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Numerical Algorithms for Non-smooth Optimization Applicable to Seismic Recovery

In: Handbook of Geomathematics

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  • Ignace Loris

    (Université libre de Bruxelles)

Abstract

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.

Suggested Citation

  • Ignace Loris, 2015. "Numerical Algorithms for Non-smooth Optimization Applicable to Seismic Recovery," Springer Books, in: Willi Freeden & M. Zuhair Nashed & Thomas Sonar (ed.), Handbook of Geomathematics, edition 2, pages 1905-1942, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54551-1_65
    DOI: 10.1007/978-3-642-54551-1_65
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