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On Numerical Reconstruction of a Function from Incomplete Data on Arc Means in Seismic Tomography

Denisiuk A.

Machine Graphics and Vision

2011

Vol. 20, No. 4

413-437

Consider the problem of reconstruction of a small perturbation of the acoustic wave speed field from traveltime data with linear background slowness. Mathematically, the problem is equivalent to reconstruction of a function from the data of integrals along the circle arcs. The data is limited, in the sense that the base points belong to a compact set. We propose and numerically test a new approach, based on reduction of the problem to the inverse problem for the Radon transform. The data completion procedure is considered as well.