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I have a color image and I know geographic coordinates of its 4 corners. Now I'd like to place this image on basemap in GMT using any projection. Any idea how to do that?

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The process that you need to do in order to reproject your image is called georeferencing. For basic/linear georeferencing, the minimum number of points you need is 3 so if you have 4 corners you should be fine.

There's a few tutorials available on the net based on Arc and QGIS tools that can show you how to perform this on raster images. I've never used Generic Mapping Tools, so I can't say whether GMT has that functionality, but if you're using QGIS at all I'd suggest you check out this walkthrough as the process is relatively simple to perform:

http://www.qgistutorials.com/en/docs/georeferencing_basics.html

Hope that helps,

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