Inversion Methods

Duality Methods for Waveform Inversion

We show in this paper how the application of convex duality leads to various reformulations of the classical non optimizable least squares approach to waveform prestack inversion. These reformulations search all for i) a background velocity model and ii) a re-ectivity model deened in the time domain, and linked to the usual depth reeectivity model by prestack depth migration. We show that the d...

A Comparison of Tabular PDF Inversion Methods

The most common form of tabular inversion used in computer graphics is to compute the cumulative distribution table of a pdf and then search within it to transform points, using an O(logn) binary search. Besides the standard inversion method, however, several other discrete inversion algorithms exist that can perform the same transformation in O(1) time per point. In this paper, we examine the ...

Stability of Methods for Matrix Inversion

Inversion of a triangular matrix can be accomplished in several ways. The standard methods are characterised by the loop ordering, whether matrix-vector multiplication, solution of a triangular system, or a rank-1 update is done inside the outer loop, and whether the method is blocked or unblocked. The numerical stability properties of these methods are investigated. It is shown that unblocked ...

Iterative Inversion Methods for Statistical Inverse Problems

In this paper we discuss general regularization estimators. This class includes Tikhonov type and spectral cut-off estimators as well as iterative methods, such as ν-methods and the Landweber iteration. The latter estimators achieve the same (optimal) convergence rates as spectral cut-off, but do not require explicit spectral information on the operator and are often much faster to compute than...

Numerical Methods for Laplace Transform Inversion