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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
() and () are also very different: from a
problem with one unknown, 343#343, we end-up with a problem with
two unknowns, 348#348 and 347#347. Fortunately, this preconditioning
should speed-up the convergence toward the signal vector 343#343.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