Conjugate-direction Huber regression

Jon Claerbout

jon@sep.stanford.edu

ABSTRACT

A straight-forward way to make conjugate-direction regressions robust (insensitive to bursty data noise) is based on the objective function of Huber (least squares for small residuals and least absolute values for large ones). The gradient is based on the clipped residual instead of the residual itself. Likewise the clipped residual is used to define the plane of the gradient and previous step (plane search). This method does not apply to the deconvolution problem because there noisy field data enters into the operator for the determination of the prediction-error filter.