par Loris, Ignace 
Editeur scientifique Freeden, Willi;Nashed, M. Zuhair;Sonar, Thomas
Référence Handbook of Geomathematics, Springer, Ed. 2, page (1-33)
Publication Publié, 2014-09-17
Editeur scientifique Freeden, Willi;Nashed, M. Zuhair;Sonar, Thomas
Référence Handbook of Geomathematics, Springer, Ed. 2, page (1-33)
Publication Publié, 2014-09-17
Partie d'ouvrage collectif
| Résumé : | Inverse problems in seismic tomography are often cast in the form of an optimization problem involving a cost function composed of a data misfit term and regularizing constraint or penalty. Depending on the noise model that is assumed to underlie the data acquisition, these optimization problems may be non-smooth. Another source of lack of smoothness (differentiability) of the cost function may arise from the regularization method chosen to handle the ill-posed nature of the inverse problem. A numerical algorithm that is well suited to handle minimization problems involving two non-smooth convex functions and two linear operators is studied. The emphasis lies on the use of some simple proximity operators that allow for the iterative solution of non-smooth convex optimization problems. Explicit formulas for several of these proximity operators are given and their application to seismic tomography is demonstrated. |
