nonlinear conjugate gradient method for identifying Young's modulus of the elasticity imaging inverse problem
Abdelhamid, Talaat | Chen, Rongliang | Alam, Md. MahbubInverse Problems in Science and Engineering, Vol. 29 (2021), Iss. 12 P.2165
https://doi.org/10.1080/17415977.2021.1905638 [Citations: 4] -
Global approach for transient shear wave inversion based on the adjoint method: a comprehensive 2D simulation study
Arnal, B | Pinton, G | Garapon, P | Pernot, M | Fink, M | Tanter, MPhysics in Medicine and Biology, Vol. 58 (2013), Iss. 19 P.6765
https://doi.org/10.1088/0031-9155/58/19/6765 [Citations: 8] -
Detection of point-forces location using topological algorithm in Stokes flows
Ferchichi, J. | Hassine, M. | Khenous, H.Applied Mathematics and Computation, Vol. 219 (2013), Iss. 12 P.7056
https://doi.org/10.1016/j.amc.2012.11.095 [Citations: 5] -
Analyzing the role of the Inf-Sup condition for parameter identification in saddle point problems with application in elasticity imaging
Jadamba, Baasansuren | Khan, Akhtar A. | Richards, Michael | Sama, Miguel | Tammer, ChristianeOptimization, Vol. 69 (2020), Iss. 12 P.2577
https://doi.org/10.1080/02331934.2020.1789128 [Citations: 2] -
Detection of point-like scatterers using one type of scattered elastic waves
Gintides, Drossos | Sini, Mourad | Thành, Nguyen TrungJournal of Computational and Applied Mathematics, Vol. 236 (2012), Iss. 8 P.2137
https://doi.org/10.1016/j.cam.2011.09.036 [Citations: 18]