photo source), although it has deteriorated considerably since it was documented in the 19th century, when one could see the full purple-toga clad magnificence of Caesar ... (drawings below from JSTOR) - and since several Caesars were shown, the images must show the Tetrarchs. The cult is linked to a castrum of Diocletian near-by, and probably later became a Christian chapel. Other scenes show a procession, and are important evidence for these in Late Antiquity - as well as arms and armour (note the saddles but still no stirrups here)
What's interesting is that although one can draw parallels between the drapery and the armour at Luxor and in the Great Hunt mosaic at Piazza Armerina ... in the Egyptian scenes the men are all shown in togas and bare legs, whilst in the Sicilian ones wear trousers. The emperors' heads were lost when they were turned into Christian saints.
The Piazza Armerina villa dates to the time of the Tetrarchs, and is sometimes linked to Maximian or his son Maxentius. The emperor shown in the Hunt is presumably one of them. The amazing photos are pinched from the galleries here.
The older bearded man in very elaborate dress must have been the emperor:
Valerius Romulus, the son of Maxentius was in his early teens when he died. Maxentius himself died at 34, so this makes it more likely he is the prince depicted here, and that his father Maximian was the emperor in the mosaics - and possibly the builder of the villa.