antoine@sep.stanford.edu, symes@caam.rice.edu

## ABSTRACTTheHuber function is one of several robust error measures which interpolates
between smooth (l) treatment of small residuals and robust (^{2}l) treatment of
large residuals. Since the Huber function is differentiable, it may be minimized reliably with
a standard gradient-based optimizer. Tests with a linear inverse problem for velocity analysis,
using both synthetic and field data, suggest that (1) the Huber function gives far more robust
model estimates than does least squares, (2) its minimization using a standard quasi-Newton method
is comparable in computational cost to least squares estimation using conjugate gradient
iteration, and (3) the result of Huber data fitting is stable over a wide range of choices for
threshold and total number of quasi-Newton steps.
^{1} |

- Introduction
- Application to velocity estimation
- Synthetic data tests
- Field data examples
- Conclusion
- Acknowledgements
- REFERENCES
- About this document ...

4/20/1999