The data-space regularization approach is closely related to the
concept of *model preconditioning* Nichols (1994).
Regarding the operator from equation () as a
preconditioning operator, we can introduce a new model with
the equality

(21) |

(22) |

(23) |

(24) |

System () is clearly underdetermined with respect to the compound model . If from all possible solutions of this system we seek the one with the minimal power , the formal (ideal) result takes the well-known form

(25) |

Although the two approaches lead to similar theoretical results, they behave quite differently in the process of iterative optimization. In Chapter , I illustrate this fact with many examples and show that in the case of incomplete optimization, the second (preconditioning) approach is generally preferable.

The next chapter addresses the choice of the forward interpolation operator - the necessary ingredient of the iterative data regularization algorithms.

12/28/2000