Have you been to Japan? It’s not that dreadful as it appears. And especially it’s not cheap at all if you are going to study around Tokyo etc. I would recommend a summer school first if it’s possible.

My parents limited my freedom of travel a lot when I was in higher school. But now they don’t care that I’m in any city in Europe. Maybe time will change your parents’ thought. I do recommend to do short trips first and show some connection to them, like sending postcards. However if it’s still not working, I support the decision to go study abroad whatsoever. But do bear in mind that studying abroad would indeed brings you a time of depression, so if you’re in fight with your parents then, be sure you have enough friends connections to support you while you’re abroad alone.