Displaying an image for each post *ONLY* on blog homepage?

Is it possible to have an image in a post that gets displayed only on my blog’s homepage? Then once you click to read the post a different image is used? What we are trying to do is use an image that is cropped more like a square for display on the homepage. Then when you click the post a different image is used with a wider/rectangular crop.

If this is possible how would I go about doing it?