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With thoroughly chosen parameters, I have shown that the *l*^{1} problem can be approached using either the
Huber along with an appropriate non-linear solver or with IRLS algorithms along with an appropriate
weighting function.
For the particular problem of velocity stack inversion, however,
the Huber solver generally bears better convergence properties. From the practical point of view,
the IRLS algorithms pose cumbersome problems for the choice of (1) the weighting function (2) the restart
parameter and (3) the damping factor. With only one parameter to set up a priori, the Huber
solver appears far easier to operate. This ease of use should encourage more people to use the
Huber norm when implementing the hybrid *l*^{2}-*l*^{1} norm.

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Stanford Exploration Project

4/27/2000