In this Chapter I have proposed minimizing the Huber function with a quasi-Newton method called limited-memory BFGS. This method has the potential of being faster and more robust than conjugate-gradient for solving non-linear problems. Tests with noisy synthetic and field data examples demonstrate that our method is robust to outliers present in the data space, as expected.
The possible applications of the Huber norm are endless in geophysics.
I illustrate in Chapter how the Huber norm
helps removing spikes in bathymetry data. In addition, I show in
Chapter
how the Huber norm helps
separating primaries and multiple reflections better.