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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