The development of this inversion principle into an algorithm can take
any number of forms. Guitton and Symes (2003) choose the Huber norm to
effect an *l ^{1}*-like measure of the inversion error. We will cast the
problem through the primal-dual Linear
Programming (LP) structure resulting in a methodology wherein the concept of
convergence is central to the algorithm. This fact has two important
consequences. Firstly, the precision of the output model space is one
of (the very few) input parameters. Secondly, the parameter space is
insensitive to manipulation as compared to in
regularized least squares problems or the cutoff value needed
for Huber norm approaches.

Conventionally, LP methods deal almost exclusively in a small world of conveniently short time signals such as bursts of speech. Application of these methods to geophysical problems of much larger size may prove prohibitive. While at its best the complexity of this method can be comparable to IRLS, in practice the method is usually several times slower to produce optimal solutions.

As an example of the method, the hyperbolic radon transforms are used as analysis operators of seismic and synthetic seismic data. An exploration of the method comparable to Guitton and Symes (1999) will be used to highlight the strengths and weaknesses of the method compared to conventional least squares and Huber norm inversion for velocity from seismic data.

10/14/2003