Decon in the log domain with variable gain |

(30) |

Note that . The gradient search direction is

(31) |

where is a diagonal matrix of weights. Again for six components, the diagonal contains .

Here are the modifications needed to incorporate
regularization on
:

(32) | |||

(33) | |||

(34) | |||

(35) |

In a least squares problem we compute a step size as minus a ratio over . Adding a least squares regularization to any convex fitting problem we simply add to the numerator and to the denominator.

Actually, another regularization is desireable. We should also request to be small for large anticausal lags, lags more negative than the range we are considering for the antisymmetry regularization. This might be handled by truncating the gradient rather than as a regularization.

A third regularization can be added to weaken at its large positive lags in circumstances where we feel we have insufficient data to estimate trace-long filters.

Decon in the log domain with variable gain |

2012-05-10