How can I overlay a Vector Layer on a Raster Layer and assign NoData Values on the Raster where the Vector Layer does not cover the Raster Layer?
(preferable with ArcGIS)
What you are describing can be accomplished using Extract by Mask. For example, the image on the left shows raster imagery with a polygon overlay. The image to the right shows the result of the extract by mask operation. By default, ArcGIS assigns NoData pixels as no-color. For display purposes, I reassigned the NoData pixel color from no-color to black via: Layer Properties > Symbology > Display NoData as "Black".