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Using the IRLS method showed definite improvement in the interpolation
of both test cases presented in this paper. However, there are
problems with using the IRLS method. One of them is that it adds to
an already large parameter space, requiring a significant amount of
trial and error to set the parameters, especially when using IRLS on
the second stage of the interpolation. Next, this method does not
deal with the underlying problems that are caused by noise in the
data, such as errors in the operator in the first step, and the
fixing of the bad values in the second step. More sophisticated
approaches, such as total least squares
Brown (2002) that can account for errors in the operator, could be used to further reduce these issues.
We have also seen that the multi-scale PEF estimation appears to be much
less susceptible to the noise than a single-scale estimation. This is attributed
to some noise attenuation that happens during the rescaling of the data. This
benefit of the multi-scale method could be further enhanced by using a more sophisticated
rescaling operator than the current linear-interpolation based method, so that the
rescaled copies of the data (**d_i**) would provide more reliable information.

Another approach of dealing with bursty noise could be in
pre-processing, where the noise is identified and removed prior to
the interpolation or the rescaling. This would then avoid the need for overly robust
optimization methods, or more sophisticated rescaling methods. Problems arise with this
avenue of research, since most signal-noise separation methods require regularly-sampled data.

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Stanford Exploration Project

7/8/2003