Solving or resolving inadequate and noisy tomographic systems (Q1074329)

The determination of seismic velocity leads to the inversion of the Radon transform; i.e., line integrals of the searched-for distribution are given. In contrast to medicals application the data cannot be collected uniformly, resulting in a highly ill-posed problem. Also the recovery is complicated by very noisy data. The projection of the solution onto a finite dimensional pixel space then leads to very ill-conditioned linear equations. The author compares different stabilization methods, namely singular value decomposition (SVD), conjugate gradients (CG) and the Dines-Lytle method, which is a version of the Landweber iteration. It turns out that the CG-method is cheaper than SVD and that it picks up the recoverable part of the solution after a few steps. The Dines-Lytle method is much slower. In a resolution analysis the trade-off between resolution and noise damping is studied.