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IRLS-based interpolation

The use of IRLS has been successful where erratic data is present, and the operators used to model such data are relatively error free. However, in the first stage of this interpolation process, the data ($\bf{d}$) is also present in the operator as $\bf{D}$, convolution with the data. Where a single bad data point would only destroy one fitting equation in other problems, in this case it would destroy a number of fitting equations proportional to the size of the filter multiplied by the number of scales.

Since the convolution occurs with multiple scales of data, the noise could be partially attenuated by the scaling process. The multi-scale approach does provide more fitting equations that are less compromised by the noise than with a single-scaled approach, but with the current linear-interpolation-based method this is only partially successful, as the noise is only being attenuated by simple averaging.

The second stage of the interpolation is also not ideally suited to IRLS, but is more likely to benefit from the approach. The errors in the data are constrained to their previous (incorrect) values, but are not directly convolved with the interpolated model. So, instead of destroying the filter, these errors will be more subtle, and centered around the bad data points.


next up previous print clean
Next: Synthetic Example Up: Curry: Iteratively re-weighted least-squares Previous: BACKGROUND
Stanford Exploration Project
7/8/2003