To further enhance the characterization of the signal, a two-dimensional annihilation filter is used. This filter is represented in this section by

(131) |

(132) |

Since the 2-D filter is expected to have much different characteristics than the 1-D noise filter, the regressions are scaled to each other as follows:

(133) |

(134) |

Expanded to predict the signal, these minimizations become the single system of regressions that follows:

(135) |

If the inversion of system () is attempted with the initial value of being zero, many iterations of the solver are needed to produce a reasonable result. In Abma1995, I showed that initializing the value of to the result obtained from prediction-error filtering reduced the cost of the inversion and improved the results. Although the estimated signal from prediction-error filtering is not a perfect fit, it appears close enough to reduce the number of iterations by an order of magnitude, making this process a practical production technique.

2/9/2001