Filling raster gaps in arcmap based a zone layer

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I have the following raster layer that has data gaps. I can use focal statistics to fill them:

Con(IsNull("raster"), FocalStatistics("raster", NbrRectangle(5,5, "CELL"), "MEAN"), "raster")However, I want to use a zonal layer and limit the neighbors based on that layer so that the function only uses the mean of all the neighboring values that are in the same zone.



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