Proximal methods for the elastography inverse problem of tumor identification using an equation error approach

Authors

Mark Gockenbach, Michigan Technological UniversityFollow
Baasansuren Jadamba, Rochester Institute of Technology
Akhtar A. Khan, Michigan Technological University
Christiane Tammer, Martin-Luther-University of Halle-Wittenberg
Brian Winkler, Michigan Technological University

Document Type

Book Chapter

Publication Date

2-25-2015

Abstract

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.

Publisher's Statement

© Springer International Publishing Switzerland 2015. Publisher's version of record: https://doi.org/10.1007/978-3-319-14490-0_7

Publication Title

Advances in Variational and Hemivariational Inequalities

Recommended Citation

Gockenbach, M., Jadamba, B., Khan, A. A., Tammer, C., & Winkler, B. (2015). Proximal methods for the elastography inverse problem of tumor identification using an equation error approach. Advances in Variational and Hemivariational Inequalities, 173-197. http://doi.org/10.1007/978-3-319-14490-0_7
Retrieved from: https://digitalcommons.mtu.edu/math-fp/18