The Malankara Orthodox vestments pictured above represent the "Archdeacon and the Gate of All India (Malankara Side), the Syro Malabar Hierarch shares a similar title “Metropolitan and the Gate of All India”. The origins I believe were an offshoot of old Latin Vestments with a Malankara twang but the mitre is a distinct creation of their own. These vestments as a whole however are only used by the Malankara Orthodox Catholicos, the Jacobite Catholicos does not have a counterpart vesture.
I believe - and correct me if I’m wrong - this is some kind of blend vestment with the 16th Cent. Latin Cardinal-Patriarch of Goa. It looks too similar to a Cardinal’s vestment to be accidental.
It could very well be, I cannot find any sources from the Malankara Church related to the origins however.
Melkites (and Antiochian Orthodox) were greatly Byzantinized, but that was so long ago that it’s debatable whether it fits with your question.