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Inverse problems and controllability with applications in elasticity and MRI

Abstract : The aim of this thesis is to study, from a theoretical point of view, the exact controllability of some partial differential equations modeling the vibrations of an elastic structure and to apply the to apply these theoretic results to solve some inverse problems coming from magnetic resonance imaging (MRI). This thesis has two parts. The first one, entitled "Controllability and observability of some plate equations", discuss the controllability and, by duality, the observability of some plate equations perturbed by some linear or nonlinear terms. The second part of the thesis concerns the magnetic resonance imaging. More precisely, we study some methods to reconstruct the magnetic resonance images of a moving object, the typical example being the cardiac imaging reconstruction from MRI data acquired in free-breathing.
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Submitted on : Monday, November 12, 2012 - 5:49:31 PM
Last modification on : Tuesday, April 20, 2021 - 12:20:10 PM
Long-term archiving on: : Wednesday, February 13, 2013 - 3:47:10 AM


  • HAL Id : tel-00750955, version 1


Nicolae Cindea. Inverse problems and controllability with applications in elasticity and MRI. Optimization and Control [math.OC]. Université Henri Poincaré - Nancy I, 2010. English. ⟨NNT : ⟩. ⟨tel-00750955⟩



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