Preconditioning a non-linear problem and its application to bidirectional deconvolution |

where is the data, and are the unknown causal filters, and the superscript denotes the time reverse of filter . The hybrid norm is applied to , and the reflectivity model is simply plus a time shift.

We notice that there is only model regularization in this deconvolution problem. Now we change our model from and to and using and :

(8) |

Thus, we focus on estimating and instead of and . By applying the prior knowledge in the preconditioners and , we can avoid unwelcome local minima.

Preconditioning a non-linear problem and its application to bidirectional deconvolution |

2011-09-13