Summary

The ``Huber function'' (or ``Huber norm'') is one of several robust error measures which interpolates between smooth ($\ell^2$) treatment of small residuals and robust ($\ell^1$) 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.