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Mathematical Methods in Elasticity Imaging$
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Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

Print publication date: 2015

Print ISBN-13: 9780691165318

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691165318.001.0001

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Stability of Topological Derivative Based Imaging Functionals

Stability of Topological Derivative Based Imaging Functionals

(p.112) Chapter Seven Stability of Topological Derivative Based Imaging Functionals
Mathematical Methods in Elasticity Imaging

Habib Ammari

Elie Bretin

Josselin Garnier

Hyeonbae Kang

Hyundae Lee

Abdul Wahab

Princeton University Press

This chapter performs a detailed stability analysis of the topological derivative based imaging functionals with respect to medium and measurement noises. It begins with a discussion of the stability analysis with respect to measurement noise. In particular, it considers how the result with respect to the resolution of the imaging functional in the ideal situation will be modified when the measurement is not accurate but is corrupted by noise. The simplest model for the measurement noise is used in this case. The chapter then analyzes the stability with respect to medium noise of the proposed imaging functionals. For simplicity, a medium that fluctuates in the density parameter only is used. Finally, the case when the random fluctuations occur in the elastic coefficients is described.

Keywords:   stability analysis, topological derivative, imaging functional, measurement noise, medium noise, density parameter, random fluctuation, elastic coefficient

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