Abstract. This work aims to compare the performance of a variety of gradient-based and extragradient methods for the solution of the elastography inverse problem arising in the identification of cancerous tumors. From a mathematical standpoint, this inverse problem requires the identification of a variable parameter in a system of incompressible elasticity. We use an equation error approach to formulate the inverse problem as a convex optimization problem. The necessary and sufficient optimality condition then leads to a variational inequality which is solved using various extragradient methods, which have received great attention in recent years. 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 projected gradient method, fast projected gradient method (fast iterative shrinkage-thresholding (FISTA)) [3], scaled projected gradient method, and several extragradient methods including the Marcotte variants, He-Goldstein-type method, the projection-contraction method proposed by Solodov and Tseng, and a hyperplane method.

Gradient and Extragradient Methods for the Elasticity Imaging Inverse Problem Using an Equation Error Formulation: A Comparative Numerical Study

RACITI, Fabio;
2016-01-01

Abstract

Abstract. This work aims to compare the performance of a variety of gradient-based and extragradient methods for the solution of the elastography inverse problem arising in the identification of cancerous tumors. From a mathematical standpoint, this inverse problem requires the identification of a variable parameter in a system of incompressible elasticity. We use an equation error approach to formulate the inverse problem as a convex optimization problem. The necessary and sufficient optimality condition then leads to a variational inequality which is solved using various extragradient methods, which have received great attention in recent years. 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 projected gradient method, fast projected gradient method (fast iterative shrinkage-thresholding (FISTA)) [3], scaled projected gradient method, and several extragradient methods including the Marcotte variants, He-Goldstein-type method, the projection-contraction method proposed by Solodov and Tseng, and a hyperplane method.
2016
978-1-4704-1736-9
File in questo prodotto:
File Dimensione Formato  
conm13154-ilovepdf-compressed.pdf

solo gestori archivio

Tipologia: Versione Editoriale (PDF)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 812.27 kB
Formato Adobe PDF
812.27 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/73413
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? ND
social impact