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.
Advances in Variational and Hemivariational Inequalities
Khan, A. A.,
Proximal methods for the elastography inverse problem of tumor identification using an equation error approach.
Advances in Variational and Hemivariational Inequalities, 173-197.
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