You cannot have a separate image for particular document set because the same aspx page is reused for each item. So any web parts you add to the page will be the same for all instances/items of the same document set (aka content type).
But you can create a new column on the document set content type of type "Image with formatting and constraints for publishing" and call it say "Image Thumbnail". Then you can edit the document set from the document library (via "document set settings"), and then add the "Image Thumbnail" column as the last column in "welcome page columns". Do not make it a "shared column" unless you want every item to have the image on it, which is totally unnecessary if all you want is to display a unique image for each item on the document set page.
You would then have a generic image of the left hand side of the document set web page but a unique image for each item would display as the last column in the in the "welcome page columns". Looks quite good.