XORing a random bitstream will result in a practically random output, because each bit changes with a probability of 0.5 (see Shannon, 1949). If you have neither the key nor the image, you have no way to recover the image, or the key itself.
If this is some kind of a challenge, you can try and use the properties of XOR to your advantage. If for example there is another image XORed with the same key, and you have that image plaintext and encrypted, you can obviously find the key by XORing the unencrypted image to the encrypted one. Or you can for example try guessing at keys that are for some reason obvious in your context.
Also one time pad has all the great features if the key is truly random, and has the same length as the input. Your key may for example be shorter and repeated.
One thing you can exploit is the fact that an image file has a known format, so quite a few bits of the key you can find out if you know what format it should be. At the beginning there is the magic number to identify the file format, and then depending on the actual image type some fields have few or just one potential value. Let's fill those in in your key being constructed and see if there is a pattern. But again, if the key is truly random, never reused, and as long as the image, it is not possible to recover the image file.