Interesting article about Iris algorithm and headphones (I have ordered one).
I had hope that the technology behind the algorithm should have been uncovered even more. Testing myself with different recordings my guess is that information from both left and right channels are compared and the algorithm uses similarities and differences processing the sound. I have tested mono recordings, recordings done with one stereomicrophone only, binaural recordings, digitally remastered analog recordings and more. In some cases there is no difference in sound at all (I leave for you to test yourself), in other cases the sound is blured but in many cases (reflecting my CD archive) the "improvement" make listening much more enjoyable.
Regarding phase information and ambience nothing beats analog recordings or recordings made digitally with higher sample frequencies (4x) than what is used for standarad CDs/DVDs. But if your record archive is rather old, the IRIS algorithm is nice to switch on for some of the material (when you do not get disturbed by that the stereo image is slightly changed).
Hope that more sound compression formats will be supported in the future!