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PEF Estimation with incomplete data

Modern reservoir characterization efforts take a pragmatic view of collected data. Rather than wait for collection of the elusive ``perfect'' dataset, the desire is to incorporate a wide variety of possibly incomplete data types into a single inversion scheme (Caers and Journel, 1998). Often the only data available is spatially incomplete. Figure 8 shows the result of texture synthesis on training images with large void regions. As noted earlier, the blank areas in the center panels of the figure correspond to regions where the filter can't fit without falling on one or more missing points. Each of the ``in-bounds'' data points contributes one equation to the LS estimation of the 100 or so filter coefficients. Even when well over half of the data points are removed from the training image this result shows that we can still safely estimate a filter and synthesis a believable texture.

holes
holes
Figure 8.
Comparison showing the effects of missing data on the PEF texture synthesis result, for two different ``holes''. Although half or more of the equations are removed from the PEF estimation problem, the synthesized textures still capture the character of the training image. Fourier transforms are ill-defined on irregular coordinate systems, but the PEF makes an estimate of the known data's spectrum regardless.
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2013-03-03