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How can I remove no data pixels completely from an Image such that it won't be considered in any geoprocessing tasks?

For example, raster to polygon still creates polygons for no data pixels and I don't want that.

I am using ArcMap with a Basic level license

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  • Raster to polygon won't create polygons in no data areas. What you see are holes inside created polygons. Use fill color for your polygons symbology, to see them. – FelixIP Mar 16 at 6:52
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See NoData in raster datasets for help on editing NoData values or try focal statistics by follow How To: Remove and replace no data values within a raster using statistical information from the surrounding data values..

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