Iterative Methods for the Elastography Inverse Problem of Locating Tumors

B. Jadamba (), A. A. Khan (), F. Raciti (), C. Tammer and B. Winkler ()
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B. Jadamba: School of Mathematical Sciences, Rochester Institute of Technology, Center for Applied and Computational Mathematics
A. A. Khan: School of Mathematical Sciences, Rochester Institute of Technology, Center for Applied and Computational Mathematics
F. Raciti: University of Catania, Department of Mathematics and Computer Science
C. Tammer: Martin-Luther-University of Halle-Wittenberg, Institute of Mathematics
B. Winkler: Martin-Luther-University of Halle-Wittenberg, Institute of Mathematics

A chapter in Essays in Mathematics and its Applications, 2016, pp 101-131 from Springer

Abstract: Abstract The primary objective of this work is to present a rigorous treatment of various iterative methods for solving the elastography inverse problem of identifying cancerous tumors. From a mathematical standpoint, this inverse problem requires the identification of a variable parameter in a system of partial differential equations. We pose the nonlinear inverse problem as an optimization problem by using an output least-squares (OLS) and a modified output least-squares (MOLS) formulation. The optimality conditions then lead to a variational inequality problem which is solved using various gradient, extragradient, and proximal-point methods. Previously, only a few of these methods have been implemented, and there is currently no understanding of their relative efficiency and effectiveness. We present a thorough numerical comparison of the 15 iterative solvers which emerge from a variational inequality formulation.

Keywords: Inverse Problem; Variational Inequality; Saddle Point Problem; Projected Gradient Method; Extragradient Method (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31338-2_6

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DOI: 10.1007/978-3-319-31338-2_6

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