A Convenient Iterative Algorithm for the Solution of an Optimization Problem involving two convex functions, with applications in seismic tomography

Ignace Loris^*

Inverse problems in seismic tomography are often cast in the form of an optimization problem involving a data misfit term and regularizing constraint or penalty. Depending on the noise model that is assumed to underlie the data acquisition these problems may be non-smooth. Another source of lack of smoothness may arise from the regularization method chosen to deal with the ill-posed nature of the inverse problem. A number of numerical algorithms that can be used for the solution of these optimization problems are studied. Using some simple proximity operators, a convenient iterative algorithm for non-smooth convex optimization problems involving two convex functions and two linear operators is presented. Explicit formulas for several of these proximity operators are given and their application to seismic recovery is demonstrated.

Mathematics Subject Classification: 65K10 65F22

Keywords: convex optimization; inverse problems; seismic tomography

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