Proximal Methods for the Elastography Inverse Problem of Tumor Identification Using an Equation Error Approach
In this chapter, we study a nonlinear inverse problem in linear elasticity relating to tumor identification by an equation error formulation. This approach leads to a variational inequality as a necessary and sufficient optimality condition. We give complete convergence analysis for the proposed equation error method. Since the considered problem is highly ill-posed, we develop a stable computational framework by employing a variety of proximal point methods and compare their performance with the more commonly used Tikhonov regularization.
KeywordsVariational inequality Elasticity imaging Elastography inverse problem Tumor identification Proximal point method Regularization
AMS Classification.35R30 65N30
The authors are grateful to the referees for their careful reading and suggestions that brought substantial improvements to the work. The work of A.A. Khan is partially supported by RIT’s COS D-RIG Acceleration Research Funding Program 2012–2013 and a grant from the Simons Foundation (#210443 to Akhtar Khan).
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