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The preceding section derives the relationship between the
filtering and subtraction methods. The preconditioning changes the nature
of the problem quite deeply: from a filtering algorithm we end-up with
a prediction/subtraction method. The least-squares inverses in equations
(3) and () are also very different: from a
problem with one unknown, , we end-up with a problem with
two unknowns, and . Fortunately, this preconditioning
should speed-up the convergence toward the signal vector .In addition, this transformation separates the data space
in its natural components, e.g, the signal and noise vectors more
explicitely than with the filtering method.

** Next:** Stability of the Hessian
** Up:** From the filtering to
** Previous:** Preconditioning the filtering method
Stanford Exploration Project

6/7/2002