Exclude regions in a Raster by Polygon and recalculate

[JacobWächter]

Dear community,

I want to exclude values inside regions of a raster dataset by Polygon Shapefile and recalculate the raster by using surrounding values for interpolation in this area. Values outside of the polygons should not be changed. The border of the original raster is represented by a mask and should be the same for the recalculated raster.

Which oppurtunities do I have?

Best regards,

Jacob

[DanPatterson]

Nibble (Spatial Analyst)—ArcGIS Pro | Documentation

but this would require that the polygon shapefile be converted first, then the function used.

[JacobWächter]

Thank you very much, I think this will work. One little question: For the nibble tool I need a raster where values inside the polygons are set no data value and outside the polygon a constant value. How do I do that? 

Creating a raster where values inside polygons are set to a constant value would work with Polygon to Raster, but I need the reverse case.