I have a raster with black, white and red which represent no data value.

I can remove them with ArcGIS using Nodata but i can only do that for only one color.

Is there any possibility to remove multiple nodata?

[Requires Spatial analyst] You could try to reclassify your image with "All you want = 1" and "All you dont want (red, white, black values) = NoData". Then you multiply your image with your "filter image". It's the same way as with the "Con" tool, but easier to understand (maybe less powerful)

If you have multiple band images, you'll have to do this for each band then recreate your composite image after. Hope I'm clear enough and that I got your question properly.

NB : you could also use QGIS raster tools to reclass the data if you don't have Spatial analyst.

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