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The ``Huber function'' (or ``Huber norm'') is one of several robust
error measures which interpolates between smooth (
) treatment of
small residuals and robust (
) treatment of large residuals.
Since the Huber function is differentiable, it may be minimized reliably with
a standard gradient-based optimizer. I propose to minimize the Huber
function with a quasi-Newton method that has the potential of being
faster and more robust than conjugate-gradient when solving non-linear
problems. Tests with a linear inverse problem
for velocity analysis with both synthetic and field data suggest that
the Huber function gives far more robust model estimates than does
least-squares with or without damping.
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Stanford Exploration Project
5/5/2005