I have a raster image of water depth, float point values 1-15, in a very small area some erroneous values are in the raster with values of 100 - 375. I'm looking for a repeatable work flow in ArcMap 10.5, Spatial Analyst level. I've used one work flow to set the values to nodata, one work flow to set to a fixed float point value, but what I'd really like is to create polygon or raster mask, and then have the grids of the original raster, within the mask area, to be replaced with nearest neighbor values from the original raster outside the mask area.
The tool you are looking for is nibble. Nibble does exactly what you are asking for. Your work flow would be something along the lines of using your polygons to create a mask raster as the second input. Other related tools to consider (but probably not what you want for this use-case) are shrink and expand.